Prioritizing complex health levels beyond autism triage using fuzzy multi-criteria decision-making

Abstract

This study delves into the complex prioritization process for Autism Spectrum Disorder (ASD), focusing on triaged patients at three urgency levels. Establishing a dynamic prioritization solution is challenging for resolving conflicts or trade-offs among ASD criteria. This research employs fuzzy multi-criteria decision making (MCDM) theory across four methodological phases. In the first phase, the study identifies a triaged ASD dataset, considering 19 critical medical and sociodemographic criteria for the three ASD levels. The second phase introduces a new Decision Matrix (DM) designed to manage the prioritization process effectively. The third phase focuses on the new extension of Fuzzy-Weighted Zero-Inconsistency (FWZIC) to construct the criteria weights using Single-Valued Neutrosophic 2-tuple Linguistic (SVN2TL). The fourth phase formulates the Multi-Attributive Border Approximation Area Comparison (MABAC) method to rank patients within each urgency level. Results from the SVN2TL-FWZIC weights offer significant insights, including the higher criteria values "C12 = Laughing for no reason" and "C16 = Notice the sound of the bell" with 0.097358 and 0.083832, indicating their significance in identifying potential ASD symptoms. The SVN2TL-FWZIC weights offer the base for prioritizing the three triage levels using MABAC, encompassing medical and behavioral dimensions. The methodology undergoes rigorous evaluation through sensitivity analysis scenarios, confirming the consistency of the prioritization results with critical analysis points. The methodology compares with three benchmark studies, using four distinct points, and achieves a remarkable 100% congruence with these prior investigations. The implications of this study are far-reaching, offering a valuable guide for clinical psychologists in prioritizing complex cases of ASD patients.

Introduction

The prevalence of autism spectrum disorder (ASD) diagnoses has exhibited a noteworthy upsurge in recent years, a trend underscored by the World Health Organization (WHO) [1]. The diagnosis of ASD traditionally encompasses a multitude of factors, including magnetic resonance imaging (MRI), electroencephalogram (EEG), and demographic data [2,3,4]. However, there has been a shift towards an innovative approach to diagnosing and triaging autism patients that harmonizes medical and sociodemographic characteristics [5, 6]. This integrated approach has not only garnered attention but has also given rise to intelligent methodologies aimed at streamlining the labeling and detection of autism patients, thereby enhancing the efficiency of the triage process [7].

ASD triage serves as a pivotal mechanism for classifying individuals with autism into distinct priority levels, encompassing Urgent, Moderate, and Minor categories. This process plays a critical role in ensuring that individuals with autism receive prompt access to essential services, thereby expediting early diagnosis and intervention [7]. In an era characterized by rapid technological advancement and real-time prediction applications [8, 9], context-based triage has become an indispensable tool, enabling the prioritization of system issues and vulnerabilities across domains such as telehealth systems. Triage plays a central role in guaranteeing the optimal performance and efficiency of real-time applications [10].

Prioritization tools are valuable in ASD diagnosis, supporting evidence-based decision-making in medical tests and treatment strategies. In the literature, triage and priority-based healthcare diagnoses for autism have been extensively reviewed [6]. The prioritization concepts of ASD research are contributed from different perspectives, such as gene priority [11], development of machine learning models based on prioritizing the demographic and family characteristics features [12], and patients' prioritization based on medical and sociodemographic criteria [13]. From a gene perspective, prioritization approaches have been utilized to identify genes contributing to ASD. These methods prioritize genes based on their importance in specific cell types, which may have etiological relevance to ASD [11]. Certain autism centers have implemented criteria-based prioritization, considering factors like age, urgency of needs, and additional complexities that may impact treatment decisions [14]. However, ASD is a complex neurodevelopmental disorder that requires careful evaluation and prioritization towards the integration of medical and sociodemographic criteria [15].

Furthermore, the prioritization of ASD patients is an intricate decision-making process laden with many challenges and considerations [16]. One of the primary issues faced is the presence of conflicts and trade-offs among the various criteria employed for prioritization. Healthcare professionals and decision-makers are tasked with navigating through conflicting factors and making tough decisions when determining the priority of ASD patients [7]. Furthermore, the significance of distinct ASD criteria introduces an additional layer of complexity to the prioritization process. Each criterion is unique and contributes to the comprehensive evaluation of a patient's condition. Striking a balance between the significance of diverse criteria and appropriately weighting them is imperative to ensure equitable and accurate prioritization [5]. The existing literature demonstrates the utilization of various techniques employing multiple evaluation processes for the prioritization of ASD patients. Nevertheless, a notable gap exists in the form of standardized guidelines for ASD patient prioritization, which could effectively benefit healthcare sectors, medical practitioners, and patients alike.

In ASD research, the triage process can effectively differentiate the patients' health situations into three emergency levels: Urgent, Moderate, and Minor. However, the patients within a particular level still have the same health degree of importance. In contrast, the patient in the most critical situation is different from the less critical patient, who, in turn, needs to provide the required health services [17]. Although triage is considered a powerful recruitment tool, it cannot provide priority to patients inside specific health levels [18]. For example, several ASD patients they triaged at an Urgent level all have the same degree of importance. At the same time, the prioritization of them can elaborate a better understanding of their health situations [19]. This complex task motivated us to develop guidelines for evaluating and prioritizing ASD patients who were triaged but not differentiated yet. Several key issues are addressed in the current body of literature on ASD patient prioritization:

First issue: despite the availability of diverse approaches, the academic literature lacks a consensus on an evaluation guideline for ASD patients encompassing the number and type of criteria to be considered [4]. Another challenge lies in assigning appropriate weights to these criteria based on their significance. Furthermore, numerous studies have not fully incorporated the input of healthcare professionals in determining the importance of criteria and resolving conflicts or trade-offs among various criteria. Consequently, this often necessitates subjective decisions by medical specialist committees, particularly when making precise medical determinations related to the prioritization of ASD patients using numerous criteria [7].

Second issue: prioritization of ASD patients must be a dynamic process within the context of an autism medical center, as the dynamic nature of the process is essential when managing the prioritization of ASD patients in a busy clinical environment with a high patient volume. This underscores the need for integrated methodologies that can effectively handle the process's dynamic nature, considering evolving patient conditions and changing criteria sets [20]. The prioritization methodology should be adaptable and flexible to accommodate updates and adjustments in patient prioritization, aligning with the evolving needs and circumstances within the autism medical center [21].

These challenges are encompassed within complex decision-making processes, where multi-criteria decision making (MCDM) emerges as a viable and compelling solution. MCDM plays a pivotal role in the prioritization of ASD patients [6], as it adeptly tackles the aforementioned issues, yielding excellent results. In decision-making, a procedure characterized by numerous alternatives and predefined evaluative criteria, the goal is to arrive at reasoned and well-informed outcomes [22]. The MCDM approach has a broad scope within the realm of traditional decision theory, covering multiple objective decision-making problems [13, 23,24,25]. The MCDM is a holistic approach to determining different alternatives according to different criteria, many of which are sometimes not consistent (i.e., the values may not be comparable), and it comes up with the final evaluation of all [26]. This approach encompasses multiple stages, including structuring, planning, and the resolution of multifaceted decision problems that involve numerous criteria [27,28,29,30]. As time passes, many MCDM approaches have been invented and used to address the problems of evaluation and prioritization from different domains [7, 31, 32].

Out of these methods, implementing the Multi-Attributive Border Approximation Area Comparison (MABAC) method has proved to be most suited for assessing ASD patients while caring for the previous challenges and recommendations [33]. The MABAC method is a powerful and reliable mechanism for building robust decision-making models. It has applications in selecting medical and sociodemographic methodologies and dealing with issues related to MCDM [34, 35]. The MABAC method is a purely mathematical approach that gives an elegant and robust system of equations, ensuring the stability and consistency of the solution. This characteristic enables it to work harmoniously with MCDM methods, particularly in criteria weighting. As a result, it becomes flexible and adaptable in assessing and prioritizing patients with ASD. However, it is essential to note that no weights have been assigned to this stage's critical medical and sociodemographic criteria. To address this, an external weighting method is required. It is worth noting that AHP and BWM (the Analytic Hierarchy Process and the Best Worst Method), the weighing methodologies, can be used to assign weights in the prioritization process [36].

In contrast, these methodologies could come up with inconsistencies, which in some cases will impact the accuracy and reliability of the results [1, 37]. As a result, this study uses a thorough weighting method known as the Fuzzy-Weighted Zero-Inconsistency (FWZIC) method to address these consistency difficulties [12, 38,39,40,41]. The FWZIC technique effectively ensures consistency in decisions about the relevance weights of medical and sociodemographic factors. The FWZIC concept has gained widespread use due to the superior weighting advantages which allow it to be applied in different academic disciplines. Rich in its clarity, citing it in various fields of study has become common. Some other relevant examples are its importance in stem-cell transfusion, [42] e-tourism [43] and industrial community characterization during the design and application of advanced driver-assistance systems [44]. The FWZIC approach excels at dealing with inconsistencies among a panel of experts' subjective choices.

In many MCDM weighting approaches, choice problems are usually vague and imprecise. Hence, developing accurate preference rates for each criterion is not easy. Fuzzy approaches, such as fuzzy numbers, solve this issue by determining the relative value of imprecise and ambiguous criteria [45,46,47]. However, single-valued neutrosophic 2-tuple linguistic (SVN2TL) has significant advantages, particularly in addressing the intricacy of the challenges raised. SVN2TL comprises truth-membership (TM), indeterminacy-membership (IM), and faulty-membership (FM), which may describe incomplete, indeterminate, and inconsistent information precisely while minimizing information and accuracy loss during the aggregation process [48]. Some MCDM approaches were developed to tackle complicated decision-making problems using SVN2TL, with reasonable assessment results [49, 50].

The invention of the MCDM weighting strategy based on SVN2TL offers numerous advantages [48, 50]. The SVN2TL (Single-Valued Neutrosophic 2-Tuple Linguistic) architecture is especially well-suited for real-world applications, as demonstrated by its use in the current study on ASD. SVN2TL can handle inaccurate and ambiguous information. They are appropriate for conveying an element's TM, IM, and FM in a 2-tuple linguistic word, which can influence the decisionmaker's confidence level during the evaluation [49]. As a result, decision-makers may find it more flexible and convenient to convey their thoughts via SVN2TL [50].

Additionally, MCDM methods based on such operators with SVN2TL are not only simple to calculate but can also achieve a reasonable and stable ranking of alternatives, which is especially important given the complexity of the ranking objective of ASD patients due to the large number of ASD criteria; thus, the new MCDM method requires such simple calculations. Furthermore, prioritization of ASD patients concerning the different triage levels involves dealing with complex and uncertain information related to various criteria, such as medical tests and sociodemographic criteria. The SVN2TL's ability to handle uncertainty, imprecision, and incomplete information makes it an effective tool for evaluating the intricacies of ASD-related medical tests and sociodemographic criteria. This framework empowers decision-makers to navigate the challenges of prioritization of ASD patients by providing a robust mechanism for expressing linguistic preferences and capturing the inherent vagueness in real-world scenarios, thereby enhancing the reliability and accuracy of the ranking process.

Consequently, the MABAC model is highly adaptable in the prioritization of ASD patients from a pool of options [33]. It is a process that entails a detailed analysis of the existing frameworks and their specific criteria and then a matching with the mathematical model that corresponds with it [51]. In addition, we found that the MABAC method has been suitable and improved with SVN2TL calculations, as detailed in [48]. Therefore, we have extended a new SVN2TL-FWZIC method for assigning the proper weights to the 19 medical tests and sociodemographic criteria and then used the MABAC for prioritization of the ASD patients. As a result, the amalgamation of both models offers immense potential for streamlining the priority of ASD patients. The combined use of the dimensions from the SVN2TL-FWZIC approach and the adaptability of the MABAC model allow us to make well-informed decisions.

The characteristics of the SVN2TL-FWZIC and MABAC models will be a great asset in the pursuit of ASD research and the attainment of our evaluation and prioritization priorities. The establishment of scores using the SVN2TL-FWZIC model for the assessment of medical and sociodemographic factors in the choice of ASD patients is a milestone and a sign of progress towards the improvement of the prioritization of the patients [42]. This process permits the inclusion or revision of new criteria and offers valuable insights into which criteria hold paramount importance for development and updating. These weightings provide a clear picture of the relative significance of various medical and sociodemographic criteria, serving as an invaluable resource for healthcare providers. Furthermore, the combination of the SVN2TL-FWZIC and MABAC approaches should include a dynamic approach to prioritizing ASD patients. This perspective is critical when implementing new frameworks or crucial decisions, as it facilitates adaptation without unnecessary complexity. As a result, using a freshly developed Decision Matrix is critical to overcoming static limits and allowing for a flexible and dynamic prioritization process.

This study bridges the gap between theory and practice by using real-world ASD patients to demonstrate the actual use of the established technique for decision-makers [15]. Rather than just instructions for implementation, it also provides a tool for those who decide to integrate the technique into their actions as a policymaking roadmap [52,53,54,55]. The next step is to examine the methodology on the medical and sociodemographic criteria and apply mathematical methods to improve the judgment accuracy and standard operations. Also, it is a fruitful base for advancing medical and sociodemographic evaluation approaches and prioritization in assessing upcoming trends and uncharted areas of great importance. This study's contributions can be concisely stated as follows:

• 1) Establishing a guiding methodology for the prioritization of complex situations of ASD patients.

• 2) Designing a new Decision Matrix (DM) that reflects the prioritization of ASD patients based on the medical and sociodemographic criteria, thus serving as a multifaceted evaluation tool and can be used for each triage level.

• 3) The study introduces a novel extension of the MCDM weighting method called SVN2TL-FWZIC. This method addresses the weighting of evaluation medical and sociodemographic criteria and helps overcome the mentioned issues.

• 4) Assessing the effectiveness of the developed methodology through a rigorous sensitivity analysis evaluation process.

The rest of this paper is organized as follows: Sect. "Methodology" presents the proposed methodology through four sections. Sect. "Results and discussion" presents the results of the weighting and prioritization from the proposed methodology, and several points are summarized as a discussion of the results obtained. Sect. "Sensitivity analysis" addresses the evaluation of the proposed methodology through sensitivity analysis approaches. In Sect. "Comparative Study", the comparison of the methodology is outlined. Finally, Sect. "Conclusion" contains the conclusions, policy implications, and future works.

Methodology

The methodology included four phases, as shown in Fig. 1, to reach the study’s aim. In the first phase, the ASD dataset is identified and explained in detail. The dataset’s history is extensively explained to show how it has reached the current contents of ASD patients and criteria and why it is essential to be used in this study. The second phase presents the DM as the first important step for handling the prioritization process. The developed DM is constructed by identifying the medical and sociodemographic criteria and autism alternatives. This DM can be used for three triage levels: minor, moderate, and urgent. However, the DM needs to weigh and rank MCDM methods to complete the evaluation and prioritization of ASD patients. Therefore, the formulation of the SVN2TL-FWZIC method is presented in the third phase to evaluate the medical and sociodemographic criteria and construct the weights. Finally, the MABAC method is formulated in the fourth phase for prioritizing ASD patients based on SVN2TL-FWZIC weights. The following subsections explain the four methodology phases in more detail.

Fig. 1

Methodology phases for prioritization of ASD patients in three emergency levels

Phase 1: dataset identification

The choice of the ASD dataset supports the current study's objective, which is to develop a prioritization methodology for autism patients' emergency levels based on medical and sociodemographic criteria. Diagnosing autistic patients based on integrated medical and sociodemographic criteria acquired more attention in the literature [5, 6]. Incorporating both types of criteria into the diagnosis of ASD is crucial to ensuring accuracy. Medical tests determine underlying factors and rule out other conditions with similar symptoms. Sociodemographic details shape the expression of symptoms and are research-focused in the literature [56]. Considering these factors allows for tailored assessments, ensuring cultural sensitivity and accurate diagnosis. This comprehensive approach enhances diagnostic accuracy, supports personalized interventions, and comprehensively understands ASD in diverse individuals and populations.

Consequently, the development of a triage process for differentiating autism patients' emergency levels based on both medical tests and sociodemographic features can improve the efficiency and effectiveness of healthcare delivery. By incorporating medical test results, healthcare professionals can swiftly identify critical health issues while considering sociodemographic factors, ensuring a more personalized and culturally sensitive approach to care. This tailored triage system not only streamlines the diagnosis and treatment process but also contributes to superior overall outcomes, fostering a more inclusive and patient-centered healthcare environment for individuals with ASD [6, 19].

The current ASD dataset comes from a previous research project that used both criterion-set viewpoints for triaging autism patients [7]. The data came from a pre-diploma study conducted at the Informatics Institute for Postgraduate Studies in Baghdad, Iraq, and collected from the Iraqi Association for Psychotherapy. As described in [7], the authors collected and created a real-world ASD dataset and an intelligent triage method for the literature based on scientific reasoning.

There were 988 individuals at the foundation and 42 medical and sociodemographic criteria. Examples of medical test criteria include zinc, B12, and D3—also, the patient's and father's blood types. In contrast, examples of sociodemographic indications are being scared of loud noises, crying for no apparent reason, and nodding with the head. Even though the medical professionals differ on the criteria involved in the triage process and which criteria should be excluded, the final criteria for all countries could be the same. As a result, the developed triage method required the collaboration of thirteen psychologist experts, AI specialists, and fuzzy decision-making experts to select the most affected ASD criteria and differentiate the autism patients into three triage levels based on the severity of the recommendation that can be urgent, moderate, and minor, as discussed in [7, 57].

To summarize the triage process in these previous studies, there are three techniques: Fuzzy Delphi Method (FDM), Fuzzy Weighted Zero-Inconsistency (FWZIC), and PTAP as a 'Processes for Triaging Autism Patients' within the Triangular Fuzzy Numbers (TFNs) environment were used to develop a triage approach for ASD, in FDM, which involves eight steps, the most essential medical and sociodemographic criteria are chosen by assessing 13 psychologist experts' opinions. It is considered an effective process since only the affected factors that produce 19 out of 42 were selected for inclusion. The next is the FWZIC method, which has five steps and assigns the proper weights to the 19 medical and sociodemographic criteria generated from FDM. FWZIC weights were thought to be fundamental elements of the PTAP estimation. Therefore, there are six phases of PTAP used for the transition levels assignment, which is done by classifying the targets (classes) and providing the legal grounds for post-triage. The outcome of the intelligent triage method is composed of authentic information from 538 patients and classified into three triage levels: Urgent (70 cases), Moderate (432 cases), and Minor (36 cases), with nineteen medical and sociodemographic criteria in each. Furthermore, the ASD dataset was structured numerically based on the intelligent triage results [7]. A description of the ASD criteria and the corresponding coding data is provided below:

• 1. Patient’s gender: indicates whether the patient is male (2) or female (1).

• 2. Marital relationship: indicates whether the patient is in a marital relationship, with "yes" representing (2) and "no" representing (1).

• 3. Kinship: indicates whether the patient has kinship, with "yes" representing (2) and "no" representing (1).

• 4. Unnecessary drugs: indicates the patient's need for unnecessary drugs, with "yes" representing (2) and "no" representing (1).

• 5. Maternal diseases during pregnancy: indicates whether the patient's mother had any diseases during pregnancy, with "good" indicating no diseases (1) and "not good" indicating the presence of diseases (2).

• 6. Complications of childbirth: indicates whether the patient experienced complications during childbirth, with "yes" representing (2) and "no" representing (1).

• 7. Premature baby: indicates whether the patient was born prematurely, with "yes" representing (2) and "no" representing (1).

• 8. Taste the food: indicates the patient's ability to taste food, with "yes" representing (2) and "no" representing (1).

• 9. Wave: indicates whether the patient can wave, with "yes" representing (2) and "no" representing (1).

• 10. Patient movement at home: indicates the patient's movement at home, with "yes" representing (2) and "no" representing (1).

• 11. Frightened by loud noises: indicates whether the patient is frightened by loud noises, with "yes" representing (2) and "no" representing (1).

• 12. Laughing for no reason: indicates whether the patient laughs for no reason, with "yes" representing (2) and "no" representing (1).

• 13. Crying for no reason: indicates whether the patient cries for no reason, with "yes" representing (2) and "no" representing (1).

• 14. No verbal communication: indicates whether the patient has no verbal communication, with "yes" representing (2) and "no" representing (1).

• 15. Pointing with the index finger: indicates whether the patient points with the index finger, with "yes" representing (2) and "no" representing (1).

• 16. Notice the sound of the bell: indicates whether the patient notices the sound of the bell, with "yes" representing (2) and "no" representing (1).

• 17. Bathroom skills: indicates the patient's bathroom skills, with "yes" representing (2) and "no" representing (1).

• 18. Nodding: indicates whether the patient nods, with "yes" representing (2) and "no" representing (1).

• 19. Spinning round things: indicates whether the patient spins round things, with "yes" representing (2) and "no" representing (1).

Figures 2, 3, and 4 provide visualizations of the dataset points to represent the criteria of a dataset circularly. In simpler terms, it portrays a dimensional of each level in the ASD dataset encompassing both 19 medical and sociodemographic criteria and the corresponding number of patients. For a more comprehensive understanding of the dataset, its description, and feature definitions, readers are encouraged to refer to the previous study [7, 57].

Fig. 2

Medical and sociodemographic criteria assessing ASD patients at level-3 (Urgent)

Fig. 3

Medical and sociodemographic criteria assessing ASD patients at level-2 (Moderate)

Fig. 4

Medical and sociodemographic criteria assessing ASD patients at level-1 (Minor)

Phase 2: development of decision matrix (DM)

The evaluation DM plays a pivotal role within the MCDM methodology, serving as the cornerstone of the prioritization process. This matrix comprises two fundamental components: alternatives (the triaged ASD patients) and decision criteria (the 19 ASD medical and sociodemographic criteria). An overview of the steps involved in developing and constructing the DM for the prioritization of ASD patients is provided in Table 1.

Table 1 Structure of the developed decision matrix for prioritizing ASD patients

The resulting DM is employed for each triage level, facilitating the prioritization of patients. This means that each set of the three patients' levels from the chosen ASD dataset, Urgent (70 cases), Moderate (432 cases), and Minor (36 cases), are employed in the developed DM to prioritize the related autism patients. For example, the process of the DM is employed to prioritize the urgent level, which includes 70 patients, with the incorporation of SVN2TL-FWZIC and MABAC methods, and so on, for other levels.

Phase 3: formulation of SVN2TL-FWZIC

The SVN2TL-FWZIC method is being developed to address the need to weigh the 19 medical and sociodemographic criteria in decision-making. These weights are subsequently utilized for the prioritization of ASD patients across the three emergency levels. The developed Decision Matrix (Table 1) consists of various alternatives and criteria, with each alternative being evaluated based on 19 medical and sociodemographic criteria. Therefore, developing the SVN2TL-FWZIC method is crucial as it provides a robust and effective approach to weighting the criteria. This method enables decision-makers to incorporate subjective judgments and linguistic preferences while maintaining consistency and eliminating inconsistencies.

The SVN2TLFS approach allows linguistic terms to express the relative importance of criteria, offering more flexibility and interpretability compared to traditional numerical weights. Additionally, the FWZIC method ensures zero inconsistency in the weighting process, where assigned weights align logically and mathematically. FWZIC computes and calculates the weight coefficient values of each criterion separately and accurately to achieve zero consistency, eliminating the potential for mistakes compared to zero pairwise comparisons.

Incorporating the FWZIC principle guarantees consistent and reliable assigned weights, reducing bias and ambiguity in the decision-making process [42]. Therefore, using SVN2TLFSs and FWZIC contributes to more accurate and transparent decision-making, particularly in complex scenarios where multiple criteria must be considered. Figure 5 illustrates the steps of FWZIC through five essential processes [58].

Fig. 5

Key processes of SVN2TL-FWZIC for weight construction

The five essential processes depicted in Fig. 5 are a crucial component of the SVN2TL-FWZIC methodology. They are integral to constructing weights for each criterion, contributing to the thorough evaluation and prioritization of ASD patients.

Task 1: define and explore the medical and sociodemographic criteria

In this task, the research delves into the intricate world of medical and sociodemographic criteria, a vital step toward achieving the systematic prioritization of ASD patients. Each criterion identified in the previous stage undergoes a meticulous process to ascertain its significance and relevance in the context of this study.

Task 2: structured expert judgment (SEJ)

The SEJ process is the cornerstone of our methodology, bridging the gap between expert insights and numerical analysis. It begins with the careful selection of experts who are prominent figures in the field of psychology, a crucial element of our aim to prioritize ASD patients. These chosen experts comprise our SEJ panel, including reputed experts who afford valuable critiques and opinions. The last step in the SEJ process is creating an evaluation form. This crucial document records the SEJ panel's agreed medical and sociodemographic criteria to support quantitative analysis, quantitative conversion procedure, and translated linguistic scales as numerical representations. In the subsequent sub-points, we have delved deeper into these processes, demonstrating their integral roles toward systematically prioritizing ASD patients.

• (A) Expert identification and selection: we rely on the knowledge of the individuals we work with as key to the success of our project. Academically, one may specify an `'expert' as someone with specialized practical and theoretical knowledge in a topic related to our project. Thus, our group included four psychologists, each with at least 5 years of practice, expertise, and experience in the psychological field. These specialists carry not just extensive knowledge but also a wealth of practical insights to the table, guaranteeing that the findings of our study are accurate and reliable. Their participation also helps reduce bias and variance across expert perspectives, improving our analysis's quality and thoroughness. Their cumulative expertise helps shape our case study, providing vital insights that directly contribute to our research objectives.

• (B) Evaluation form development: this process involves formulating the evaluation form, which is consensus-oriented. The form has been set up to collect input from our highly esteemed team of specialists. The questionnaire review is conducted before the conclusion of the process to enforce its thoroughness, clarity and perfect alignment with the research objectives. In addition, online interviews with experts are carried out to clarify the form and the questionnaire. Therefore, it can give us a clear explanation of the goal and objectives of the research.

• (C) Defining the level of importance scale: in this stage, a group of experts comes together to determine the level of importance for each medical and sociodemographic criterion. Using a 5-point Likert scale, they assign significant values to these criteria. Table 2 visualizes this conversion process, converting linguistic scales into numerical representations. The 5-point scale has been purposefully chosen as it provides the necessary detail to ensure that the comparison objectives are communicated and the two comparison dimensions for the respondent are well-managed. Both the evaluation form in the form of an evaluation and a questionnaire are key factors in this.

Table 2 Linguistic variables and their corresponding SVN2TLFSs for evaluating the criteria

Using the Likert scale, our methodology assigns varying levels of significance to medical and sociodemographic criteria. These levels range from "Insignificant," represented as (1), to the highest linguistic scale, "High-priority," denoted by (5). This approach aligns perfectly with our mission to prioritize ASD patients, ensuring that each criterion is weighed in the decision-making process. To provide a clearer understanding of how linguistic terms are utilized in the weighting process using the SVN2TL-FWZIC method. For example, the criteria "C11 = Laughing for no reason" is crucial in assessing the severity and progression of ASD symptoms. When assigning weights using linguistic terms with the SVN2TL-FWZIC method (refer to Table 2), we might use terms such as "High-priority (H.P)" or "Valuable (V)" to express the relative importance of this criterion. By assigning linguistic terms from the experts, we can capture the qualitative nuances of each criterion's importance. These linguistic terms help convey the degree of significance associated with specific ranges of values for each criterion.

Task 3: constructing EDM

In the previous stage, we meticulously compiled the invaluable input of our expert panel, encapsulating their individual choices concerning specific medical and sociodemographic criteria. This wealth of expert insight is instrumental in constructing the EDM, a pivotal component of our methodology. As illustrated in Table 3, the EDM features two primary elements: ASD patients and the array of medical and sociodemographic criteria. Each criterion (Cj) within the attribute, representing the medical and sociodemographic criteria, interfaces with every selected expert (Ei) who represents the realm of academic psychology.

Table 3 EDM

This collaborative endeavor evaluates the degree of relevance for each medical and sociodemographic criterion, providing a comprehensive assessment that underpins our systematic prioritization of ASD patients. The EDM is the nexus where expert perspectives converge with patient criteria, forging the foundation for our prioritization process.

This intricate intersection of expert evaluation and patient criteria is instrumental in our mission to systematically prioritize ASD patients, ensuring that each criterion is considered from the vantage point of academic expertise. Table 3 combines the evaluation criteria from medical and sociodemographic criteria and the SEJ panel. Each criterion (Cn) intersects with each selected expert (Eh), and the expert assigns the corresponding significance level for each criterion. The EDM serves as the basis for the subsequent analysis processes of the proposed SVN2TL-FWZIC method, which will be elaborated on in the upcoming sections.

Task 4: formulation process of SVN2TLFSs: the SVN2TLFSs and the corresponding operations required for processing the SVN2TL-FWZIC method are defined as follows.

Definition

[59]. An SVNFS $\widetilde{N}$ on a universe of discourse X is represented in the form:

$$\widetilde{N}=\left\{\langle x,\left({T}_{\widetilde{N}}\left(x\right){, I}_{\widetilde{N}}{\left(x\right),F}_{\widetilde{N}}\left(x\right)\right)|x\in X\rangle \right\},$$

(1)

with truth-membership ${T}_{\widetilde{N}}\left(x\right)$, indeterminacy-membership ${I}_{\widetilde{N}} (x)$, and falsity-membership ${F}_{\widetilde{N}}\left(x\right)\in \left[{0,1}\right]$ and.

$$0\le {T}_{\widetilde{N}}\left(x\right){+ I}_{\widetilde{N}}{\left(x\right)+F}_{\widetilde{N}}\left(x\right)\le 3,$$

(2)

Definition 1

[60] (Herrera and Martinez 2000). For a linguistic term set (LTS), $L=\left\{{l}_{0,}{l}_{1},\dots ,{l}_{{\rm K}}\right\}$, with an odd cardinality $\left({\rm K}+1\right)$, e.g. $L=\left\{{l}_{0}=not important, {l}_{1}=important,{l}_{2}=very important\right\}$, suppose that the result of aggregating the indices of some labels in $L$ is $\beta \in \left[0,{\rm K}\right]$ and $\beta \notin \left\{0,\dots ,{\rm K}\right\},$ then the information equivalent to $\beta$ can be defined by the 2-tuple linguistic term $\left({l}_{k},{\mathcalligra{k}}\right)$ with $k=round \left(\beta \right),{l}_{k}\in L$ and ${\mathcalligra{k}}=\beta -k, {\mathcalligra{k}}\in [-{0.5,0.5})$.

Definition 2

[60] (Herrera and Martinez 2000). To get the 2-tuple linguistic term (2TLT) corresponding to $\beta$, the following mapping is used.

$$\Delta :\left[0,{\rm K}\right]\to L\times \left[-{0.5,0.5}\right),$$

$$\Delta \left(\beta \right)=\left( {l}_{k},{\mathcalligra{k}}\right), {\text{with}} \left\{\begin{array}{c}{l}_{k}, k=round \left(\beta \right), \\ {\mathcalligra{k}}=\beta -k,{\mathcalligra{k}}\in \left[-{0.5,0.5}\right).\end{array}\right.$$

(3)

Conversely, to get the basic value $\beta \in \left[0,{\rm K}\right]$ from the 2TLT, an inverse mapping ${\Delta }^{-1}$ is used

$${\Delta }^{-1}:L\times \left[-{0.5,0.5}\right)\to \left[0,{\rm K}\right],$$

$${\Delta }^{-1}\left( {l}_{k},{\mathcalligra{k}}\right)=k+{\mathcalligra{k}}=\beta $$

(4)

Definition 3

[50]. A SVN2TLS is defined as.

$$\widetilde{\mathbb{N}}=\left\{\langle x,\left({l}_{\theta (x)},{{\mathcalligra{k}}}_{\theta (x)}\right),\left({T}_{\widetilde{\mathbb{N}}}\left(x\right){, I}_{\widetilde{\mathbb{N}}}{\left(x\right),F}_{\widetilde{\mathbb{N}}}\left(x\right)\right)\rangle |x\in X\right\},$$

(5)

where ${l}_{\theta \left(x\right)}\in L=\left\{{l}_{0,}{l}_{1},\dots ,{l}_{{\rm K}}\right\}$, ${{\mathcalligra{k}}}_{\theta \left(x\right)}\in \left[-{0.5,0.5}\right)$, ${T}_{\widetilde{\mathbb{N}}}\left(x\right){, I}_{\widetilde{\mathbb{N}}}{\left(x\right), F}_{\widetilde{\mathbb{N}}}\left(x\right)\in \left[{0,1}\right]$ represent, the truth-membership, the indeterminacy-membership, and the falsity-membership of $x$ to the 2TLT $\left({l}_{\theta (x)},{{\mathcalligra{k}}}_{\theta (x)}\right)$, respectively, and $0\le {T}_{\widetilde{\mathbb{N}}}\left(x\right){+ I}_{\widetilde{\mathbb{N}}}{\left(x\right)+F}_{\widetilde{\mathbb{N}}}\left(x\right)\le 3$.

For convenience, an SVN2TLS is simplified as $\widetilde{\mathbb{N}}=\langle \left({l}_{\theta },{{\mathcalligra{k}}}_{\theta }\right),\left({T}_{\widetilde{\mathbb{N}}}{, I}_{\widetilde{\mathbb{N}}}{,F}_{\widetilde{\mathbb{N}}}\right)\rangle$

Definition 4

[48]: The score of an SVN2TLS is evaluated by:

$$S\left(\widetilde{\mathbb{N}}\right)=\Delta \left({\Delta }^{-1}\left({l}_{\theta },{{\mathcalligra{k}}}_{\theta }\right)*\left(\frac{2+{T}_{\widetilde{\mathbb{N}}}{-I}_{\widetilde{\mathbb{N}}}{-F}_{\widetilde{\mathbb{N}}}}{3}\right)\right), {\Delta }^{-1}\left(S\left(\widetilde{\mathbb{N}}\right)\right)\in \left[0,{\rm K}\right]$$

(6)

Definition 5

[48]: The scalar multiplication of an SVN2TLS by a scalar $\lambda >0$ is given as.

$$\lambda \cdot \widetilde{\mathbb{N}}=\langle \Delta \left(\lambda {\Delta }^{-1}\left({l}_{\theta },{{\mathcalligra{k}}}_{\theta }\right)\right), \left({\left(1-(1-{T}_{\widetilde{\mathbb{N}}}\right)}^{\lambda },{{ (I}_{\widetilde{\mathbb{N}}})}^{\lambda },{{ (F}_{\widetilde{\mathbb{N}}})}^{\lambda }\right)\rangle ,\lambda >0$$

(7)

Definition 6

[48]: Given $n$ SVN2TLSs $\left\{{\widetilde{\mathbb{N}}}_{1},{\widetilde{\mathbb{N}}}_{2},\dots ,{\widetilde{\mathbb{N}}}_{{\text{n}}}\right\} ,{ t}$ he weighting averaging aggregation operator using the weight vector${\varvec{\upomega}}=\left[{\omega }_{1},{\omega }_{2},\dots ,{\omega }_{{\text{n}}}\right]$, ${\omega }_{i}\in \left[{0,1}\right]$ and $\sum_{i=1}^{{\text{n}}}{\omega }_{i}=1$.

$$SVN2TLFWA\left({\widetilde{\mathbb{N}}}_{1},{\widetilde{\mathbb{N}}}_{2},\dots ,{\widetilde{\mathbb{N}}}_{{\text{n}}}\right)=\left\langle \Delta \left({\rm K}\left(\sum_{i=1}^{n}{{\omega }_{i}\Delta }^{-1}\frac{\left({l}_{\theta },{{\mathcalligra{k}}}_{\theta }\right)}{{\rm K}}\right)\right),\left(\sum_{i=1}^{n}{\omega }_{i}{T}_{{\widetilde{\mathbb{N}}}_{i}},\sum_{i=1}^{n}{\omega }_{i}{I}_{{\widetilde{\mathbb{N}}}_{i}},\sum_{i=1}^{n}{\omega }_{i}{F}_{{\widetilde{\mathbb{N}}}_{i}}\right)\right\rangle .$$

(8)

Table 2 demonstrates that converting all linguistic variables into SVN2TLSs is possible. This conversion assumes that the fuzzy number represents each expert $\left(E\right)$ variable. As data scientists, experts were responsible for determining the crucial extent of the evaluation criteria within variables evaluated using linguistic variables.

Task 5: calculating the definitive weight coefficients: this task derives the conclusive values of the weight coefficients, denoted as ${(w1,w2, ...,wn)}^{T}$, for evaluating the 19 medical and sociodemographic criteria. These weight coefficients are pivotal in quantifying the relative importance of each ASD criterion within the comprehensive evaluation process. The fuzzy data obtained from the prior step plays a central role in determining these weight coefficients. The computation of these weight coefficients is a critical component of our data analysis process, marking the culmination of our efforts in this task. This process unfolds through the following two sequential steps:

1) Eqs. (6) and (7) determine the ratio of the fuzzified data. As demonstrated in Table 4, the preceding equations are employed with SVN2TLFSs.

$$\frac{Imp\left(\frac{\widetilde{EI}}{CJ}\right)}{\sum_{j=1}^{n}Imp\left(\frac{EI}{{C}_{IJ}}\right)},$$

(9)

where $Imp\left(\widetilde{EI}/CJ\right)$ represent the SVN2TLFS of $Imp(EI/CJ)$

Table 4 Fuzzy EDM ($\widetilde{{\text{EDM}}}$)

2) The mean values are computed to determine the final fuzzy weighting coefficients of the evaluation criteria${(\widetilde{w1},\widetilde{w2}, ...,\widetilde{wn})}^{t}$. The Fuzzy EDM $(\widetilde{{\text{EDM}}})$ is utilized to calculate the final weight value of each criterion using Eq. (10):

$$\widetilde{{{\varvec{w}}}_{j}}=\left(\sum_{i=1}^{h}\frac{\widetilde{Imp({E}_{ij}/{C}_{ij})}}{\sum_{j=1}^{n}Imp({E}_{ij}/{C}_{ij})})/m \right), {\rm for }\,i={1,2},3,..h\, and\, j={1,2},3,..n .$$

(10)

3) Finding the final weights: The score function (6) is utilized in this process to determine the precise value of each weight. Subsequently, the obtained crisp weights are normalized by dividing the weight of each criterion by the sum of all the crisp weights of the criteria.

The five steps proposed above are applied systematically to the outcomes of the medical and sociodemographic criteria, thereby ensuring that the weight coefficients for all kinds of criteria are determined coherently. The aggregated weight coefficients should be summed up to be equal to 1, meaning that the whole gravity or plus-like properties of medical and social-demographic criteria in the whole evaluation process are reflected by this total.

Phase 4: formulation of MABAC

The weight coefficients of the ASD criteria were calculated in the previous phase. Accordingly, this phase is presented to formulate a mathematical equation for MABAC. The MABAC method is applied to rank patients suffering from ASD according to each emergency level. This technique estimates the distance between the criterion functions of individual ASD patients and the border approximation area (BAA). The MABAC application is associated with the six crucial stages.

STEP 1: in the initial step, a set of $m$ alternatives is assessed using $n$ criteria. The denoted selections of $m$ and $n$ are resented as vectors: ${A}_{i}=({X}_{i1}{, X}_{i2},\dots ,{ X}_{in}$), where ${X}_{ij}$ signifies the score attributed to the $i-th$ choice concerning the $j-th$ ASD criterion. The index $i$ ranges from 1 to $m$, and the index $j$ ranges from 1 to $n$.

$$\begin{array}{cccc}{C}_{1}& {C}_{2}& \cdots & {C}_{n}\end{array}$$

$$X=\begin{array}{c}{A}_{1}\\ {A}_{2}\\ \begin{array}{c}\vdots \\ {A}_{m}\end{array}\end{array}\left[\begin{array}{llll}{x}_{11}&\quad {x}_{12}&\quad \cdots &\quad {x}_{1n}\\ {x}_{21}&\quad {x}_{22}&\quad \cdots &\quad {x}_{2n}\\ \vdots &\quad \vdots &\quad \vdots &\quad \vdots \\ {x}_{m1}&\quad {x}_{m2}&\quad \dots &\quad {x}_{mn}\end{array}\right]$$

(11)

Here, $m$ represents the number of ASD patients within each level being considered, and $n$ numerates the overall count of ASD criteria involved in the prioritization procedure.

STEP 2: normalization is achieved for all the ASD criteria to make them comparable and less the bias of variances in the magnitude and units of the criteria's value. The next processes are typically utilized to normalize the elements of the initial matrix $X$.

$$\begin{array}{cccc}{C}_{1}& {C}_{2}& \cdots & {C}_{n}\end{array}$$

$$N=\begin{array}{c}{A}_{1}\\ {A}_{2}\\ \begin{array}{c}\vdots \\ {A}_{m}\end{array}\end{array}\left[\begin{array}{llll}{n}_{11}&\quad {n}_{12}&\quad \cdots &\quad {n}_{1n}\\ {n}_{21}&\quad {n}_{22}&\quad \cdots &\quad {n}_{2n}\\ \vdots &\quad \vdots &\quad \vdots &\quad \vdots \\ {n}_{m1}&\quad {n}_{m2}&\quad \dots &\quad {n}_{mn}\end{array}\right]$$

(12)

Step 2 is to determine the elements of the normalized matrix ($N$) using appropriate equations based on the type of ASD criteria:

(a) The normalized matrix's components are generated using Eq. (13) designed for ASD criteria from the type of benefit, where a higher criterion value is preferred:

$${n}_{ij}=\frac{{x}_{ij}-{x}_{i}^{-}}{{x}_{i}^{+}-{x}_{i}^{-}}$$

(13)

(b) The normalized matrix's components are computed using the Equation designed for cost-type criteria, where a lower criterion value is considered preferred:

The components of the normalized matrix are generated using Eq. (14) designed for ASD criteria from type of cost, where a lower criterion value is considered preferred:

$${n}_{ij}=\frac{{x}_{ij}-{x}_{i}^{+}}{{x}_{i}^{-}-{x}_{i}^{+}}$$

(14)

Here, ${X}_{ij}$ denotes the $X$ matrix member corresponding to $i$ (autism patients) and $j$ (ASD criterion).

The values for ${x}_{i}^{+}$ and ${x}_{i}^{-}$ are defined as follows:

• ${x}_{i}^{-}$: represents the lowest observed value for criterion $j$ amongst all ASD patients $\left({x}_{i}^{-}={\text{min}} \left({X}_{1},{ X}_{2},\dots ,{ X}_{m}\right)\right)$.

• ${x}_{i}^{+}$: indicates the highest observed value for criterion $j$ among all ASD patients $\left({x}_{i}^{+}={\text{max}} \left({X}_{1},{ X}_{2},\dots ,{ X}_{m}\right)\right)$,

By suitably normalizing the matrix dependent on the type of ASD criteria, each patient's relative importance and performance in relation to each criterion may be efficiently compared and studied in the MABAC formulation steps.

STEP 3: in this stage, the weighted matrix ($V$) elements are calculated by Eq. (15) to determine the values assigned to each element in $V$.

$${v}_{ij}={w}_{j}.\left({n}_{ij}+1\right)$$

(15)

In this equation, ${n}_{ij}$ denotes the element from the normalized matrix $N$ corresponding to $i$ and $j$, whereas ${w}_{i}$ represents the weight coefficient assigned to criterion $j$. Using Eq. (15), the elements of the weighted matrix ($V)$ are calculated by multiplying each element of the $N$ normalized matrix by its weight coefficient $({w}_{i})$.

$$V=\left[\begin{array}{cccc}{v}_{11}& {v}_{12}& \dots & {v}_{1n}\\ {v}_{21}& {v}_{22}& \dots & {v}_{2n}\\ \vdots & \vdots & \vdots & \vdots \\ {v}_{m1}& {v}_{m2}& \dots & {v}_{mn}\end{array}\right]=\left[\begin{array}{cccc}{w}_{1}.\left({n}_{11}+1\right)& {w}_{2}.\left({n}_{12}+1\right)& \cdots & {w}_{n}.\left({n}_{1n}+1\right)\\ {w}_{1}.\left({n}_{21}+1\right)& {w}_{2}.\left({n}_{22}+1\right)& \cdots & {w}_{n}.\left({n}_{2n}+1\right)\\ \vdots & \vdots & \vdots & \vdots \\ {w}_{1}.\left({n}_{m1}+1\right)& {w}_{2}.\left({n}_{m2}+1\right)& \cdots & {w}_{n}.\left({n}_{mn}+1\right)\end{array}\right]$$

It is worth noting that in this context, `$n$' represents the entire count of ASD criteria. The `m' specifies the total number of ASD patients (alternatives). This ensures a comprehensive and systematic evaluation within the MABAC method.

STEP 4: the $\left(\mathsf{g}\right)$ specifies the border approximation area matrix determined using Eq. (16) for each ASD criterion. This equation is pivotal in defining the BAA associated with each ASD criterion.

$${\mathsf{g}}_{j}={\left(\prod_{i=1}^{m}{v}_{ij}\right)}^{1/m}$$

(16)

The computation process in this step incorporates the values of ${v}_{ij}$ derived from the $V$ matrix and the ASD patients (alternatives denoted as $m$). These computations contribute to establishing the elements within the border approximation area matrix ($G$).

Equation (17) is employed to construct the G, which evaluates the ${\mathsf{g}}_{i}$ value for each ASD criterion. The resultant $G$ exhibits a shape of $n\times 1$, where `$n$' represents the number of medical and sociodemographic criteria applied in the prioritization of ASD patients.

$$\begin{array}{cccc}{C}_{1}& {C}_{2}& \dots & {C}_{n}\end{array}$$

$$G=\left[\begin{array}{cccc}{\mathsf{g}}_{1}& {\mathsf{g}}_{2}& \cdots & {\mathsf{g}}_{j}\end{array}\right]$$

(17)

This step ensures a comprehensive assessment of the BAA, facilitating the subsequent stages of the MABAC method.

STEP 5: in this step, the proximity of each alternative to the border approximation area $Q^{\prime}$ s is determined for each criterion. This computation assesses how closely or distantly each alternative aligns with the border approximation area.

$$Q=\left[\begin{array}{cccc}{q }_{11}&\quad {q }_{12}&\quad \dots \dots &\quad {q}_{ 1n}\\ {q}_{ 21}&\quad {q}_{ 22}&\quad \dots \dots &\quad {q }_{2n}\\ \vdots &\quad \vdots &\quad \vdots &\quad \vdots \\ {q }_{m1}&\quad {q }_{m2}&\quad \dots \dots &\quad {q }_{mn}\end{array}\right]$$

(18)

To determine the distance between each alternative and the BAA, a disparity value (${Q}_{ij}$) is calculated by comparing the elements of the weighted matrix ($V$) to the value of the border approximation area ($G$).

$$Q=V-G=\left[\begin{array}{cccc}{v}_{11}& {v}_{12}& \dots & {v}_{1n}\\ {v}_{21}& {v}_{22}& \dots & {v}_{2n}\\ \vdots & \vdots & \vdots & \vdots \\ {v}_{m1}& {v}_{m2}& \dots & {v}_{mn}\end{array}\right]-\left[\begin{array}{cccc}{\mathsf{g}}_{1}& {\mathsf{g}}_{2}& \dots & {\mathsf{g}}_{n}\\ {\mathsf{g}}_{1}& {\mathsf{g}}_{2}& \dots & {\mathsf{g}}_{n}\\ \vdots & \vdots & \vdots & \vdots \\ {\mathsf{g}}_{1}& {\mathsf{g}}_{2}& \dots & {\mathsf{g}}_{n}\end{array}\right]$$

(19)

$$Q=\left[\begin{array}{cccc}{v}_{11}-{\mathsf{g}}_{1}& {v}_{12}-{\mathsf{g}}_{2}& \dots & {v}_{1n}-{\mathsf{g}}_{n}\\ {v}_{21}-{\mathsf{g}}_{1}& {v}_{22}-{\mathsf{g}}_{2}& \dots & {v}_{2n}-{\mathsf{g}}_{n}\\ \vdots & \vdots & \vdots & \vdots \\ {v}_{m1}-{\mathsf{g}}_{1}& {v}_{m2}-{\mathsf{g}}_{2}& \dots & {v}_{mn}-{\mathsf{g}}_{n}\end{array}\right]=\left[\begin{array}{cccc}{q}_{11}& {q}_{12}& \dots & {q}_{1n}\\ {q}_{21}& {q}_{22}& \dots & {q}_{2n}\\ \vdots & \vdots & \vdots & \vdots \\ {q}_{m1}& {q}_{m2}& \dots & {q}_{mn}\end{array}\right]$$

(20)

The distance between each alternative and the boundary approximation area is expressed by Eqs. (19) and (20). It considers each criterion's weighted matrix elements, total counts (n and m), and border approximation area (${\mathsf{g}}_{i}$). The distance computation divides each alternative (${A}_{i}$) into three groups: $G$, the higher approximation area (${G}^{+}$), and the lower approximation area (${G}^{-}$). The optimal alternative (${A}^{+}$) is positioned in ${G}^{+}$, while the unpleasant alternative (${A}^{-}$) is in ${G}^{-}$.

Equation (21) is utilized to determine the categorization of each alternative (${A}_{i}$) into one of the three approximation areas ($G$, ${G}^{+}$, or ${G}^{-}$).

$${A}_{i}\in \left\{\begin{array}{ll}{G}^{+} &\quad if {q}_{ij}>0\\ G &\quad if {q}_{ij}=0\\ {G}^{-} &\quad if {q}_{ij}<0\end{array}\right.$$

(21)

Determine the best option from the set by having an alternative option (${A}_{i}$) with a higher proportion of criteria falling under ${G}^{+}$. As an illustration, if an alternative ( ${A}_{i}$) matches 10 out of 19 criteria to the region of the upper approximation boundary and the case where the alternative becomes different from the ideal alternative by falling into the area of the lower approximation boundary (${G}^{-}$), in this situation, the alternative satisfies these criteria with resemblance or equality. However, the one that is being emphasized corresponds to the anti-ideal alternative.

Where ${q}_{ij}$ was greater than 0 in the MABAC model, it insinuates that the group is ${G}^{+}$. This indicates that, in this case, the alternative ${A}I$ is close to or equal to the perfect alternative from the standpoint of that criterion. A positive value of ${q}_{ij}$ indicates how closely the performance value of the alternative (${A}_{i}$) approaches the verified performance set represented by the area above.

When ${q}_{ij}$ is smaller than 0, such means that it belongs to ${G}^{-}$. This shows that the alternative (${A}_{i}$) can be considered similar to or equal to the ideal-anti alternative with respect to that criteria. The negative ${q}_{ij}$ value means that the performance of alternative ${A}_{i}$ approaches or has some common characteristics with poor performance as indicated by the lower approximation region. In conclusion, the goal of the methodology is for (${A}_{i}$) to have a higher number of criteria in ${G}^{+}$, thus making ${A}_{i}$ the most attractive among the alternatives (see Fig. 6).

Fig. 6

Visualization of the areas of the border approximation, lower and upper [33]

Step 6. The values of criterion functions are calculated by averaging the distance from their ${q}_{i}$. These criteria functions are the main elements that distinguish the MABAC approach's alternatives. The column entries of the ${Q}_{n}$ matrix show the distances between every alternative and the alternative boundaries, and summing up for each row will lead to criteria functions for these options.

Equation (22) outlines the calculation process, where '$n$' represents the number of ASD criteria, and '$m$' represents the total number of ASD patients (alternatives) within each level.

$${S}_{i}=\sum_{j=1}^{n}{q}_{ij}, j={1,2},\dots n,i={1,2},\dots ,m$$

(22)

The resulting values serve as the ASD criterion functions for ASD patients, allowing for their ranking based on proximity to the border approximation areas.

Results and discussion

This section delves into the outcomes of the prioritization process for ASD patients, considering the predefined medical and sociodemographic criteria. Firstly, the results of the weight constructed from the SVN2TL-FWZIC method are shown. Then, the MABAC method is elaborated to provide the prioritization results.

Weighting results

The SVN2TL-FWZIC method has been instrumental in determining the importance of the weight allocated to each criterion concerning others. Every step of the SVN2TL-FWZIC procedure was meticulously executed to establish the weights for the 19 medical and sociodemographic evaluation criteria. An expert panel comprised of four seasoned psychologists played a pivotal role in creating the EDM. These experts, chosen for their specialized knowledge, were requested to offer their subjective evaluations of the 19 medical and sociodemographic criteria using a five-point Likert scale, corresponding to a numerical scale, as the obtained results are presented in Table A1 (Supplementary file). Table 5 presents the outcomes of consistency weighting for the medical and sociodemographic criteria based on the SVN2TL-FWZIC method in these contexts. The consistency weighting stage is integral to the SVN2TL-FWZIC approach, ensuring the robustness and consistency of the medical and sociodemographic criteria assessment.

Table 5 SVN2TL-FWZIC weights result for medical and sociodemographic criteria

The weights assigned to the various criteria, as presented in Table 5, play a pivotal role in the prioritization and decision-making process. The precise SVN2TL-FWZIC weights for the 19 criteria suggest a comprehensive approach to evaluating and prioritizing ASD patients based on medical and sociodemographic factors. Each criterion appears to capture different aspects of the patient's condition and behavior, reflecting the multidimensional nature of ASD. These SVN2TL-FWZIC weights reflect the relative importance of these criteria within the specific context of analysis or research. Criteria with higher weights are considered more influential in the prioritization of ASD patients, while those with lower weights have less impact.

The criteria "C1 = Patient's Gender", "C2 = Marital Relationship", and "C3 = Kinship" reflect sociodemographic criteria that impact the patient's condition and treatment. Meanwhile, criteria like "C6 = Complications of childbirth" and " C7 = Premature baby" highlight potential prenatal and perinatal criteria that could contribute to ASD development. Besides, criteria reflect the behavior indicators such as "C11 = Frightened by loud noises", " C12 = Laughing for no reason", and "C13 = Crying for no reason" shed light on specific symptoms and manifestations of autism. These criteria provide insights into the patient's sensory sensitivities, emotional responses, and communication challenges. Functional abilities and adaptive skills are considered, as evident from ASD criteria like "C17 = Bathroom skills" and "C18 = Nodding", which assess the patient's daily living skills and communication methods.

Furthermore, criteria like "C12 = Laughing for no reason" and " C16 = Notice the sound of the bell" are assigned relatively higher weights with 0.097358 and 0.083832, indicating their significance in identifying potential ASD symptoms. Meanwhile, "C15 = Pointing with the index finger" and "C11 = Frightened by loud noises" are assigned relatively average weights with 0.050589 and 0.046669, indicating their moderate in identifying potential ASD symptoms. In addition, "C13 = Crying for no reason" and " C6 = Complications of childbirth" are assigned relatively low weights with 0.031853 and 0.031438, indicating their moderate in identifying potential ASD symptoms.

The SVN2TL-FWZIC weights of the 19 ASD criteria provide the first necessary process for prioritizing ASD patients encompassing medical and behavior dimensions. This analysis provides insights into the impact of these criteria and their role in the prioritization context, offering guidance for decision-making across different emergency levels. However, further ranking processing using the MABAC method based on these criteria weights is presented in the next section.

Prioritization results

In the prioritization process, the calculated weights are utilized with the MABAC method to rank the three emergency levels of ASD patients. This process involves using the developed DM in phase 1 (Table 1) for each emergency level, with the weights obtained from the SVN2TL-FWZIC (Table 5). The MABAC's positive and negative numbers measure how close or far away an action is from the BAA matrix. BAAs with negative values within particular criteria reveal a weakness in those regions, which means that these options may not work in high-urgency situations, and negative BAAs with positive values indicate strong points in the area. These deviations from the BAA template show the alternatives' strengths and weaknesses with respect to the 19 medical and sociodemographic criteria. All alternatives that almost match the BAA matrix on most or all criteria are regarded as high-priority alternatives and should be placed at the top of the list. Tables 6, 7, and 8, which represent the final prioritization results for the minor, moderate, and urgent emergency levels of ASD patients, follow the principles of the MABAC method, particularly Step 6. These tables show an essential mission in the decision-making development, clearly ranking ASD patients based on their performance across the defined criteria.

Table 6 Prioritization results of ASD patients for minor emergency level

Table 7 Prioritization results of ASD patients for moderate emergency level

Table 8 Prioritization results of ASD patients for urgent emergency level

Tables 6, 7, and 8 comprehensively overview the prioritization analysis conducted on ASD patients across various emergency levels. These tables rank the ASD patients based on their order and values sum. The higher sum represents the preferable overall alternative's performance. The deviations of the ASD patients from the BAA matrix highlight substantial differences in their performance concerning the 19 medical and sociodemographic criteria. The "Order" column in these tables signifies the ranking of ASD patients based on the "MABAC Sum." This ranking can offer insights into how patients are prioritized or categorized based on the presence or absence of specific attributes or conditions.

Further analysis and context are required to fully comprehend the implications of these findings, as the significance of specific criteria and their relationship to prioritization outcomes should be understood. The analysis of the ranking results focuses on the ASD emergency levels for the patients ranked within the top three orders. Therefore, after checking the dataset history for these patients within each level and matching the MABAC sum and orders, Table 9 provides the data history of these patients, offering a deeper understanding of their characteristics and attributes.

Table 9 Historical dataset of the first three top-ranked ASD patients for three emergency levels

It is essential to mention that the historical data shown in Table 9 are obtained from the ASD dataset collected from the Iraqi Association for Psychotherapy. The "MABAC Sum" and "Order" columns provide a quantifiable means to compare ASD patients based on their distinct combinations of medical and sociodemographic criteria, influencing the urgency or support required for each patient. In minor-level assessment, all top-ranked patients are female, and the gender in this minor level does not affect the prioritization process significantly. The impact of male gender might be more pronounced in moderate and urgent levels in this specific assessment as all top ranks in both emergency levels are male. The summary of the influence of medical and sociodemographic criteria on the ranking results shown in Table 9 are below:

• Minor Level: the prioritization of the first top-ranked patients is based on the cumulative impact of various criteria, with each criterion's weight determining its significance in the ranking process. Patient (P19) obtained the first rank, and there are several criteria for this patient are marked as `NO' such as C2, C3, C4, C5, C6, C7, C10, C13, C15, C17, C18, and C19. The remaining criteria are marked with Yes'' which means the patient has these symptoms. In addition, the criteria C8, C9, C11, C12, C14, and C16 contribute positively to the patient's ranking due to their higher weights. Additionally, the presence of C10 and C15 further enhances the patient's ranking compared to P19. We can recognize that the criteria that affected the ranking of this patient obtained significant weights by the SVN2TL-FWZIC method (Table 5), which put the patient in this top order. Patients (P15 and P34) share several similarities in terms of criteria presence and absence. The presence of criteria C8, C10, C12, C13, C14, C15, C16, and C17 contributes to the second and third-ranking results.

• Moderate level: for patient (P225), this patient ranks highest for the moderate emergency level. Criteria such as C2, C4, C5, C7, C15, C17, and C19 are absent. The presence of other criteria is significantly contributing positively to the patient's ranking. Patient (P51), this patient ranks second for the moderate emergency level. Several criteria such as C2, C3, C4, C5, C6, C7, C14, C15, and C17 are absent. The present of highly weights criteria such as C8, C9, C10, C11, C12, C13, C16, C18, and C19 are greatly impact the patient's ranking. Patient (P58) ranks third for the moderate emergency level, and criteria such as C3, C7, C8, C9, C10, C11, C12, C14, C15, C16, and C18 are present. Other criteria such as C2, C4, C5, C6, C13, C17, and C19 are absent. High-weighted criteria such as C9, C10, C11, and C12 significantly affect the patient's ranking.

• Urgent Level: patient (P14) ranks highest for the urgent level. Criteria such as C2, C3, C14, C15, and C17 are absent. The remaining criteria are marked with 'Yes'. This means that the presence criteria significantly affect the patient's ranking and contribute positively to the top higher ranking. Patient (P38) ranks second for the urgent level. Similar to P14, several criteria such as C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C15, C16, C17, and C19 are marked with 'Yes', contributing positively to the ranking. The absence of C2, C15, and C117 does not greatly impact the patient's ranking. Patient P8 ranks third for the urgent level. Criteria such as C4, C6, C7, C8, C9, C10, C11, C12, C13, C16, C18, and C19 are marked with 'Yes' while the absence of C2, C3, C5, C14, C15, and C17 does not significantly affect the patient's ranking.

Based on the earlier discussion, it is observed that medical history-related criteria are commonly found among the highest-ranked patients in the urgent category but not at other levels. This emphasizes the importance of these factors in evaluating the urgency of ASD cases. Moreover, sociodemographic criteria indicate their significance in identifying all emergency levels. These interesting findings provide compelling evidence that the developed methodology effectively recognizes different levels of patients and prioritizes them based on high-weighted criteria obtained from the SVN2TL-FWZIC method. In the context of ASD, assessing and ranking patients based on medical and sociodemographic criteria can be valuable for healthcare professionals, researchers, and caregivers. It helps prioritize patients based on their unique needs, enabling tailored support and care plans. The specific interpretation of these rankings and the importance of individual criteria would depend on the clinical or research context and the specific assessment goals for ASD patients.

Summary points

The prioritization process for the three emergency levels elaborates on addressing issues associated with the importance of medical and sociodemographic criteria. Here are some key points to highlight how this methodology effectively addressed these issues:

• Trade-offs and disagreements frequently occur when ranking patients with ASD because several medical and sociodemographic criteria may have contradictory requirements or performance. By taking into account the performance and relative importance of each criterion, the combination of SVN2TL-FWZIC and MABAC aids in the resolution of these disputes. The fuzzy set theory-based SVN2TL-FWZIC method provides an adaptable and versatile way to deal with uncertainty and imprecision. Giving weights to medical and sociodemographic criteria and applying the idea of the SVN2TL set (SVN2TLS) allows for trade-offs and disputes. 2TLN-FWZIC captures the relative relevance of each assessment criterion by allocating weights based on importance, enabling a balanced consideration of trade-offs and conflicts during the prioritization procedure.

• When resolving trade-offs and disputes during the prioritization of ASD patients, MABAC has shown to be a helpful strategy. MABAC measures the dominating area for each autistic patient within each level by comparing alternatives using numerous weighted criteria, making it evident whether the alternative is superior or inferior. The dominance area is computed considering the trade-offs and conflicts that arise from various sociodemographic and medical assessments. As a result, MABAC successfully integrates the relative fulfilment of evaluation criteria and the trade-offs accompanying them into the prioritization process. In the context of ASD patient prioritizing, this nuanced evaluation guarantees a thorough and balanced approach, which is necessary for making informed decisions.

• Both the SVN2TL-FWZIC and MABAC approach guarantee that these significant issues are adequately addressed. Medical and sociodemographic criteria are vital in the priority process. The FWZIC technique, which weights ASD criteria according to their significance, is incorporated into SVN2TL. SVN2TL-FWZIC ensures that the criteria thought to be more critical for ASD patients are given more weight throughout the prioritization process by considering the weights of the evaluation criteria for ASD. This methodology efficiently addresses pertinent concerns and ensures that the assessment outcomes precisely characterize the importance of comparing every medical and sociodemographic criterion. MABAC captures the priorities and preferences related to the ASD criteria by contrasting the alternatives. To ensure that the results of prioritizing appropriately reflect the relative significance of each medical and sociodemographic criterion, the dominance area calculation within MABAC considers these factors. This dual methodology improves the process of prioritizing ASD patients by ensuring that the evaluation results accurately reflect the significance of each medical and sociodemographic criterion.

• A comprehensive and robust approach is established to effectively address the conflict, importance, and trade-off issues associated with the medical and sociodemographic criteria for ASD patients. These methodologies integrate weighting, fuzzy logic, and comparisons, enabling a thorough evaluation of the 19 ASD criteria. This approach ensures that the prioritization process considers the diverse considerations inherent in the evaluation, ultimately leading to the ranking of ASD patients across the three emergency levels. Therefore, it becomes evident that employing an MCDM approach is imperative when selecting ASD patients, as it considers all 19 criteria for medical and sociodemographic evaluation, thus enhancing the decision-making process in emergency healthcare scenarios.

• It is crucial to prioritize medically essential cases, such as those with ASD, by combining a variety of skills. This critical need was identified by our study, which included four varied experts on the panel. Relying exclusively on the opinions of a small group of specialists can raise serious issues. A limited pool of experts could lead to a limited viewpoint in the process of analysis and ranking. Because ASD is a multifaceted area, different perspectives frequently result in more thorough understandings. Limited sample sizes can lead to criticism in various fields because they may not fully convey the breadth and depth of the subject matter.

• Furthermore, every psychology specialist takes with them their own biases and predispositions, irrespective of their background and credentials. We can reduce these biases and achieve a more unbiased and thorough viewpoint by broadening the group of specialists. On the other hand, when a small number of experts are engaged, their individual opinions and preferences can significantly impact the study's general course and findings.

• Recognizing that the methodology used in our investigation retains its theoretical validity is comforting. Our approach's intrinsic versatility is further demonstrated by our ability to address fresh outcomes and incorporate the mathematical process effortlessly on several occasions. This flexibility shows up as a significant asset, especially when considered from an application standpoint. As previously mentioned, a significant benefit of our methodology is its adaptability to new ASD patients as well as altered, added, or deleted medical and sociodemographic criteria. This feature dramatically improves our methodology's applicability in real-world scenarios by allowing it to adapt to new information and circumstances. This flexibility is essential in dynamic domains like medicine, where new ideas and factors emerge. We highlight the theoretical resilience of our methodology and its practical applicability by highlighting its adaptability to real-world developments. As such, this gives confidence to scholars and practitioners alike who might wish to use our method in various settings. The work being presented in various venues presents a dynamic technique for ASD that greatly influences therapeutic treatment.

• Clinical psychologists can leverage this methodology to ensure that patients with urgent needs receive timely interventions and support, improving overall patient outcomes. Policymakers can utilize our methodology to optimize resource allocation in healthcare settings, particularly in the context of ASD diagnosis and treatment. By prioritizing patients according to the severity of their symptoms and other relevant criteria, policymakers can allocate limited resources, such as specialist consultations, diagnostic assessments, and therapeutic interventions, more effectively. This ensures that resources are directed towards those who need them most, maximizing the impact of available healthcare resources and improving overall healthcare delivery.

• Continuous improvement and adaptation: our methodology is designed to be dynamic and adaptable, allowing continuous improvement and refinement based on feedback and changing priorities. Clinical psychologists and policymakers can monitor the performance of the prioritization process over time, making adjustments as needed to ensure that it remains responsive to evolving patient needs and healthcare priorities. This iterative approach facilitates ongoing improvement in the delivery of services for ASD patients, ultimately leading to better outcomes and enhanced quality of life.

Sensitivity analysis

Sensitivity analysis is essential for evaluating the robustness and stability of the ranking outcomes. Decision-makers can better grasp how sensitive the results are to changing weights and assumptions by closely examining how rankings change under various conditions. This study helps identify crucial criteria significantly affecting the rankings and advances a more thorough evaluation of ASD patients across three levels. A sensitivity analysis was conducted to assess how variations in the SVN2TL-FWZIC weights assigned to the medical and sociodemographic factors impacted the overall rankings of the alternatives. This analysis is used to evaluate the stability and reliability of the decision-making process. A sensitivity analysis was performed to determine how differences in the SVN2TL-FWZIC weights allocated to the medical and sociodemographic criteria affected the overall ranks of the alternatives. The stability and robustness of the decision-making process are assessed using this analysis.

We used weight exchange, a method frequently used in sensitivity analysis for MCDM. It entails switching the weights given to various criteria and tracking how the MABAC decision outcomes change [61]. Decision-makers can determine how responsive a decision is to shifts in the relative relevance of two criteria by swapping their weights [62]. This process sheds light on the relative significance of the criteria and assists in making informed decisions under different weight scenarios. By analyzing how changes in medical and sociodemographic criteria weights affect the overall MABAC prioritization, we gain a deeper understanding of the factors driving the decision-making process. This insight allows us to refine the SVN2TL-FWZIC weighting scheme to reflect the priorities and preferences of stakeholders better, thus enhancing the reliability of the prioritization results.

By profiting through the exchange of weights and observing the following changes in the MABAC rankings, the decision-makers can know deeply about the trade-off relationship between each medical and demographic criteria and how these factors weigh on the decisions made to identify ASD patients in different crisis levels. This insight is useful to have the criteria of the most significance, to consider possible biases or uncertainties during the decision-making process, and to strengthen the effectiveness of the decision-making process. The sensitivity analysis involves three scenarios:

• 1st Scenario: exchanging the weight values of the maximum (max) and minimum (min) criteria.

• 2nd Scenario: exchanging the weight values of max and mid criteria.

• 3rd Scenario: exchanging the weight values of min and mid criteria.

The weight values of the criteria, namely C12 = 0.097358 (max), C6 = 0.031438 (min), and C11 = 0.046669 (mid), are derived from the SVN2TL-FWZIC weights presented in Table 5. After applying the exchanged weights to the MABAC method again using the three scenarios above, the rank results of sensitivity analysis vary, as provided in Tables A2, Table A3, and Table A4 for emergency levels 1, 2, and 3, respectively. These sensitivity analysis results are visually represented in Figs. 7, 8, and 9, allowing for a clear comparison with the original MABAC rankings.

Fig. 7

Visualization of rank variations by different sensitivity analysis for emergency level 1 (Minor)

Fig. 8

Visualization of rank variations by different sensitivity analysis for emergency level 2 (Moderate): (A) for ASD patients from sequence 1 to 108, (B) for ASD patients from sequence 109 to 216, (C) for ASD patients from sequence 217 to 324, (D) for ASD patients from sequence 325 to 432

Fig. 9

Visualization of rank variations by different sensitivity analysis for emergency level 3 (Urgent)

The application of three sensitivity analysis scenarios, employing weight exchange within the MABAC method, assists in discerning the relative importance of each ASD patient and their performance. The results in Figs. 7, 8, and 9 demonstrate that the ranking outcomes exhibit a degree of instability across the three emergency levels, displaying some variability when considering different scenarios. These sensitivity results offer valuable insights into how the rankings of ASD patients fluctuate under diverse scenarios.

According to the sensitivity study, changes in the weights assigned to the evaluation criteria significantly impact ASD patient rankings. Different scenarios affect the patients' respective values and placements. The evidence presented in this study calls upon us to reflect on how we assess weights and rethink how to come up with the final result of the assessment, allowing for the possibility of tampering. They point out the necessity of knowing the qualities of rankings and that medical and sociodemographic factors impact the decisions taken. The researchers can use these calculation formulas to understand the stability and reliability of rankings; this helps them make intelligent decisions accounting for the observed variances. This offers better comprehension of emergency performance levels, which can deal with various weight distributions, increasing the credibility and reliability of the proposed decisions.

Comparative study

This section encompasses a thorough comparative analysis of the proposed framework against existing literature, employing a checklist prioritization approach [63, 64]. Checklist prioritization has become a prevalent method in recent literature comparisons, involving the evaluation of various essential checklists to accentuate the uniqueness and novelty of the presented work [57, 65]. The following outlines the definitions of these checklists, and Table 10 provides an overview of how the proposed methodology contributes to the current body of literature based on the results obtained:

• Prioritization of ASD patients' emergency levels: this aspect underscores the consideration of ranking the three emergency levels of ASD patients through MCDM methods.

• Development of decision matrices: this point emphasizes the creation of new decision matrices for prioritizing ASD patients within each level, introducing a novel perspective to the existing body of literature.

• Development of weighting method: this comparison point indicates that the study presents a new MCDM method for assigning the proper weight to the Medical and sociodemographic criteria. Due to the large number of criteria used, this is considered a complex task and essential to list as a comparison point.

• Incorporation of medical and sociodemographic criteria: including medical and sociodemographic features has illustrated its significant influence on the prioritization of ASD emergency levels. Therefore, this checklist item underscores the integration of both criteria categories in developing the study methodology for prioritizing autistic patients.

Table 10 Comparison of the proposed methodology with literature

This checklist prioritization approach is a valuable tool for highlighting the contributions and distinctiveness of the proposed framework in relation to existing literature [66, 67]. The definitions provided clearly understand the specific criteria against which the proposed methodology is evaluated. Table 10 showcases how the proposed framework addresses these checklist items, thereby underlining its innovative nature.

The comparative analysis of the proposed methodology with existing literature reveals substantial distinctions among benchmark studies. The total score, which reflects how effectively each study and the proposed methodology have addressed the comparison points, demonstrates that the planned methodology attains a 100% seamless score. In contrast, the benchmark studies exhibit varying scores, ranging from 25 to 75%.

Notably, Benchmark #1 emerges as the most relevant among the benchmarks, mainly due to its emphasis on developing a decision matrix using medical and sociodemographic criteria. However, it falls short when addressing the prioritization of ASD patients and developing the weighing MCDM method. Interestingly, it is evident that none of the benchmark studies considered the prioritization of ASD patients. This analysis underscores the unique contributions and areas for improvement in both the proposed methodology and the benchmark studies. It underscores the need for a more comprehensive approach in future research to encompass these critical aspects, particularly the prioritization of ASD patients, as the proposed methodology addresses.

Conclusion

The systematic prioritization of ASD using medical and sociodemographic criteria is a critical and complex process. The proposed methodology combines the SVN2TL-FWZIC and the MABAC methodology within a designed mathematical model to achieve robust and comprehensive results. The systematic ranking of ASD patients into three emergency levels, Minor, Moderate, and Urgent, based on 19 distinct criteria, facilitates informed decision-making for healthcare professionals, researchers, and caregivers. We ensure that the evaluation process reflects their relative importance by assigning appropriate weights to these criteria using the SVN2TL-FWZIC method. The calculated weights, as presented in Table 5, offer valuable insights into the significance of each criterion in the context of ASD prioritization. The MABAC method, complemented by the weighted criteria, allows for the comparison of ASD patients and the generation of rankings for each emergency level. The processing of these rankings provides a clear understanding of the performance of each patient across the numerous criteria, as seen in Tables 6, 7, and 8. Furthermore, the sensitivity analysis conducted through weight exchange scenarios underscores the influence of varying criterion weights on the ranking outcomes. It highlights the need for careful consideration of weights and their potential impact on the prioritization process, further enhancing the robustness and credibility of the results. Overall, the proposed methodology demonstrates its utility in prioritizing ASD patients based on medical and sociodemographic criteria, ensuring that individuals receive appropriate care and support. It addresses trade-offs, conflicts, and important issues within the criteria, ultimately contributing to more effective decision-making in autism spectrum disorder. The application of this methodology has the potential to improve the quality of life for ASD patients and their families, making it a valuable tool for healthcare professionals and researchers in this field. For future work, prioritizing patients based on autism gene contributions could significantly enhance the field, especially by comparing the criteria used (medical and sociodemographic) and different gene types in prioritization. This approach may yield new conclusions and implications. Leveraging sophisticated parametric models holds promise for further enhancing decision-making solutions in triage processes. These models can analyze complex data patterns to predict outcomes, providing insights to optimize resource allocation and prioritize system issues in real-time.