1 Introduction

Indeed, the fast development of population and industrialization, both of which are caused by an increase in product consumption, places a significant emphasis on the need for effective waste management (Narayanswamy et al., 2022; Torkayesh et al., 2022). The gathering, handling, transportation, and waste disposal are the four principal components of refuse management. Appropriate waste management is essential for the preservation of public health as well as aesthetic and environmental quality. However, as a result of a rise in the total quantity of garbage caused by factors such as population expansion and urbanization, the old ways of collecting waste have become both inefficient and expensive. To collect rubbish under the conventional method of waste management, collection vehicles and their operators always take the same path from one location to another (Delgado et al., 2020). Therefore, while trash trucks drive to containers that are only half full to collect waste without checking the amount of garbage already present in the containers, containers that are completely full may wait for the next collection time. This circumstance results in wasted time in the system, an increase in the amount of fuel used and excessive use of the available resources. Traditional methods of garbage collection have a number of drawbacks, including the fact that they are unable to detect fires or detect movement inside the containers. In addition, the exhausts of collection trucks are contributing to an ever-increasing amount of air pollution. This pollution occurs due to the liberation of hurtful gases as well as greenhouse gases (Awan et al., 2021).

Thence, the implementation of technological innovations and advancements has been made for making the existing system enhanced and to avoid the shortcomings that were discussed earlier. These inventions and advancements were applied in order to accumulate waste on a more consistent basis and to decrease the effect that waste has on the environment and the air. Because of this, intelligent waste management has emerged as a prominent topic around the globe in an effort to improve the operational efficiency of businesses in response to advances in technology (Fadlil et al., 2022). A variety of approaches to trash management has also been suggested (Fan et al., 2023). To accomplish sustainable development objectives, viable and intelligent waste management schemes that enable policy-suitable processing technologies are essential. Optimum waste and resource rehabilitation strategies also contribute to the achievement of these goals. This system's goal is to deliver the most possible benefit to society while simultaneously reducing the amount of unprocessed material, lowering energy consumption, and minimizing the amount of harm done to the environment (Luo et al., 2022).

With the introduction of recent improvements in smart gadgets, the concept of linking commonplace things over current networks has become very desirable. The Internet of Things (IoT) is a network of web-connected objects that can sense the surrounding environment in order to collect and share data. As a consequence of the growth of traditional networks that connect billions of linked entities, practically anything may now connect and interact in a more intelligent manner than previously (Silva et al., 2018). IoT has been boosted by technological advances in machine-to-machine (M2M) communication, wireless sensor networks (WSN) and ubiquitous computing (UC) (Ali et al., 2020). In addition, connected devices exchange their data and access the allowed data of other devices to facilitate circumstantial decision-making. Because of these advancements, several smart city and smart factory ideas have emerged as new business sectors and prospects. In the last several periods, the continuing growth of smart cities was the primary issue due to rapid global urbanization. Information and communication technology (ICT) has improved the cities’ efficiency in several ways. However, adding merely ICT does not adequately represent the notion of a smart city. In general, a smart city is an urban environment that employs ICT with other associated technologies to boost the efficacy performance of routine municipal procedures and the level of service offered to urban people (Baldo et al., 2021). IoT connects multiple smart city operations/areas into holistic entities, as presented in Fig. 1.

Fig. 1
figure 1

Concept of IoT-enabled smart city (Bellini et al., 2022)

Full size image

The intelligent management of waste is one of the essential concerns in the formation of modern and sustainable cities. The number of people living on our planet is expected to attain nine billion by the year 2050 (Agamuthu & Masaru, 2014). In addition to that, the growing degree of development will guide a significant demand being placed on the existing infrastructures and practices of towns all over the world. Because of this, the researchers decided to look into the most effective procedures for refuse administration. In order to implement the required steps according to the rules, a successful waste handling system needs a range of waste management methods, some of which may have competing goals or unanticipated outcomes. Given the potentially life-changing repercussions, selecting a sustainable intelligent waste management technology may be a difficult undertaking that requires taking into consideration a number of various criteria that are at odds with one another. Because investments in technology will be used for a significant amount of time in the future, it is essential to take into consideration the importance of the assessment factors for such funds. The intention of this research paper is to pick a refuse administration technology that is both sustainable and smart based on the technology available today taking into consideration ICTs and IoT throughout the nation with the goal of creating better and more sustainable communities. Waste management in Egypt has become a progressively important national issue due to the nation's growing urbanization and industrialization alongside its population. Egypt is confronted with several concerns in the field of refuse administration, including those connected to the rubbish collection, transportation, and processing.

In this research, IoT-based intelligent waste management technologies for one of Egypt's cities will be assessed. The issue was approached as a multifaceted issue due to the fact that for sustainable waste management, the chosen IoT-based intelligent waste management technologies need to be economically feasible, environmentally friendly, socially passable to the general audience and compatible with contemporary city design. The assessment of the intelligent refuse management technologies based on IoT needs to be done with multi-criteria decision-making (MCDM) methods, and it needs to include mutually qualitative and quantitative facets. This is necessary with a view to treating the problems that are related to the situation.

1.1 Motivation for emerging the hybrid T2NN-ITARA-MARCOS methodology

In the context of actual life events, human perspectives tend to be marked by fuzziness, imprecision, and ambiguity. Linguistic expressions are one way for experts to convey their sentiments about, or desire for, a certain choice based on certain characteristics. In order to account for the imprecision and uncertainty inherent in the judgment of the experts, the neutrosophic set is used. This involves the transformation of semantic terms into neutrosophic numbers, which may then be subjected to further manipulation. Smarandache (1998) presented the theory of neutrosophic as a generalization of the intuitionistic fuzzy set (IFS) and fuzzy set (FS). It was represented by a triplet form (T, I, F). Where T denotes membership value, I denotes indeterminacy value, and F denotes non-membership value. Also, the values of T, I, and F are limited to the range [0, 1]. In this regard, type-2 neutrosophic numbers (T2NNs) were developed by Abdel-Basset et al., (2019a, 2019b) to more accurately represent information and ambiguity and reduce information loss. T2NN is presented in the form \(\left\langle \left({T}_{T}, {T}_{I}, {T}_{F}\right), \left({I}_{T}, {I}_{I}, {I}_{F}\right), \left({F}_{T}, {F}_{I}, {F}_{F}\right)\right \rangle\), that is, each part is divided into sub-parts. Accordingly, T2NN is an effective way for decreasing ambiguity in experts' decision-making predilections.

Also, the fact that the overall result of any MCDM approach, in general, relies heavily on the weights that are assigned to the assessment criteria is one of the things that has served as a driving force behind this research. The assignment of criteria weights, which might be derived by objective, subjective, or combinative approaches, is perhaps the most important input in any MCDM method. Methods that are objective place more of a focus on the actual performance of the various options depending on the criteria for assessment. In this regard, Hatefi (2019) provided an overview of the Indifference Threshold-based Attribute Ratio Analysis (ITARA) approach that showed its significant advantages in comparison with many other criterion weighting methodologies. It does this by calculating the relevance of semi-thematic quantitative indicators straight from a primary evaluation matrix. This technique's calculating procedure is straightforward and based on sound reasoning. In a novel and effective way, the ITARA approach makes use of the indifference threshold notion. Because it is likewise predicated on the idea of dispersion logic, this approach has the propensity to place a larger emphasis on the criteria that are characterized by a greater degree of data dispersion. Hence, the ITARA technique has been developed in the T2NN environment to treat imperfect and conflicting information to find out the weights of the evaluation criteria for ranking intelligent waste management technologies based on IoT.

Again, choosing between several options involves the use of approaches that are resilient, efficient, and robust. Stević et al. (2020) developed the Measurement of alternatives and ranking according to COmpromise solution (MARCOS) approach based on the reference point sorting and ratio methodologies. Hence, the MARCOS method was boosted in the T2NN environment to deal with treat imperfect and conflicting information to rank the intelligent waste management technologies based on IoT.

To sum up, to date, to the best of the researchers' knowledge, there has been no hybrid approach combining ITARA and MARCOS decision-making methods under the T2NN environment to evaluate and rank intelligent technologies based on IoT for waste management. Accordingly, this methodology was presented to deal with the decision-making issue and to hold this significant investigation gap.

1.2 Contributions of the study

Based on the above discussion, the main objective of this paper is to offer a decision support tool based on T2NN and ITARA-MARCOS methods to evaluate and rank intelligent waste management technologies based on IoT. The following list presents the contributions that the paper makes:

  • This research introduces a comprehensive decision-making methodology for the assessment of intelligent waste management technologies based on the IoT proposed. To meet sustainable development awareness, the approach includes a collection of sustainability criteria.

  • The evaluation criteria system for evaluating and ranking intelligent waste management technologies based on IoT was determined by referring to relevant literature and relevant institutional reports.

  • The computations for assigning weights to the criteria are carried out with the use of a neutrosophic set, which provides a larger semantic scale of the judgments made by experts and accurately portrays the decision-making process in unpredictably complex settings.

  • Applicability of the suggested methodology is evaluated using the waste management-based IoT evaluation problem for the Administrative capital, Egypt.

  • Validation of the suggested methodology is carried out by doing sensitivity studies and making comparisons with previously developed approaches.

  • The study is directed toward providing a suggestion for the government and practitioners for evaluating intelligent waste management technologies based on IoT.

1.3 Organization of the paper

The remaining sections of this study are prepared as follows: Sect. 2 offers an investigation of the most recent associated studies. Section 3 introduces preliminaries of the T2NN and discusses the suggested T2NN-ITARA-MARCOS methodology. Section 4 gives a brief description of various intelligent waste management technologies based on IoT and the selection criteria. Section 5 discusses the application of the suggested methodology and validates the findings with current methodologies and sensitivity analysis. Section 6 draws concluding remarks of the research. Finally, additional computations can be found in the appendix.

2 Literature review

In this section, an overall literature review is conducted. Literature are examined in three parts. The first part presents studies related to evaluating waste management methods using MCDM methodologies. The second part provides some papers related to decision-making issues in different domains using T2NNs. In the third part, some literature related to the ITARA and MARCOS method was reviewed.

2.1 Literature that applied MCDM and IoT techniques for assessing waste management

Evaluation and selection of the correct methods of waste management is essential with regard to financing investment and preserving the environment (Budijati et al., 2022). For this reason, there is a lot of literature that attempts to provide many solutions to deal with the waste problem. This literature has valuable contributions in identifying appropriate technologies. In addition, there is some literature that deals with the problem of selecting modern technologies, including ICT, IoT, and others, in waste management. Some of this literature is summarized as follows. Delgado et al. (2020) recommended a paper that proposes a model for planning biowaste administration methods. The authors utilized four indicators, including environmental, social, technical, and economic indicators, in their assessment. Seker (2022) developed a paper that evaluates intelligent waste management technologies based on IoT in Istanbul using interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). Sharma et al. (2020) presented a structural approach of the IoT to overcome obstacles in the waste management technologies of smart cities. Their approach incorporates the Total Interpretative Structural Modeling (TISM) technique, Decision Making Trial and Evaluation Laboratory (DEMATEL) technique and the Fuzzy Matriced'Impacts Croisés Multiplication Appliquéan Classement (MICMAC) model. Pamučar et al. (2021) presented a paper for assessing and choosing an infectious waste management facility. Their approach integrates two MCMD methods the Multi-Attributive Border Approximation Area Comparison (MABAC) and the Best–Worst Method (BWM) by using D numbers for handling fuzzy semantic information. Torkayesh et al., (2021a, 2021b) presented a research for selecting the appropriate waste disposal technology take into consideration any uncertainty using MCDM methods. Zewdie and Yeshanew (2023) performed a paper for investigating appropriate waste disposal location in Dejen town, Ethiopia by employing the geographic information system (GIS) and the analytical hierarch process (AHP) method.

2.2 Literature that applied T2NN environment

Undoubtedly, the neutrosophic set applies good tools to deal with the problem of indeterminacy and uncertainty. In this regard, the T2NN can more accurately and distinctly deal with complex uncertainties, address them and provide a more logical result. Hence, T2NN has become a preferred tool by scholars and researchers in the recent period (Abdel-Basset et al., 2019a, 2019b). Also, it has been employed to various decision-making issues in real-life domains. Simic et al. (2022a, 2022b) introduced a hybrid approach that combines the CRiteria Importance Through Intercriteria Correlation (CRITIC) method and the Multi-Attributive Border Approximation area Comparison (MABAC) method for rating the public transportation pricing methods. They performed their study under a neutrosophic environment using T2NNs. Görçün et al. (2023) presented research for extending the version of the Weighted Aggregated Sum Product ASsessment (WASPAS) technique under T2NNs based on the Bonferroni function (WASPAS’B) for selecting the suitable Ro-Ro vessel that has been used in the second-hand vessel market. Cali et al. (2022) suggested a paper for assessing and rating a number of current use cases of an energy blockchain method. Their approach suggested T2NN-based Evaluation based on Distance from Average Solution (EDAS). Hashemkhani Zolfani et al. (2022) developed a study for extending the version of the Gray Relation Analysis (GRA) method under type-2 neutrosophic fuzzy sets (T2NFN) for determining a suitable container vessel form for building a healthier container shipping architecture.

2.3 Studies about the ITARA and MARCOS method

There are various MCDM techniques that have been employed to deal with several real-world decision-making issues (Abdel-Monem et al., 2023). The ITARA technique and the MARCOS technique are one of these methods. The authors present some of the literature through which these methods were applied as follows. Lo et al. (2021) presented a forward-looking framework for determining high-disaster methods in goods and systems. Their framework uses MCDM methods as the primary approach to problem solving. Their framework consists of two MCDM methods, namely the developed ITARA and the modified technique for order preference by similarity to an ideal solution (TOPSIS). The ITARA method has been applied for generating more trusted weights for risk indicators. Whereas the TOPSIS method is employed for ranking the risk levels of the failure modes. During the COVID-19 epoch, Simic et al. (2022a, 2022b) demonstrated a research for locating the facility for dangerous healthcare waste. Their framework uses MCDM methods as the primary approach to problem solving. Their framework is based on two methods of decision-making in solving the problem, namely MARCOS and ITARA under the Fermatean fuzzy environment. Accordingly, this method has been applied for identifying the semi-objective significance of the main indicators. Torkayesh et al. (2021a, 2021b) conducted a study for selecting the landfill site for the health care waste system. They used a MCDM and GIS approach to solve the selection problem. Their approach is based on two methods of decision-making in solving the problem, namely BWM and MARCOS under gray interval set. Thus, they used the MARCOS method to rank the selected alternatives. Ali (2022) proposed a paper for exploring a new q-rung orthopair fuzzy score function and enhanced MARCOS technique. His approach applied the extended MARCOS for ranking the alternatives of solid waste management.

Eventually, the above-mentioned methods were not a hybrid approach between ITARA and MARCOS methods to solve the problem of selecting intelligent technology for waste management based on IoT. In addition, all the methods that solved the problem were performed in environments such as the q-rung fuzzy, fuzzy environment, intuitionistic fuzzy environment, and others. Thus, to the best of the researchers' knowledge, the current study is the premier in using a hybrid methodology composed of ITARA and MARCOS techniques under the environment of T2NNs for evaluating intelligent waste management technologies based on IoT.

3 Research methodology

This section contains the central axis of the study, which is the methodology presented. First, some basic concepts and definitions are introduced. Then, a detailed explanation of the hybrid methodology presented by T2NN-ITARA-MARCOS for the assessment and selection of the most proper technology for intelligent waste management is provided. Also, a flowchart of the suggested hybrid methodology is included to show the steps of the proposed methodology clearly.

3.1 Preliminaries

Definition 1

(Mohamed Abdel-Basset et al., 2019b) Suppose Y as the finite universe of discourse and \(D\left[0, 1\right],\) as the set of all triangular neutrosophic sets on \(D\left[0, 1\right]\). A type-2 neutrosophic number set (T2NNS) characterized by \(\widetilde{L}\) can be well-defined in Y as an object having the form:

$$\tilde{L} = \left\{ {\left\langle {y, \tilde{T}_{{\tilde{L}}} \left( y \right), \tilde{I}_{{\tilde{L}}} \left( y \right),\tilde{F}_{{\tilde{L}}} \left( y \right)| y \in Y} \right\rangle } \right\}$$
(1)

where \({\widetilde{T}}_{\widetilde{L}}\left(y\right) :Y \to D\left[0, 1\right], {\widetilde{I}}_{\widetilde{L}}\left(y\right) :Y \to D\left[0, 1\right], {\widetilde{F}}_{\widetilde{L}}\left(y\right) :Y \to D\left[0, 1\right]\). The T2NNS \({\widetilde{T}}_{\widetilde{L}}\left(y\right)\) = \(\left({T}_{{T}_{\widetilde{L}}}\left(y\right), {T}_{{I}_{\widetilde{L}}}\left(y\right), {T}_{{F}_{\widetilde{L}}}(y)\right)\), \({\widetilde{I}}_{\widetilde{L}}\left(y\right)\) =\(\left({I}_{{T}_{\widetilde{L}}}\left(y\right), {I}_{{I}_{\widetilde{L}}}\left(y\right), {I}_{{F}_{\widetilde{L}}}(y)\right)\), \({\widetilde{F}}_{\widetilde{L}}\left(y\right)\) = \(\left({F}_{{T}_{\widetilde{L}}}\left(y\right), {F}_{{I}_{\widetilde{L}}}\left(y\right), {F}_{{F}_{\widetilde{L}}}(y)\right)\), denote the truth, indeterminacy, and falsity memberships of \(y\) in\(\widetilde{L}\), respectively. These memberships are subject to certain conditions, which are satisfied by the following parameters:

$$0\le {{\widetilde{T}}_{\widetilde{L}}\left(y\right)}^{3}+ {{\widetilde{I}}_{\widetilde{L}}\left(y\right)}^{3}+{{\widetilde{F}}_{\widetilde{L}}\left(y\right)}^{3}\le 3, \forall y \in Y$$
(2)

For ease of simplicity,

\(\widetilde{L}=\left\langle \left({T}_{{T}_{\widetilde{L}}}\left(y\right), {T}_{{I}_{\widetilde{L}}}\left(y\right), {T}_{{F}_{\widetilde{L}}}(y)\right), \left({I}_{{T}_{\widetilde{L}}}\left(y\right), {I}_{{I}_{\widetilde{L}}}\left(y\right), {I}_{{F}_{\widetilde{L}}}(y)\right) , \left({F}_{{T}_{\widetilde{L}}}\left(y\right), {F}_{{I}_{\widetilde{L}}}\left(y\right), {F}_{{F}_{\widetilde{L}}}(y)\right)\right \rangle\) is determined as the T2NN.

Definition 2

(Mohamed Abdel-Basset et al., 2019b) Suppose.

\(\widetilde{L}=\left\langle \left({T}_{{T}_{\widetilde{L}}}\left(y\right), {T}_{{I}_{\widetilde{L}}}\left(y\right), {T}_{{F}_{\widetilde{L}}}(y)\right), \left({I}_{{T}_{\widetilde{L}}}\left(y\right), {I}_{{I}_{\widetilde{L}}}\left(y\right), {I}_{{F}_{\widetilde{L}}}(y)\right), \left({F}_{{T}_{\widetilde{L}}}\left(y\right), {F}_{{I}_{\widetilde{L}}}\left(y\right), {F}_{{F}_{\widetilde{L}}}(y)\right)\right \rangle\), \({\widetilde{L} }_{1}\)= \(\left\langle \left({T}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right), {T}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right), {T}_{{F}_{{\widetilde{L}}_{1}}}(y)\right), \left({I}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right), {I}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right), {I}_{{F}_{{\widetilde{L}}_{1}}}(y)\right), \left({F}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right), {F}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right), {F}_{{F}_{{\widetilde{L}}_{1}}}(y)\right)\right \rangle\) and \({\widetilde{L} }_{2}\) = \(\left\langle \left({T}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right), {T}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right), {T}_{{F}_{{\widetilde{L}}_{2}}}(y)\right), \left({I}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right), {I}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right), {I}_{{F}_{{\widetilde{L}}_{2}}}(y)\right), \left({F}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right), {F}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right), {F}_{{F}_{{\widetilde{L}}_{2}}}(y)\right)\right \rangle\) be three T2NNs and \(\lambda >0\). Their processes are determined as follows:

a. Addition “\(\oplus\)”

$$\tilde{L} _{1} \oplus \tilde{L} _{2} = \left\langle \begin{gathered} \left( {\begin{array}{*{20}c} {T_{{T_{{\tilde{L}_{1} }} }} \left( y \right) + T_{{T_{{\tilde{L}_{2} }} }} \left( y \right) - T_{{T_{{\tilde{L}_{1} }} }} \left( y \right) \times T_{{T_{{\tilde{L}_{2} }} }} \left( y \right), T_{{I_{{\tilde{L}_{1} }} }} \left( y \right) + T_{{I_{{\tilde{L}_{2} }} }} \left( y \right) - T_{{I_{{\tilde{L}_{1} }} }} \left( y \right) \times T_{{I_{{\tilde{L}_{2} }} }} \left( y \right), } \\ {T_{{F_{{\tilde{L}_{1} }} }} \left( y \right) + T_{{F_{{\tilde{L}_{2} }} }} \left( y \right) - T_{{F_{{\tilde{L}_{1} }} }} \left( y \right) \times T_{{F_{{\tilde{L}_{2} }} }} \left( y \right)} \\ \end{array} } \right), \hfill \\ \left( {I_{{T_{{\tilde{L}_{1} }} }} \left( y \right) \times I_{{T_{{\tilde{L}_{2} }} }} \left( x \right), I_{{I_{{\tilde{L}_{1} }} }} \left( y \right) \times I_{{I_{{\tilde{L}_{2} }} }} \left( y \right), I_{{F_{{\tilde{L}_{1} }} }} \left( y \right) \times I_{{F_{{\tilde{L}_{2} }} }} \left( y \right)} \right), \hfill \\ \left( {F_{{T_{{\tilde{L}_{1} }} }} \left( y \right) \times F_{{T_{{\tilde{L}_{2} }} }} \left( y \right), F_{{I_{{\tilde{L}_{1} }} }} \left( y \right) \times F_{{I_{{\tilde{L}_{2} }} }} \left( y \right), F_{{F_{{\tilde{L}_{1} }} }} \left( y \right) \times F_{{F_{{\tilde{L}_{2} }} }} \left( y \right)} \right) \hfill \\ \end{gathered} \right\rangle$$
(3)

b. Multiplication “\(\otimes\)”

\({\widetilde{L}}_{1} \otimes\) \({\widetilde{L}}_{2}\) =

$$\left \langle \begin{array}{c}\left({T}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right)\times {T}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right),{ T}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right)\times {T}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right), {T}_{{F}_{{\widetilde{L}}_{1}}}\left(y\right)\times {T}_{{F}_{{\widetilde{L}}_{2}}}\left(y\right)\right), \\ \left(\begin{array}{c}{I}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right)+{I}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right)- {I}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right)\times {I}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right), {I}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right)+{I}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right)- {I}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right)\times {I}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right), \\ {I}_{{F}_{{\widetilde{L}}_{1}}}\left(y\right)+{I}_{{F}_{{\widetilde{L}}_{2}}}\left(y\right)- {I}_{{F}_{{\widetilde{L}}_{1}}}\left(y\right)\times {I}_{{F}_{{\widetilde{L}}_{2}}}\left(y\right)\end{array}\right),\\ \left(\begin{array}{c}{F}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right)+{F}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right)-{F}_{{T}_{{\widetilde{L}}_{1}}}\left(y\right)\times {F}_{{T}_{{\widetilde{L}}_{2}}}\left(y\right), {F}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right)+ {F}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right)-{F}_{{I}_{{\widetilde{L}}_{1}}}\left(y\right)\times {F}_{{I}_{{\widetilde{L}}_{2}}}\left(y\right), \\ {F}_{{F}_{{\widetilde{L}}_{1}}}\left(y\right)+{F}_{{F}_{{\widetilde{L}}_{2}}}\left(y\right)-{F}_{{F}_{{\widetilde{L}}_{1}}}\left(y\right)\times {F}_{{F}_{{\widetilde{L}}_{2}}}\left(y\right)\end{array}\right)\end{array} \right \rangle$$
(4)

c. Scalar Multiplication

$$\lambda \widetilde{L}=\left\langle \begin{array}{c}\left({1-(1-{T}_{{T}_{\widetilde{L}}}\left(y\right))}^{\lambda }, {1-(1-{ T}_{{I}_{\widetilde{L}}}\left(y\right))}^{\lambda }, {1-(1-{T}_{{F}_{\widetilde{L}}}\left(y\right))}^{\lambda }\right), \\ \left({\left({I}_{{T}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda },{\left({I}_{{I}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda },{\left({I}_{{F}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }\right), \\ \left({\left({F}_{{T}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda },{\left({F}_{{I}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda },{\left({F}_{{F}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }\right)\end{array} \right \rangle$$
(5)

d. Power

$${\widetilde{L}}^{\lambda }= \left \langle \begin{array}{c}\left({\left({T}_{{T}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda },{\left({T}_{{I}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda },{\left({T}_{{F}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }\right), \\ \left({1-\left(1-{I}_{{T}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }, {1-\left(1-{I}_{{I}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }, {1-\left(1-{I}_{{F}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }\right),\\ \left({1-\left(1-{F}_{{T}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }, {1-\left(1-{F}_{{I}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }, {1-\left(1-{F}_{{F}_{\widetilde{L}}}\left(y\right)\right)}^{\lambda }\right)\end{array} \right \rangle$$
(6)

Definition 3

(Mohamed Abdel-Basset et al., 2019b) Let \(\widetilde{L}\) = \(\left\langle \left({T}_{{T}_{\widetilde{L}}}\left(x\right), {T}_{{I}_{\widetilde{L}}}\left(x\right), {T}_{{F}_{\widetilde{L}}}(x)\right), \left({I}_{{T}_{\widetilde{L}}}\left(x\right), {I}_{{I}_{\widetilde{L}}}\left(x\right), {I}_{{F}_{\widetilde{L}}}(x)\right), \left({F}_{{T}_{\widetilde{L}}}\left(x\right), {F}_{{I}_{\widetilde{L}}}\left(x\right), {F}_{{F}_{\widetilde{L}}}(x)\right)\right \rangle\) be a T2NN. Equation (7) is used to compute the score function of the T2NN \(\widetilde{L}\).

$$S\left(\widetilde{L}\right)=\frac{1}{12} \left\langle 8+\left({T}_{{T}_{\widetilde{L}}}\left(y\right)+2\left({T}_{{I}_{\widetilde{L}}}\left(y\right)\right)+ {T}_{{F}_{\widetilde{L}}}(y)\right)- \left({I}_{{T}_{\widetilde{L}}}\left(y\right)+2\left({I}_{{I}_{\widetilde{L}}}\left(y\right)\right)+ {I}_{{F}_{\widetilde{L}}}(y)\right)- \left({F}_{{T}_{\widetilde{L}}}\left(y\right)+2\left({F}_{{I}_{\widetilde{L}}}\left(y\right)\right)+ {F}_{{F}_{\widetilde{L}}}(y)\right)\right \rangle$$
(7)

Definition 4

(Mohamed Abdel-Basset et al., 2019b) Assume \({\widetilde{L}}_{S}\)=\(\left\langle \left({T}_{{T}_{{\widetilde{L} }_{S}}}\left(y\right), {T}_{{I}_{{\widetilde{L} }_{S}}}\left(y\right), {T}_{{F}_{{\widetilde{L} }_{S}}}\left(y\right)\right), \left({I}_{{T}_{{\widetilde{L} }_{S}}}\left(y\right), {I}_{{I}_{{\widetilde{L} }_{S}}}\left(y\right), {I}_{{F}_{{\widetilde{L} }_{S}}}\left(y\right)\right), \left({F}_{{T}_{{\widetilde{L} }_{S}}}\left(y\right), {F}_{{I}_{{\widetilde{L} }_{S}}}\left(y\right), {F}_{{F}_{{\widetilde{L} }_{S}}}\left(y\right)\right)\right \rangle\)

\(\left( {S = 1, 2, \ldots , q} \right)\) is a group of T2NNs, and ϣ = \(\left( {w_{1} , \ldots ,w_{S} , \ldots ,w_{q} } \right)^{T}\) denotes the weight vector of them with \(w_{j} { } \in \left[ {0, 1} \right]\) and \(\mathop \sum \limits_{S = 1}^{q} w_{S} = 1\). The following Eqs. (8 and 9) are used to calculate A T2NNWA operator.

$${\text{T2NNW}}\;A_{w} \left( {\tilde{L}_{1} , \tilde{L}_{S} , \ldots , \tilde{L}_{q} } \right) = w_{1} \tilde{L}_{1} \oplus w_{S} \tilde{L}_{S} \oplus \ldots \oplus w_{q} \tilde{L}_{q} = \begin{array}{*{20}c} q \\ \oplus \\ {S = 1} \\ \end{array} \left( {w_{S} \tilde{L}_{S} } \right)$$
(8)
$$\left\langle \begin{gathered} \left( {1 - \mathop \prod \limits_{S = 1}^{q} \left( {1 - T_{{T_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s } }} ,1 - \mathop \prod \limits_{S = 1}^{q} \left( {1 - T_{{I_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s } }} ,1 - \mathop \prod \limits_{S = 1}^{q} \left( {1 - T_{{F_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s } }} } \right) \hfill \\ \left( {\mathop \prod \limits_{S = 1}^{q} \left( {I_{{T_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s} }} , \mathop \prod \limits_{S = 1}^{q} \left( {I_{{I_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s} }} , \mathop \prod \limits_{S = 1}^{q} \left( {I_{{F_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s} }} } \right) \hfill \\ \left( {\mathop \prod \limits_{S = 1}^{q} \left( {F_{{T_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s} }} , \mathop \prod \limits_{S = 1}^{q} \left( {F_{{I_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s} }} , \mathop \prod \limits_{S = 1}^{q} \left( {F_{{F_{{\tilde{L}{ }_{S} }} }} \left( y \right)} \right)^{{w_{s} }} } \right) \hfill \\ \end{gathered} \right\rangle$$
(9)

3.2 Hybrid T2NN-ITARA-MARCOS methodology for evaluating the intelligent waste management technologies

This section presents the procedures for the suggested hybrid methodology T2NN-ITARA-MARCOS, which is designed for assessing and selecting the most appropriate intelligent waste management technologies. The methodology is split into four phases. In the first phase, the issue is deliberated in detail, experts are identified, and influencing criteria and alternatives are identified. The second phase outlines the steps for evaluating the criteria used by the T2NN-ITARA method. The third phase presents the steps for rating the selected alternatives in the assessment process using the T2NN-MARCOS method. Finally, the fourth phase introduces sensitivity analysis and comparative analysis. Figure 2 illustrates the phases of the suggested hybrid methodology.

  • Phase 1: Study the problem in detail.

Fig. 2
figure 2

Diagram showing the hybrid methodology suggested

Full size image

Step 1.1. Formation of a team of experts to participate in solving the problem and express their opinions on aspects of the problem.

Step 1.2. Determine the questions related to the study, whether to identify the criteria or the selected alternatives.

Step 1.3. Describe the problem in detail and identify the case study to be applied by the proposed hybrid methodology T2NN-ITARA-MARCOS.

Step 1.4. Determine the criteria affecting the solution of the issue and the substitutes.

  • Phase 2: Determining the criteria weights (T2NN-ITARA technique).

Suppose an array of m substitutes is denoted by A =\(\left\{ {A_{1} , \ldots , A_{i} , \ldots A_{m} } \right\}\), and an array of n criteria is symbolized by C = \(\left\{ {C_{1} , \ldots , C_{n} , \ldots , C_{n} } \right\}\). Let "experts" be a set of k experts symbolized by \(E = \left\{ {E_{1} ,{ } \ldots ,{ }E_{e} ,{ } \ldots ,E_{k} } \right\}\), who have provided their valuation reports for each alternative \(A_{i}\)(i = 1, 2… m) against each criterion \(C_{j}\)(j = 1, 2… n). Let \(w\) = \(\left( {w_{1} ,w_{2} ,{ } \ldots ,{\text{ w}}_{{\text{e}}} } \right)^{T}\) be the weight vector for the experts in \(E_{e}\)(e = 1, 2… k) such that \(\mathop \sum \limits_{j = 1}^{n} w_{l}\)=1.

Step 2.1. To show the experts preferences for the criteria, we must generate a pairwise comparison matrices \({\widetilde{V}}^{e}\), where \({\widetilde{V}}^{e}\) = \({\left[{{\widetilde{V}}_{ij}}^{e}\right]}_{m\times n}\). The comparison decision matrix is constructed via the linguistic variables constructed according to Eq. (10).

$$\begin{gathered} \begin{array}{*{20}l} {\quad \quad \quad \quad \quad \quad \quad \quad c_{1} } \hfill & {\quad \quad \quad \quad \quad \quad \quad \cdots } \hfill & {\quad \quad \quad \quad c_{n} } \hfill \\ \end{array} \hfill \\ \tilde{V}^{e} = \begin{array}{*{20}l} {A_{1} } \hfill \\ \vdots \hfill \\ {A_{m} } \hfill \\ \end{array} \left[ {\begin{array}{*{20}l} {\left\langle {\begin{array}{*{20}c} {\left( {T_{{T_{{\tilde{V}_{11}^{e} }} }} \left( y \right), T_{{I_{{\tilde{V}_{11}^{e} }} }} \left( y \right), T_{{F_{{\tilde{V}_{11}^{e} }} }} \left( y \right)} \right),} \\ {\begin{array}{*{20}c} {\left( {I_{{T_{{\tilde{V}_{11}^{e} }} }} \left( y \right), I_{{I_{{\tilde{V}_{11}^{e} }} }} \left( y \right), I_{{F_{{\tilde{V}_{11}^{e} }} }} \left( y \right)} \right), } \\ {\left( {F_{{T_{{\tilde{V}_{11}^{e} }} }} \left( y \right), F_{{I_{{\tilde{V}_{11}^{e} }} }} \left( y \right), F_{{F_{{\tilde{V}_{11}^{e} }} }} \left( y \right)} \right)} \\ \end{array} } \\ \end{array} } \right\rangle } \hfill & \cdots \hfill & {\left\langle {\begin{array}{*{20}c} {\left( {T_{{T_{{\tilde{V}_{1n}^{e} }} }} \left( y \right), T_{{I_{{\tilde{V}_{1n}^{e} }} }} \left( y \right), T_{{F_{{\tilde{V}_{1n}^{e} }} }} \left( y \right)} \right),} \\ {\begin{array}{*{20}c} {\left( {I_{{T_{{\tilde{V}_{1n}^{e} }} }} \left( y \right), I_{{I_{{\tilde{V}_{1n}^{e} }} }} \left( y \right), I_{{F_{{\tilde{V}_{1n}^{e} }} }} \left( y \right)} \right), } \\ {\left( {F_{{T_{{\tilde{V}_{1n}^{e} }} }} \left( y \right), F_{{I_{{\tilde{V}_{1n}^{e} }} }} \left( y \right), F_{{F_{{\tilde{V}_{1n}^{e} }} }} \left( y \right)} \right)} \\ \end{array} } \\ \end{array} } \right\rangle } \hfill \\ \vdots \hfill & \cdots \hfill & \vdots \hfill \\ {\left\langle {\begin{array}{*{20}c} {\left( {T_{{T_{{\tilde{V}_{m1}^{e} }} }} \left( y \right), T_{{I_{{\tilde{V}_{m1}^{e} }} }} \left( y \right), T_{{F_{{\tilde{V}_{m1}^{e} }} }} \left( y \right)} \right),} \\ {\begin{array}{*{20}c} {\left( {I_{{T_{{\tilde{V}_{m1}^{e} }} }} \left( y \right), I_{{I_{{\tilde{V}_{m1}^{e} }} }} \left( y \right), I_{{F_{{\tilde{V}_{m1}^{e} }} }} \left( y \right)} \right), } \\ {\left( {F_{{T_{{\tilde{V}_{m1}^{e} }} }} \left( y \right), F_{{I_{{\tilde{V}_{m1}^{e} }} }} \left( y \right), F_{{F_{{\tilde{V}_{m1}^{e} }} }} \left( y \right)} \right)} \\ \end{array} } \\ \end{array} } \right\rangle } \hfill & \cdots \hfill & {\left\langle {\begin{array}{*{20}c} {\left( {T_{{T_{{\tilde{V}_{mn}^{e} }} }} \left( y \right), T_{{I_{{\tilde{V}_{mn}^{e} }} }} \left( y \right), T_{{F_{{\tilde{V}_{mn}^{e} }} }} \left( y \right)} \right),} \\ {\begin{array}{*{20}c} {\left( {I_{{T_{{\tilde{V}_{mn}^{e} }} }} \left( y \right), I_{{I_{{\tilde{V}_{mn}^{e} }} }} \left( y \right), I_{{F_{{\tilde{V}_{mn}^{e} }} }} \left( y \right)} \right), } \\ {\left( {F_{{T_{{\tilde{V}_{mn}^{e} }} }} \left( y \right), F_{{I_{{\tilde{V}_{mn}^{e} }} }} \left( y \right), F_{{F_{{\tilde{V}_{mn}^{e} }} }} \left( y \right)} \right)} \\ \end{array} } \\ \end{array} } \right\rangle } \hfill \\ \end{array} } \right] \hfill \\ \end{gathered}$$
(10)

where \({{\widetilde{V}}_{ij}}^{e}\) =

$$\left\langle \left({T}_{{T}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right), {T}_{{I}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right), {T}_{{F}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right)\right), \left({I}_{{T}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right), {I}_{{I}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right), {I}_{{F}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right)\right), \left({F}_{{T}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right), {F}_{{I}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right), {F}_{{F}_{{{\widetilde{V}}_{11}}^{e}}}\left(y\right)\right)\right \rangle$$

(i = 1, 2… m; j = 1, 2 …n; e = 1, 2 …k) is the T2NN that signifies the semantic evaluation of the substitute \({A}_{i}\) under the criterion \({C}_{j}\) assumed by \({E}_{e}\) expert.

Step 2.2. Aggregate the T2NN assessment matrices by all experts \(\widetilde{G}\) = \({\left[{\widetilde{G}}_{ij}\right]}_{m\times n}\) by employing the T2NNWA operator (Definition 4) as in Eq. (11).

$$\tilde{G}_{ij} = {\text{T}}2{\text{NNW}}A_{w} \left( {\tilde{V}_{ij}^{1} , \ldots , \tilde{V}_{ij}^{2} , \ldots , \tilde{V}_{ij}^{j} } \right) = \begin{array}{*{20}c} k \\ \oplus \\ {e = 1} \\ \end{array} \left( {w_{e} \tilde{V}_{ij}^{e} } \right)$$
(11)
$$\left\langle \begin{gathered} \left( {1 - \mathop \prod \limits_{e = 1}^{k} \left( {1 - T_{{T_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e } }} ,1 - \mathop \prod \limits_{e = 1}^{k} \left( {1 - T_{{I_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e } }} ,1 - \mathop \prod \limits_{e = 1}^{k} \left( {1 - T_{{F_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e } }} } \right) \hfill \\ \left( {\mathop \prod \limits_{e = 1}^{k} \left( {I_{{T_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e} }} , \mathop \prod \limits_{e = 1}^{k} \left( {I_{{I_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e} }} ,\mathop \prod \limits_{e = 1}^{k} \left( {I_{{F_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e} }} } \right) \hfill \\ \left( {\mathop \prod \limits_{e = 1}^{k} \left( {F_{{T_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e} }} , \mathop \prod \limits_{e = 1}^{k} \left( {F_{{I_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e} }} , \mathop \prod \limits_{e = 1}^{k} \left( {F_{{F_{{\tilde{V}_{ij}^{e} }} }} \left( y \right)} \right)^{{w_{e} }} } \right) \hfill \\ \end{gathered} \right\rangle \quad {\text{i}} = {1},...,{\text{m}};\quad {\text{j}} = {1},...,{\text{n}}$$

Subsequently, the aggregated T2NN evaluations \(\tilde{G}_{ij} = \left\langle {\left( {T_{{T_{{\tilde{G}_{ij} }} }} \left( y \right), T_{{I_{{\tilde{G}_{ij} }} }} \left( y \right), T_{{F_{{\tilde{G}_{ij} }} }} \left( y \right)} \right), \left( {I_{{T_{{\tilde{G}_{ij} }} }} \left( y \right), I_{{I_{{\tilde{G}_{ij} }} }} \left( y \right), I_{{F_{{\tilde{G}_{ij} }} }} \left( y \right)} \right), \left( {F_{{T_{{\tilde{G}_{ij} }} }} \left( y \right), F_{{I_{{\tilde{G}_{ij} }} }} \left( y \right), F_{{F_{{\tilde{G}_{ij} }} }} \left( y \right)} \right)} \right\rangle\).

Step 2.3. Compute the score function for the T2NN combined assessments according to Eq. (12) based on Definition 3. Formerly, compute the normalized decision matrix \(H\) = \({\left[{H}_{ij}\right]}_{m\times n}\) according to Eq. (13).

$$\begin{aligned} S\left( {\tilde{G}_{ij} } \right) & = \frac{1}{12}\left\langle {8 + \left( {T_{{T_{{\tilde{G}_{ij} }} }} \left( y \right) + 2\left( {T_{{I_{{\tilde{G}_{ij} }} }} \left( y \right)} \right) + T_{{F_{{\tilde{G}_{ij} }} }} \left( y \right)} \right) - \left( {I_{{T_{{\tilde{G}_{ij} }} }} \left( y \right) + 2\left( {I_{{I_{{\tilde{G}_{ij} }} }} \left( y \right)} \right) + I_{{F_{{\tilde{G}_{ij} }} }} \left( y \right)} \right)} \right. \\ \quad \quad \quad \left. { - \left( {F_{{T_{{\tilde{G}_{ij} }} }} \left( y \right) + 2\left( {F_{{I_{{\tilde{G}_{ij} }} }} \left( y \right)} \right) + F_{{F_{{\tilde{G}_{ij} }} }} \left( y \right)} \right)} \right\rangle \quad {\text{i}} = {1},...,{\text{m}};\quad {\text{j}} = {1},...,{\text{n}}. \\ \end{aligned}$$
(12)
$$H_{ij} = \frac{{S\left( {\tilde{G}_{ij} } \right){ }}}{{\mathop \sum \nolimits_{l = 1}^{m} S\left( {\tilde{G}_{lj} } \right){ }}},\quad {\text{i}} = {1},...,{\text{m}};\quad {\text{j}} = {1},...,{\text{n}}.$$
(13)

where \({H}_{ij}\) represents the normalized combined evaluation of the alternative \({A}_{i}\) according to the criteria \({C}_{j}\).

Step 2.4. Sort the normalized combined evaluations in ascending order according to Eq. (14).

$$D_{\left( 1 \right)j} = \mathop {\min }\limits_{1 \le i \le m} {\text{H}}_{{{\text{ij}}}} { } < \ldots < D_{\left( m \right)j} = \mathop {\max }\limits_{1 \le i \le m} {\text{H}}_{{{\text{ij}}}} {,}\quad {\text{j}} = {1},...,{\text{n}}$$
(14)

Step 2.5. Compute the ordered distances by applying the Eq. (15).

$$B_{zj} = D_{{\left( {z + 1} \right)j}} - D_{\left( z \right)j} ,\quad {\text{z}} = {1},...,{\text{m}} - {1};\quad {\text{j}} = {1},...,{\text{n}}.$$
(15)

Step 2.6. Compute the considerable ordered distances by applying the Eq. (16).

$$Q_{zj} = \left\{ {\begin{array}{*{20}l} {B_{zj} - \mu } \hfill & {\left| {B_{z j} } \right\rangle \mu } \hfill \\ 0 \hfill & {\left| {B_{z j} } \right\rangle \mu } \hfill \\ \end{array} } \right.,\quad {\text{z}} = {1},...,{\text{m}} - {1};\quad {\text{j}} = {1},...,{\text{n}};\mu > 0$$
(16)

where \(\mu\) indicates the criteria indifference threshold parameter. If \({B}_{z j}> \mu\), then, the equivalent considerable ordered distances \({Q}_{zj}\) should enhance the significance of the criterion \({C}_{j}\). Else, it is not seen as substantial and must be overlooked via setting the value of \({Q}_{zj}\) to be 0.

Step 2.7. Compute the weights of the criteria according to Eq. (17).

$$w_{j} = \frac{{\left( {\mathop \sum \nolimits_{z = 1}^{m - 1} Q_{z j}^{\beta } { }} \right)^{1/\beta } }}{{\mathop \sum \nolimits_{l = 1}^{m} \left( {\mathop \sum \nolimits_{z = 1}^{m - 1} Q_{z j}^{\beta } { }} \right)^{1/\beta } }},\quad {\text{j}} = {1},...,{\text{ n}};\quad \beta { } \in { }\left\{ {1, \ldots ,\infty } \right\}$$
(17)

where \(\beta\) denotes the favorite metric. For example, when the value of \(\beta\) is set to be equal to 1, 2, …,\(\infty\), the significance of the criterion is determined by the Tchebycheff, Euclidian and Manhattan distances.

  • Phase 3: Rank the alternatives (T2NN-MARCOS technique)

Step 3.1. Determine the best and the worst T2NN group evaluations according to the extended T2NN decision matrix for denoting the ideal (AI) and anti-ideal (AAI) alternatives, respectively, according to Eqs. (18) and (19).

The anti-ideal alternative \({A}_{0}\) = \(\left\{{\mathrm{G}}_{01}, \dots , {\mathrm{G}}_{0\mathrm{j}}, \dots , {\mathrm{G}}_{0\mathrm{n}}\right\}\)

$$A_{0j} = \left\{ {\begin{array}{*{20}c} {\mathop {\max }\limits_{1 \le i \le m} {\text{G}}_{{{\text{ij}}}} { } |C_{j} \in C^{ - } } \\ {\mathop {\max }\limits_{1 \le i \le m} {\text{G}}_{{{\text{ij}}}} { } |C_{j} \in C^{ + } } \\ \end{array} } \right.\quad {\text{j}} = {1},...,{\text{n}}.$$
(18)

where \({A}_{0j}\)(j = 1, …, n) indicates anti-ideal group evaluations under each criterion.

The ideal alternative \({A}_{m+1}\) = \(\left\{{\mathrm{G}}_{\mathrm{m}+1 1}, \dots , {\mathrm{G}}_{\mathrm{m}+1\mathrm{ j}}, \dots , {\mathrm{G}}_{\mathrm{m}+1\mathrm{ n}}\right\}\)

$$A_{m + 1 j} = \left\{ {\begin{array}{*{20}c} {\mathop {\max }\limits_{1 \le i \le m} {\text{G}}_{{{\text{ij}}}} |C_{j} \in C^{ - } } \\ {\mathop {\max }\limits_{1 \le i \le m} {\text{G}}_{{{\text{ij}}}} |C_{j} \in C^{ + } } \\ \end{array} } \right.,\quad {\text{j}} = {1},...,{\text{n}}$$
(19)

where \({A}_{m+1 j}\)(j = 1,…, n) indicates ideal group evaluations for each of the given criteria.

Step 3.2. Compute the extended normalized decision matrix \(R\) = \({\left[{R}_{ij}\right]}_{m\times n}\) according to Eq. (20).

$$R_{ij} = \left\{ {\begin{array}{*{20}c} {\frac{{{\text{G}}_{{{\text{ij}}}} }}{{{\text{G}}_{{{\text{m}} + {\text{ij}}}} }} |C_{j} \in C^{ + } } \\ {\frac{{{\text{G}}_{{{\text{m}} + {\text{ij}}}} }}{{{\text{G}}_{{{\text{ij}}}} }} |C_{j} \in C^{ - } } \\ \end{array} } \right.,\quad {\text{i}} = 0,...,{\text{m}} + {1};\quad {\text{j}} = {1},...,{\text{n}}$$
(20)

Step 3.3. Compute the weighted normalized decision matrix \(S\) = \({\left[{S}_{ij}\right]}_{m\times n}\) according to Eq. (21).

$$S_{ij} = w_{j} { }S_{ij} ,\;{\text{i}} = 0,...,{\text{m}} + {1};\;{\text{j}} = {1},...,{\text{n}}.$$
(21)

Step 3.4. Compute the degree of utility for each anti-ideal alternative according to Eq. (22). Then, compute the utility degree for each ideal alternative according to Eq. (23).

$$U^{ - }_{i} = \frac{{\mathop \sum \nolimits_{j = 1}^{n} S_{ij} { }}}{{\mathop \sum \nolimits_{j = 1}^{n} S_{0j} { }}},\quad {\text{i}} = 0,...,{\text{m}} + {1}$$
(22)
$$U^{ + }_{i} = \frac{{\mathop \sum \nolimits_{j = 1}^{n} S_{ij} { }}}{{\mathop \sum \nolimits_{j = 1}^{n} S_{m + 1 j} { }}},\quad {\text{i}} = 0,...,{\text{m}} + {1}.$$
(23)

Step 3.5. Compute the utility function for each anti-ideal alternative according to Eq. (24). Then, compute the utility function for each ideal substitute according to Eq. (25).

$$f\left({U}^{-}\right)=\frac{{{U}^{+}}_{0}}{{{U}^{-}}_{0}+ {{U}^{+}}_{0}}$$
(24)
$$f\left( {U^{ + } } \right) = \frac{{U^{ - }_{m + 1} }}{{U^{ - }_{m + 1} + U^{ + }_{m + 1} }}$$
(25)

Step 3.6. Compute the utility function of the alternatives and rank them by employing Eq. (26). The best alternative has the greatest utility function.

$$f\left( {U_{i} } \right) = \frac{{\left( {U^{ - }_{i} + U^{ + }_{i} } \right)\left[ {f\left( {U^{ - } } \right){ } \times f\left( {U^{ + } } \right){ }} \right]}}{{f\left( {U^{ - } } \right) + f\left( {U^{ + } } \right) - f\left( {U^{ - } } \right){ } \times f\left( {U^{ + } } \right)}},\quad {\text{i}} = {1},...,{\text{m}}$$
(26)

  • Phase 4: Analyses procedures.

Step 4.1. Performing a comparative analysis with other methodologies to show the strength and durability of the recommended hybrid approach.

Step 4.2. A sensitivity analysis is performed to show the extent of change in the outcomes and the arrangement of alternatives, as well as the reliability of the proposed methodology.

4 Case study

In this part, a general description of the problem under study is given. Also, a brief description of the selected alternatives and definitions of the selected criteria is provided.

4.1 Problem description

Citizen behavior in collecting waste and the state's efforts in recycling achieve the goals of sustainability. The garbage file has become one of the thorny issues that hinder development plans in Egypt and the achievement of sustainability goals. The file has become no less important than the health or education files, despite attempts to end the garbage crises through solutions that seemed typical. However, the crisis still exists without limiting its spread or facing its damages, from which citizens and those affected are crying out. The government is currently working on implementing an integrated system to eliminate the problem of waste, raise the efficiency of recycling plants in the governorates of Egypt, and add new lines and equipment to some factories, according to the latest technology methods used in this area. Also, the government pursues to achieve the maximum possible benefit from recycling on the one hand and to conserve resources, whether energy or water on the other hand, given the dependence of this industry on consuming a lot of those resources.

Consequently, the Egyptian government has pursued applying the latest technologies in the field of garbage collection and waste handling to preserve the environment in the New Administrative Capital. And based on the success of the system, it will be circulated in the rest of the governorates. The government is seeking to apply technological solutions such as ultraviolet sensors, mineral detectors, and others that make waste observing quick and less unrestricted instead of the traditional waste collection methods that cause health problems and significant operating costs. The growth and implementation of intelligent town tools and platforms have resulted in the creation of innovative new garbage collecting methods that can be used everywhere in the globe. The utilization of ICT and the IoT proposes a modern descent of techniques for achieving the universal waste administration system in an effective and efficient manner. The IoT, digitization, and the use of ICT in garbage administration help make garbage administration more dependable, translucent, and functional, as shown in Fig. 3. However, making the incorrect decision on the technology used for waste disposal may have long-term detrimental effects on both the growth of the economy and the environment. Because many technologies for trash collecting systems each have their own set of benefits and drawbacks, the process of selecting the technology that is best suited to a given situation requires that a number of environmental, economic, and social factors be taken into consideration. Accordingly, a brief description of four technologies for intelligent waste management is presented as follows:

Fig. 3
figure 3

IoT in intelligent waste management

Full size image

4.2 Description of alternatives

  • Underground waste collection and storage containers (\({A}_{1}\))

Underground trash containers are installed vertically beneath the earth in small locations to guarantee that all trashes are gathered while minimizing the development of smell, illness, and other undesired outcomes. By implementing this technology in the streets, it is also possible to entirely eradicate visual pollution. The quantity of rubbish is noted from the vehicle or from the center using the sensors that are put in trash vessels, a substantial portion of which is concealed. This allows the routes that the trucks take to be defined.

  • Solar-powered waste compactor technology (\({A}_{2}\))

This technology consists of an intelligent gadget that recites the stuffing plane of a bin in concurrent, which in turn triggers automated compaction of trash, thereby boosting the amplitude of the container by anywhere from five to eight times. It gets its electricity from a solar panel and a battery that is constantly being charged. A solution that is both effective and economical may be found in the aforementioned IoT-based solar waste management technology. In addition, this technology offers monitoring from a distant location in real-time.

  • RFID, and GPRS combination of waste administration technology (\({A}_{3}\))

As a web-established technology for instantaneous garbage observing and administration, radio frequency identification (RFID), global positioning system (GPS), geographic information system (GIS) and general packet radio service (GPRS) technologies are included, as presented in Fig. 4. On-street container occupancy is reported in real-time via sensors mounted on the containers. Based on the amount of trash container filling, a GIS-optimized route is chosen for the garbage pickup vehicle, which minimizes fuel costs. With RFID devices mounted for cars and bins, the garbage truck's whereabouts may be traced in real-time using GPS. Given the exact monitoring of a garbage container's sequent number and position, it is feasible to predict when the bins ought to be gathered based on the tenure rate, how many vehicles must attempt to gather these bins, and furthermost crucially, which daily roads these vehicles must take.

  • Mobile application for waste collection (\({A}_{4}\))

Fig. 4
figure 4

An architecture for RFID-based waste management technology (Vishnu et al., 2022)

Full size image

For the purpose of assisting residents in fully participating in the cycle of trash management, a mobile application is being created. This technology offers an intelligent application, which incorporates intelligent monitoring and effective garbage collection, making it simpler to collect waste from the streets, particularly in small paths where it is challenging to place garbage bins. It is well-matched per the mobile systems used by Android and IOS devices. The garbage trucks that are used for the collection of trash in the streets are equipped with an integrated version of the smart application. When the truck gets closer to the street, inhabitants of the area get an SMS-based message alerting them to the impending danger. As a result, residents discharge their waste in the here and now. The shorter amount of time that garbage is allowed to remain on the ground helps to avoid environmental contamination. Through the smartphone application, citizens now have the ability to monitor the status of trucks online, as presented in Fig. 5.

Fig. 5
figure 5

An architecture for mobile application-based waste management technology

Full size image

4.3 Definitions of criteria

Figure 6 presents the 11 determined criteria that have an immediate influence on the determining of the furthermost applicable technology for intelligent waste management to be applied in the study.

  • Interaction network (\({C}_{1}\))

Fig. 6
figure 6

Final criteria identified

Full size image

It is anticipated that the IoT-established technology would feature proposition chests in which individuals may register their requirements or criticisms, a website for community response, and a gateway for engagement talks among community officials and individual inhabitants (Seker, 2022).

  • Productivity (\({C}_{2}\))

A system that is based on IoT should be able to provide substantial employment output at a small budget while using fewer resources. This should be done with the goal of making better use of available resources and cutting costs wherever possible.

  • Environmental protection (\({\mathrm{C}}_{3}\))

Applications that use artificial intelligence for waste management could make communities healthier, safer, and more able to reuse and recycle their materials.

  • Aesthetics (\({\mathrm{C}}_{4}\))

This criterion is connected to the aesthetic as well as the physical characteristics of the surrounding environment (Delgado et al., 2020). Such capabilities are provided by a technological system for trash management that is based on the IoT.

  • Quantity of wastes gathered (\({\mathrm{C}}_{5}\))

The maximum quantity of the garbage that can be gathered through an IoT mechanism is dependent on the quantity of bins, their capacities, and the ability to monitor the containers' levels of filling in instantaneous.

  • Sustainability (\({\mathrm{C}}_{6}\))

The smart waste technology that is based on the IoT has to fulfill certain sustainable requirements, such as those for the environment, the economy, and society. As a result, the IoT technology system used in waste management must be able to ensure environmental, economic, and social sustainability (Javed et al., 2022). Components of the system include suitable sensors, GPS, mobile applications, and cloud storage systems.

  • Investment cost (\({\mathrm{C}}_{7}\))

The elevated price of intelligent devices and tuning up for the purpose of disseminating information to employees is the primary obstacle to the introduction of the IoT. The IoT technology that is used for waste management has to be capable of delivering facilities that are both value-efficient and economical.

  • Operational cost and payback period (\({C}_{8}\))

The IoT system that is used for garbage administration has to have a low cost of operation and maintenance, as well as a cheap monthly service fee (Seker, 2022). The high cost of specialists, the expenses of maintenance, and the costs of training personnel to inform them are required to carry out these applications.

  • Security and privacy (\({C}_{9}\))

There is a risk of data leaking because of privacy and security concerns. Systems that use IoT technology might be vulnerable to a variety of attacks, such as cross-site scripting or consuming adjacent channels that lead to susceptibilities (Sharma et al., 2020). Mobility and interconnections between different parts of the system both increase the potential for danger.

  • Simplicity of operation (\({C}_{10}\))

Because an excessive amount of operational complexity could encourage the ratio of human mistakes, raise maintenance budgets, and possibly longer failed interruptions, ease of functioning is essential for the continuous and successful functioning of IoT systems.

  • Standardization (\({C}_{11}\))

Standardization is necessary for smart waste technology in order to facilitate communication and the sharing of information among the environment, intelligent entities, and various types of objects. Activities pertaining to principles like identity, connection, and privacy are necessary components of a successful IoT deployment (Sundar et al. 2023).

5 Research findings

In this section, the suggested hybrid framework T2NN-ITARA-MARCOS is employed through a case study to demonstrate its reliability. The results obtained, whether in evaluating criteria or arranging alternatives, are also discussed. Also, sensitivity analysis and comparative analysis are presented.

5.1 Application of the hybrid T2NN-ITARA-MARCOS methodology

In this part, the methodology steps used to evaluate smart waste management technologies are applied.

Step 1. A team of experts was formed to participate in the study and express their views on questions related to the problem and its details. The background information of the participating experts is included in Table 1. Also, a weight was assigned to each expert according to his experience and practical practices.

Table 1 Specifics on the participants of the panel of experts
Full size table

Step 2. Based on the dialogue and communication with experts to study the problem, the main objective was identified, which is to identify the most appropriate intelligent technologies for sustainable waste management. To address the problem, we have identified 11 criteria that directly impact its solution, namely: interaction network \({\mathrm{C}}_{1}\), productivity \({\mathrm{C}}_{2}\), environmental protection \({\mathrm{C}}_{3}\), aesthetics \({\mathrm{C}}_{4}\), quantity of wastes gathered \({\mathrm{C}}_{5}\), sustainability \({\mathrm{C}}_{6}\), investment cost \({\mathrm{C}}_{7}\), operational cost and payback period \({\mathrm{C}}_{8}\), security and privacy \({\mathrm{C}}_{9}\), simplicity of operation \({\mathrm{C}}_{10}\), and standardization \({\mathrm{C}}_{11}\). In addition, four alternatives were selected to be evaluated, namely: Underground waste collection and storage containers (\({\mathrm{A}}_{1}\)), solar-powered waste compactor technology (\({\mathrm{A}}_{2}\)), RFID, and GPRS blend for waste administration technology (\({\mathrm{A}}_{3}\)), and mobile application for waste collection (\({\mathrm{A}}_{4}\)).

Step 3. Semantic variables and their equivalent T2NNs as displayed in Table 2 are provided for the participants to use in the evaluation process and express their opinions on the criteria and on the ranking of the selected intelligent waste management technologies.

Table 2 Semantic variables
Full size table

Step 4. Four pairwise comparison matrices have been created by four experts between 11 criteria and 4 alternatives using linguistic terms in Table 2 based on Eq. (10) as showed in Table 3. Then, four pairwise comparison matrices have been created by four experts between 11 criteria and 4 alternatives by utilizing T2NNs as in Eq. (10), as displayed in Table 12.

Table 3 Appraisal matrix of standards utilizing semantic variables
Full size table

Step 5. T2NN decision matrices of four experts have been aggregated by applying the T2NNWA operator based on Eq. (11) as shown in Table 13.

Step 6. The standardized assessment matrix is calculated using Eq. (13) and exhibited in Table 4.

Table 4 The normalized decision matrix
Full size table

Step 7. The normalized aggregated evaluations have been sorted according to Eq. (14) and presented in Table 5.

Table 5 The aggregated normalized and sorted evaluations according to the criteria
Full size table

Step 8. The ordered distances are computed using Eq. (15), and Table 6 shows the computed results.

Table 6 Final weights of criteria
Full size table

Step 9. The considerable ordered distances are computed by utilizing the Eq. (16) as shown in Table 6. Also, the criteria indifference threshold \(\mu\) is agreed to be 0.01.

Step 10. The criteria weights are computed based on Eq. (17) with the computed results depicted in Table 6 and shown in Fig. 7. Also, the preferred metric \(\beta\) was adopted to be 2 as Euclidian distance for referring to the significance of the criterion.

Fig. 7
figure 7

Final weights of criteria

Full size image

Step 11. The ideal and anti-ideal alternatives have been identified according to Eqs. (18) and (19). Afterward, the normalized decision matrix is calculated by Eq. (20) and exhibited in Table 7.

Table 7 Normalized matrix for four intelligent waste management technologies according to all criteria
Full size table

Step 12. The weighted normalized decision matrix has been considered by Eq. (21) as demonstrated in Table 8.

Table 8 Weighted normalized matrix for four intelligent waste management technologies according to all criteria
Full size table

Step 13. The utility degree for each anti-ideal and ideal alternative has been computed according to Eqs. (22) and (23), correspondingly as demonstrated in Table 9.

Table 9 Final ranking of four intelligent waste management technologies
Full size table

Step 14. The utility function for each anti-ideal, and ideal alternative has been computed according to Eq. (24) and (25), respectively, as presented in Table 9.

Step 15. The utility function of the four alternatives is demonstrated by Eq. (26) as depicted in Table 9. Also, four substitutions are ordered in ascending order based on the greatest utility function value as displayed in Fig. 8.

Fig. 8
figure 8

Final ranking of four intelligent waste management technologies

Full size image

5.2 Discussion

This part discusses the consequences achieved from the enforcement of the suggested hybrid framework T2NN-ITARA-MARCOS for evaluating and selecting the most appropriate intelligent technologies for waste management.

Initially, the T2NN-ITARA technique was employed to estimate 11 criteria that have an immediate influence on determining of the most appropriate intelligent technologies for waste management. The findings, displayed in Table 6, specify that the sustainability criterion is the utmost important, with a weight that is equal to 0.135, then the standardization criterion with a weight that is equal to 0.134 and the environmental protection criterion comes in the last position, with a weight that is equal to 0.048.

Next, the T2NN-MARCOS technique was utilized to evaluate four intelligent waste management technologies. According to the results in Table 9, the RFID and GPRS blend for waste administration technology is the most suitable for garbage management, followed by the mobile application for waste collection technology. The underground waste collection and storage containers technology is ranked lowest among the selected technologies. The criteria that influenced the selection of the RFID and GPRS blend for waste administration technology as the most suitable intelligent technology for garbage management were the interaction network criterion, investment cost criterion, operational cost and payback period criterion, and simplicity of operation criterion. Finally, the intelligent technologies for waste management were evaluated and ranked, and the results can be used as support for decision-makers and stakeholders in picking the applicable technologies. The evaluations of the technologies used show no significant difference, indicating convergence in the evaluation process.

5.3 Sensitivity analysis

A sensitivity analysis has been performed to validate the results of the hybrid suggested T2NN-IRTARA-MARCOS methodology for the assessment and classification of intelligent waste management technologies based on IoT. The influences of the change in the criteria on the ranking results of the four technologies selected in the study were examined. In particular, the influences of criteria weights on assessment and classification outcomes were analyzed by examining twenty-three cases. Sensitivity analysis has been completed according to the alteration in the preferred metric β value found in the ITARA method. In the base scenario, the preferred metric β was adopted to be (β = 2) as Euclidian distance for referring to the significance of the criterion. Also, twenty-two further states were computed, comprising two farthest cases based on the Tchebycheff distance (β = \(\infty\)) and the Manhattan distance (β = 1). The results in Fig. 9 indicate that the four technologies have the same order in the twenty-three cases, except for one case, which is Manhattan distance (β = 1), the mobile application for waste collection technology takes the first order.

Fig. 9
figure 9

Influence of the β on the ranking of intelligent waste management technologies

Full size image

On the other hand, sensitivity analysis has been evaluated according to the alteration in the value of threshold \(\mu\) influences found in the ITARA method, the findings as shown in Fig. 10. Its values have been determined in the interval [0, 0.2] with an increased value of 0.01.

Fig. 10
figure 10

Influence of the \(\mu\) on the ranking of intelligent waste management technologies

Full size image

5.4 Comparisons

In this part, a comparison analysis is performed to validate the developed methodology T2NN-ITARA-MARCOS to evaluate and rank intelligent waste management technologies based on IoT. The analysis has been performed with two other frameworks, T2NN-TOPSIS (Mohamed Abdel-Basset et al., 2019a, 2019b), and T2NN-TOPSIS-WASPAS (Görçün, 2022). Table 10 presents the comparison faces between the proposed methodology and the two mentioned methods.

Table 10 Comparison of methodologies used for intelligent waste management technologies
Full size table

The methodologies applied in the comparison process with the developed methodology according to Table 10 assume that the weights of the criteria have been previously computed. When solving real-world MCDM issues, information about the weight of the standards is usually unknown. Therefore, the two compared methods assume that all criteria are of equal importance, which causes a loss of information. On the other hand, the T2NN-ITARA-MARCOS methodology is introduced, which can define the relative significance of criteria constructed on evaluations of substitutes, allowing for more accurate solutions. In comparison, the T2NN-TOPSIS approach does not include factors, which reduces its flexibility in dealing with real-world MCDM problems. While the T2NN-TOPSIS-WASPAS method includes one parameter, which gives the method medium flexibility in dealing with realistic MCDM problems. In contrast, the T2NN-ITARA-MARCOS method includes two parameters, \(\mu\), and β, which gives great accuracy and flexibility in dealing with real-life problems.

Also, the T2NN-TOPSIS and T2NN-TOPSIS-WASPAS approaches were employed to elucidate the issue of arranging and selecting the most suitable intelligent waste management technologies to confirm the reliability of the suggested methodology. According to Table 11, it is clear that the order of intelligent waste management technologies chosen is the same as the order using the proposed methodology. Accordingly, the results of the suggested methodology T2NN-ITARA-MARCOS are more reliable.

Table 11 Comparison findings
Full size table

6 Conclusions

An ever-increasing amount of waste is being produced, which paves the way for significant adverse effects on the ecosystem in every region of the globe. It cannot be denied that all human activities ultimately result in the production of a significant amount of garbage consisting of a variety of different types of stuff. The combination of unplanned modernization and increased industrialization, which results in a sharp rise in waste production, has a significant negative influence on our environment. The term "waste management" refers to both the process of reducing the overall quantity of garbage that is created as well as the disposal of that waste via the use of appropriate procedures. The activity of collecting garbage, transporting it, recycling, or disposing of it, and doing any necessary analyses are all part of waste management. This research aims to decrease costs and environmental damage by incorporating IoT-based technology into garbage gathering and transmission systems to provide real-time waste collecting.

This research aims to present a hybrid T2NN-ITARA-MARCOS methodology for the assessment and ranking of intelligent waste administration technologies based on IoT. In this paper, we developed a method that is consists of four stages. The first one is associated with studying the problem and defining the primary objective of this research. In addition to identifying the committee of experts participating in the study, consisting of four experts, and identifying seven linguistic variables used by the participants to give their opinions in the mandatory assessments. The second stage is associated with the evaluation of the exact indicators that have a direct effect on the selection of the best intelligent waste management technology based on IoT using T2NN-ITARA. After that, the third stage is related to the assessment and ranking of intelligent waste management technologies based on IoT using the T2NN-MARCOS method. In the end, the fourth stage is related to presenting the comparison analyses and sensitivity to demonstrate the strength and robustness of the presented methodology. The study was carried out under a neutrosophic environment. Furthermore, T2NNWA was used to gather expert preferences on either evaluation criteria or rankings of intelligent waste management technologies based on IoT.

Eleven criteria were gathered by reviewing studies, expert opinions and research to be used in the study. The criteria namely: interaction network \({\mathrm{C}}_{1}\), productivity \({\mathrm{C}}_{2}\), environmental protection \({\mathrm{C}}_{3}\), aesthetics \({\mathrm{C}}_{4}\), quantity of wastes gathered \({\mathrm{C}}_{5}\), sustainability \({\mathrm{C}}_{6}\), investment cost \({\mathrm{C}}_{7}\), operational cost and payback period \({\mathrm{C}}_{8}\), security and privacy \({\mathrm{C}}_{9}\), simplicity of operation \({\mathrm{C}}_{10}\), and standardization \({\mathrm{C}}_{11}\). Accordingly, we evaluated the criteria by using the T2NN-ITARA approach, with the obtained results indicate that the sustainability criterion is the principal one with a weight that is equal to 0.135, followed by the standardization criterion with a weight equal to 0.134, while the environmental protection criterion is the least important with a weight equal to 0.048. Also, in this paper, a case study was presented in the Administrative Capital, Egypt to reveal the application of the recommended methodology to the problem of evaluating and ranking four intelligent waste management technologies based on IoT. The four technologies were evaluated using T2NN-MARCOS. The results indicate that the RFID, and GPRS blend for waste administration technology is the most suitable intelligent technology for garbage management, followed by mobile application for waste collection technology, while underground waste collection and storage containers technology is the technology with the least ranking among the selected technologies.

Despite the fact that the study contains the contributions that were emphasized above, the study does have certain limitations that might be taken as recommendations for further research. The first limitation of this research is the small sample size of experts. To address this limitation, future studies may include additional experts' opinions. Furthermore, as the criteria, weights can significantly influence the resulting outcomes, the proposed methodology could be further boosted to incorporate a more comprehensive weight method that takes into account both the objective and subjective weights of the criteria. According to the superiority of the obtained results from the validation and verification process, the proposed method has the potential to aid important long-term decisions for different country-specific management problems, such as energy, transportation, and others.