A new hybrid reasoning model based on rules, cases and processes: application to care of individuals facing autism spectrum disorders

Abstract

Combining Rule-based reasoning and Case-based reasoning has been widely used, exhibiting quite successful results, since they have complementary capabilities. A system that can utilize both approaches could potentially take advantage of the positive aspects of both while minimizing their negative aspects. In this paper, we propose a hybrid reasoner which combines Rule based reasoning, Case-based reasoning, as well as Process Mining. To our knowledge, this work is the first one that incorporates process modeling in a hybrid reasoner. Process Mining is used in order to take into consideration possible future facts, which are justified by the current ones through a process model extracted by the cases themselves. Each case is considered as an instance of a process and a process model is extracted by applying process mining techniques. We also present PAVEFS, an intelligent system based on the proposed hybrid reasoner, supporting personalized provision of services for individuals facing autism spectrum disorders.

1 Introduction

Case-based reasoning (CBR) takes advantage of stored past cases in order to deal with new similar cases. The inference is usually performed in four phases known as the CBR cycle: retrieve, reuse, revise, retain. Retrieval regards finding in the set of stored cases one or more cases that appear to be the most similar to the new case. Reuse is concerned with using the retrieved, relevant cases to propose a solution for the new case. Revision regards the validation of the proposed solution, by testing whether it solved the problem at hand. Retain decides whether the new case is useful enough to be stored in the pool of past cases [1]. CBR is appropriate when there is a great number of past cases available, or it is easy to obtain them. CBR does not rely on creating a model of the domain.

Rule based reasoning (RBR) uses a set of rules (rule base) that represents general knowledge about a domain. A rule usually has an ‘if–then’ format, with several conditions that need to be satisfied for the rule to be activated and a set of actions or conclusions that are added in the working memory when the rule is executed. Inference takes place by introducing the input to the rule base, causing a chain of rules to be triggered and executed that eventually lead to the output [2]. RBR is appropriate when there is a clear model of the domain or there are available experts that can represent it in the form of rules.

Process Mining (PM) focuses on automatically generating a process model from event-based data (e.g., activities being executed, or messages being exchanged) created and stored in corporate information systems in order to extract knowledge and to be used as a starting point to analyze executed processes [3].

On the other hand, autism spectrum disorder (ASD) is a complex social development disorder due to neural and brain abnormalities and has considerably expanded in recent decades in children.¹ The population of people with ASD is heterogeneous, with each individual presenting a unique profile of strengths, weaknesses and support needs (Biomed Project for Autism, 2001, University of Exeter / DCACT). Understanding the heterogeneity of this diverse population is very important, since, for example, an intervention that has a beneficial effect on one patient may invoke a toxic response in a second and may have no effect on a third. So, due to the individualized nature of care for people with ASD, providing appropriate support services is labor intensive and expensive. Hence, the development of an intelligent system for the diagnosis and care of individuals facing ASD seems necessary.

Given the above characteristics of ASD, standardized approaches to support ASD care are inappropriate and often abusive. Thus, there are not adequate general rules, hence RBR by itself is not adequate. On the other hand, from a technical point of view, the individualized nature of care for people with ASD introduces a non-monotonic domain which cannot be handled efficiently by typical machine learning algorithms [5]. Given that cases, in contrast to rules, represent specific knowledge, CBR is straightforwardly applicable to such a domain.

In caring people with ASD, it is usual that after an initial response concerning an initial behavior either this behavior itself or some of its parameters are changed or a new behavior is triggered because of this response. Therefore, in providing appropriate support services, it is crucial to take into consideration the potential future behaviors triggered by proposed interventions. Obviously, a Process Model can support such functionality.

As a conclusion, a combination of RBR, CBR and PM can efficiently handle ASD cases, which is also similar to many mental health domains, addictive disorders domains, etc.

In this paper, we propose a hybrid reasoning system which combines RBR, CBR and PM. Although combination of RBR and CBR has been widely used, exhibiting quite successful results [4], to the best of our knowledge, this work is the first one that incorporates process modeling in an RBR-CBR hybrid reasoner. PM is used to be able to take into consideration possible future facts, which are justified by the current ones through a process model extracted from the cases themselves. Each case is considered as an instance of a process and a process model is extracted by applying process mining techniques. This makes the reasoner more efficient and more effective.

We also present an intelligent system for handling people with ASD, called PAVEFS, which uses the proposed hybrid reasoner as its decision-making mechanism. Experimental application of the system shows the advantages of the proposed reasoner resulting in a high performance.

In the rest of the paper, we first present background knowledge concerning RBR, CBR and PM (Sect. 2). In Sect. 3, we present an overview of CBR-RBR integrations and models as well as related work. Section 4 presents the proposed hybrid reasoner, while Sect. 5 deals with a reasoning example, to illustrate how the hybrid reasoner works. In Sect. 6, we present PAVEFS, a medical system for supporting provision of personalized services for individuals facing ASD, which is based on the proposed hybrid reasoner. Section 7 presents evaluation method and results, whereas Sect. 8 concludes the paper.

2 Background knowledge

2.1 Rule based reasoning

Symbolic rules are one of the most popular knowledge representation and reasoning methods. Their popularity comes from the fact that they are natural representations of human knowledge, which makes them easy to comprehend the represented knowledge. Medical domain is one of those where rule-based expert systems are used for diagnoses. In such cases, each rule represents a knowledge that reflects the way an expert doctor makes diagnoses: from various evidence (clinical symptoms, blood test results etc.) he/she makes a hypothesis (diagnosis) about the disease of a patient. The basic structure of a rule is thus the following:

if < antecedents > 

then < consequence > 

where < antecedents > represent evidence and < consequence > the hypothesis. The antecedents of a rule are connected between each other with logical connectives, commonly with and. When the antecedents of a rule hold (or observed), the consequence is derived, and the rule is said to be fired. Rules represent general knowledge regarding a domain. The following is an example of a simple medical rule:

if pain is continuous and

fever is high

then disease is inflammation

We use the following notation for a rule r:

r = if a₁ and a₂ and … a_p then c

where a₁, a₂, …, a_p are the antecedents and c is the consequence.

Rules are used to make inferences, to produce results. A rule-based reasoning (RBR) system consists of

• A set of facts FS = {f₁, f₂, …, f_n}, which represent the data of a problem, for example the symptoms of a patient.

• A rule base RB = {r₁, r₂, …, r_l}, where each rule r_i = if e_i1 and e_i2 and … e_ip then h_i and represents general (diagnostic) knowledge related to the problem domain.

• A rule inference engine, which use the facts and the rules to derive hypotheses, that is new facts. When there are facts that match all the antecedents of a rule, then its consequence is derived. For example, if “pain is continuous” and “fever is high” ∈ FS, then “disease is inflammation” is derived.

In the above, facts, antecedents and consequences have the same structure:

f_i /e_i /h_i = <attribute_i> <predicate_i> <value_i>.

For example, in the first antecedent of the above rule: <attribute> = pain, <predicate> = is, <value> = continuous, whereas in the consequence: <attribute> = disease, <predicate> = is, <value> = inflammation.

2.2 Case based reasoning

Case-based reasoning (CBR) is another popular knowledge representation and reasoning method. The main idea is to store a large set of previous (solved) cases with their solutions in a case base (CB) and use them to deal with (solve) new (similar) cases [6,7,8]. Cases, in contrast to rules, represent specific knowledge.

CBR works in a way that can be represented by the so-called CBR cycle [1]: retrieve the most similar case(s), reuse those case to create a solution, revise the solution to adapt to the case, retain the produced case as a new case. Whenever a new input case has to be dealt with, the case-based system performs an inference following those four phases. In the retrieval phase, the system retrieves from the case base the most relevant stored case(s) to the new case. In the reuse phase, a solution for the new case is created based on the retrieved most relevant case(s). The revise phase validates the correctness of the proposed solution, perhaps with the intervention of the user. Finally, the retain phase decides whether the knowledge learned from the solution of the new case is important enough to be incorporated into the system’s case base.

According to [9], CBR is a methodology, not a technology. So, it can be implemented in various ways. For example, there is no specific way for representation of stored cases. Various representation schemes can be used for that, like semantic nets, frames, objects, patterns, even rules. Given that, CBR is a reasoning method rather than a representation one.

Α case base consists of a finite number l of cases: CB = {c₁, c₂, …, c_l}. Each case can be represented as a tuple consisting of p attributes: c_i = (c_i1, c_i2, …, c_ip). Attributes are related to the problem domain and can be of different data types. In our problem, we use attributes that are of numerical, categorical, multi-valued and ontological type (node of an ontology).

As it is obvious, the most important phase in the CBR cycle, and the one where some kind of inference is made, is retrieving the most similar case(s) to the case at hand (new case). To assess the similarity of the retrieved case(s) to the new case, similarity metrics are necessary. There are various such metrics as well as different similarity methods that use the similarity metrics in different ways [10, 11]. When we have different types of attributes in the cases, hybrid similarity metrics/methods are required, which include different metrics for different types of attributes.

In our problem, we use the following metrics, each for a different type of attribute.

• For numerical attributes we use the normalized distance between two values of numerical attributes [12]:

  $$ Sim\_num\left( {c_{ik} ,c_{jk} } \right) \, = { 1 } - \, \left| {c_{ik} - c_{jk} } \right|/\left( {c_{i}^{max} - c_{i}^{min} } \right) $$

  (1)

  where c_ik, c_jk denote the values of attribute k in cases c_i, c_j respectively and c_i^max, c_i^min represent the maximum and minimum values of attribute k, respectively.

• For categorical attributes we use the Eskin similarity [13] between the two categorical values:

  $$ Sim\_cat\left( {c_{ik} ,c_{jk} } \right) = \left\{ {\begin{array}{*{20}c} {1, c_{ik} = c_{jk} } \\ {\frac{{n_{k}^{2} }}{{n_{k}^{2} + 2}}, c_{ik} c_{jk} } \\ \end{array} } \right. $$

  (2)

  where n_k is the number of different values of attribute k.

• For multivalued attributes, we use the Jaccard similarity [14] between two values of multivalued attributes:

  $$ Sim\_multi\left( {c_{ik} ,c_{jk} } \right) \, = { 1 } - \frac{A \cap B}{{A \cup B}} $$

  (3)

  where A = {c_ikq | c_ikq ∈ c_ik and c_ikq ∈ domain(k)} and B = {c_jkq | c_jkq ∈ c_jk and c_jkq ∈ domain(k)}.

• For ontological attributes, we use a function of node distance within a tree-structure [15], between two values of attributes that are represented by nodes of a given ontology:

  $$ {1 }{-}d\left( {c_{ik} ,c_{jk} } \right) $$

  (4)

  where

  $$ \begin{aligned} d\left( {c_{ik} ,c_{jk} } \right) &= \frac{1}{{fl\left( {c_{ik} ,c_{jk} } \right)}} \times Average\left( {\frac{{l\left( {c_{ik} } \right) - fl\left( {c_{ik} ,c_{jk} )} \right.}}{{max\left( {p\left( {c_{ik} } \right))} \right.}}, \frac{{l\left( {c_{jk} } \right) - fl\left( {c_{ik} ,C_{jk} } \right)}}{{{\text{max}}\left( {p\left( {c_{jk} } \right)} \right)}}} \right) \\ &\quad \times \left( {\frac{{p\left( {c_{ik} ,c_{jk} } \right)}}{{\max \left( {p\left( {c_{ik} } \right)} \right) + {\text{max}}\left( {p\left( {c_{jk} } \right)} \right)}}} \right) \\ \end{aligned} $$

  (5)

  where c_ik and c_jk represent two nodes in the ontology, fl(c_ik, c_jk) is the level of the nearest common father node of them, l(c_ik) is the level of node c_ik, max(p(c_ik)) is the length of the maximum path starting from the root to a leaf and containing node c_ik and p(c_ik, c_jk) is the length of the directed path (number of edges) connecting c_ik and c_jk. The first part (1/fl(c_ik, c_jk)) supports the postulate suggesting that the distance between terms/values which represent more specific concepts must be smaller (i.e. less dissimilar) than the distance between term/values which represent more general ones. The second part supports the postulate suggesting that the more general are specifications of a concept the more similar they are. Finally, the third part supports the postulate suggesting that the distance between c_ik and c_jk must be smaller as the maximum path containing c_ik and c_jk becomes larger.

2.3 Process mining

Process mining is defined [3, 16, 17] as the analysis of processes by using event data logs focusing on end-to-end processes, available in information systems. Process mining is a steadily developing field mainly due to the growing need for the information systems to support business processes. Today information systems are recording a large number of events and a detailed history of processes is provided. Process Mining “focuses on extracting knowledge from data generated and stored in databases of (corporate) information systems in order to build event logs” [18].

Process mining has also addressed informative gaps that most organizations face due to very limited information about what is actually happening in their structures. Significant gaps between what is prescribed or supposed to happen, and what actually happens are frequently reported. Process mining delivers a concise assessment of the organizational reality and since the verification of process models is achieved, a process redesign effort is initiated [19].

Through the process mining techniques useful knowledge can be extracted. Additionally, its three basic types, (i.e., the discovery, the conformance, and the enhancement), enhances the evidence-based analysis and proves the applicability of process mining in real-life. Process mining objective is to retrieve a process model from an event log and to use it as an objective starting point during the deployment of process-aware information systems in order to (re)design and improve processes [20].

There are several process mining algorithms. The α-algorithm is an algorithm, aimed at reconstructing causality from a set of sequences of events [16]. Ιt constructs Petri nets with special properties (workflow nets) from event logs and each transition in the net corresponds to an observed task. The α-algorithm at first reads the log and gets the set of tasks then it infers the ordering relations and builds the net based on inferred relations. As a final step it outputs the net. In general, the input of the α-algorithm is a workflow log and the output, after examining causal relationships between tasks, is a “constructed” workflow net. The workflow net is usually represented as a Petri net, like the one in Fig. 1.

Fig. 1

Example of a petri net workflow model

A Petri net N is represented as N = (P,T,F), where P = {p₁, p₂, …, p_m}a nd T = {t₁, t₂, …, t_n} are disjoint finite sets of places (circles) and transitions (rectangles) respectively, and F ⊆ (P X T) ∪ (T X P) is a set of directed arcs (flow relations). Places represent situations of the system. Transitions represent actions that lead to changes of the system situations (e.g., production of new situations or results). An arc connects a place with a transition or a transition with a place. A transition may have input and output places connected to it. When the (input) places (called conditions) of a transition t_i are activated, then t_i is fired and its (output) place(s) is(are) activated (or become true), which leads to change of the state of the system. For example, in Fig. 1, when the (input) place ‘a’ of t1 and t2 transitions is activated, then t1 and t2 are fired and the (output) places ‘b’, ‘e’ and ‘c’ are activated, which in turn lead to firing of transitions t3 and t4, thus (output) place ‘d’ is activated (or becomes true). The state of the system at each moment consists of all active places of the network.

There are various applications of process mining presented in the literature, e.g., in Smart Cities [21, 22], in health care [23,24,25], in predicting processes’ completion time [3, 26], in data security [27], in manufacturing [28], in management [29] etc. They identify the need for i) the development of new mining techniques or ii) a more innovative usage of the existing ones and iii) a broader implementation of the process mining.

3 Hybrid reasoning models and related work

Integration of different knowledge representation and reasoning (KRR) methods, such as FOL (first-order logic), RBR, FBR (frame-based representations), ONT (ontologies), KG (Knowledge Graphs), CBR etc., is an active research area. The aim is to create integrated or hybrid methods that benefit from each of their components. Hybrid methods consisting of two different components dominate the area. Well-known such integrations include FOL-FBR, FBR-RBR, ONT-RBR and RBR-CBR, which belong to what is called symbolic-symbolic integration. On the other hand, KRR methods can be combined with ML (machine learning) ones, like NN (neural networks) resulting in what is called neuro-symbolic integration. Integration of RBR and NN is one of the most common ones.

CBR-RBR hybrids are of the most popular and have been widely used in systems in various application domains, with most notable the Legal, Medical and Agriculture ones, with quite successful results. In this section, we concentrate on medical and home care domains, which are relevant to our application. The main reason for the success of CBR-RBR integrations, and all other such integrations, is that the constituent methods have complementary capabilities/characteristics [4], so that the integrated method can potentially take advantage of the positive aspects of both constituents, while minimizing their negative aspects. Furthermore, the combination of general (rules) and specific (cases) knowledge emulates the human way of thinking.

The way that the components are combined in a hybrid system varies greatly and there have been a few attempts to categorize them. In [30] a general categorization for combining intelligent techniques has been proposed considering whether and how the different integrated components interact with each other. That categorization was later extended [4] to better represent all hybridizations with CBR components. The proposed scheme first categorizes the integrations to ‘Standalone’ and ‘Coupling’. In standalone models, the individual components do not interact with each other during reasoning. They can work in parallel, and each component will arrive on a separate solution. Individual solutions are not combined in any way, but there are multiple conclusions that can be compared. In coupling models, the constituent components are interacting in various ways. So, coupling integrations are further categorized to ‘Embedded processing’, ‘Co-processing’ and ‘Sequential processing’.

In embedded processing coupling models, one of the components is the primary inference model and it embeds other components for some of its internal reasoning tasks. In most approaches CBR is the primary component, but there are cases where CBR is one of the internal components. For example, in [31], RBR is used within the CBR cycle to help in better case retrieval for diagnosis of gastrointestinal cancer. Also, in [32], an ontology is used in the CBR cycle to provide explanations for the hypothyroid disease diagnosis. Also, in [33] a deep learning model is used for similarity checking in a CBR model for production of radiology reports. In [34] and [35], a machine learning algorithm (random forest) is used for extracting the weights for the attributes to be used in the similarity estimation process. Finally, in [36] two ontologies are used for case adaptation in the CBR cycle of a system aiming at diet and physical exercises recommendation.

In co-processing coupling approaches, the different components interact during reasoning, so the flow of information is bidirectional. For example, in [37] the proposed system, called RBR-config, uses a co-processing approach by employing CBR for parameter configuration of rules for therapy modification for diabetic patients. [38] proposes RACER, a system that helps General Practitioners in prescription making, by combining association rules mining and case-based reasoning in a co-processing mode.

In sequential processing coupling approaches, information must pass sequentially through some components in order to reach the final result. Sequential processing approaches can be further categorized in ‘loosely coupled sequence’, and ‘tightly coupled sequence’. In the loosely coupled sequential processing approach, the output of one component does not play an important role in the internal process of the next component. Such an example is [39], where a FCM (fuzzy cognitive map) approach is first used for a decision and, in case of inability to provide a certain decision, a CBR approach is employed. The hybrid approach was applied to two medical problems, language impairments diagnosis and external beam radiation therapy choice. In [40] for an Acute Bacterial Meningitis Clinical Decision Support System, a set of diagnostic rules is used to identify situations in which the symptoms indicate a disease without any doubt. If the case is not obvious, the CBR method is used. If the similarity degree is above a threshold the solution of the previous case is used directly, otherwise an adaptation process is used that also uses an integration of CBR and RBR components and which allows carrying out suitable transformations to the solutions. Another example is [41], where a rule-based system is first used to make a diagnosis about primary headache disorder. If it fails or cannot provide an accurate answer, a CBR system takes over to make the diagnosis. In a more recent work [42] a RBR system is combined in a loose sequential way with a CBR system for diagnosis of herpes disease. The RBR component is first employed and if fails then the CBR one is activated.

In the tightly coupled sequential approaches, the output of one component is crucial in the reasoning process of the next one. Such an approach is used in HIDES [43], a system for herbicide injury diagnosis, first invokes RBR to identify suspect herbicide(s) for causing the observed injury and to determine possible sources of the suspect herbicide(s) and passes the results to CBR to propose a probable cause of injury. Also, in [44] the Cognitive Maps (CM) method is combined with the CBR method to early detect child autism, which is also the application of our system. The information about a child is going through a CM module, the output of which is a case that is fed to the CBR module of the system for making the diagnosis. Another more recent such system that deals with autism spectrum disorders (ASD) is that of [45]. It uses a combination of an ontology and CBR approaches. An ontology is used to represent the context of an autistic person, considering several conditions. Based on real time observations, it configures an autistic context, which then goes as a new case to a CBR system that results to suitable retrieved case(s) recommending appropriate actions to face the autistic behavior at hand. Similarly, in [46] a Markov model is used to analyze the scenario evolution of an infectious disease outbreak, to create input cases for a dynamical CBR system, which outputs prediction on the development of the epidemic outbreak, to face emergency situations.

On the other hand, CBR is also suitable for integrating with more than one other method [47]. For example, in [48] RBR, NN and CBR are integrated. There are very few such efforts in the medical and home care domains. In [49] a fuzzy neural network is used for case retrieval and an induction tree for case selection in the CBR cycle of a system for medical diagnoses; an embedded model is followed. Also, in [50] NN, RBR and CBR are combined in an effort to include conflicts resolving capability in a virtual assistant in a multi-user smart home environment; a tightly sequential model is used here.

The approach presented in this paper, is based on a combination of tightly sequential and embedded models, where RBR, CBR and PM are combined to improve decision success rate of the CBR component, which is the main component. RBR is used to enhance information of input cases, which are then passed to the CBR model; this follows the tightly sequential model. Retrieval of similar cases from the case base are further enhanced by the PM module; this follows the embedded model: PM is part of the retrieval phase of the CBR component. To the best of our knowledge, this is the first approach that integrates CBR with RBR and PM, a data mining method.

In Table 1, we summarize the high-level features of the systems presented above. It is quite clear that only a few of the systems [49, 50] use a combination of three reasoning methods, but none of them is based on a combination of two different model architectures, as our system (PAVEFS) does. A unique feature of our hybrid method is how RBR is used: it enhances the input case by producing new facts, whereas in existing approaches rules are mainly used to make (final or intermediate) decisions [37, 40,41,42] or help in retrieval of similar cases [31] or help in solution adaptation [40]. Also, only one other system [45] deals with the very important problem of autism spectrum disorders (ASD) care, and another one [44] with diagnosis of ASD. A difference between the system in [45] and our system is that system in [45] cannot predict potential future behaviors of the individual under care, as our system does by PM integration, and take them into account in selecting similar cases, due to the static nature of ontology it uses. The same happens in [44], where a concept map structure is used instead of an ontology.

Table 1 Systems with hybrid reasoning models in the medical domain

Autism is a serious, neuropsychiatric disorder, caused by a malfunction of the brain, characterized by qualitative differences in social interaction and relationship building, in verbal and non-verbal communication and in game-thinking-imagination. These divergences have a profound effect on the way a person learns, behaves, adapts, and operates in daily life. In this context, the lack of supporting services for the individuals facing ASD and their parents or caregivers has been identified and the proposed solution pursues to bridge this gap. Although several information systems have been designed in the health sector, ASD is a field that has not been adequately covered.

The proposed intelligent system, based on a combination of CBR, RBR, and PM, aims at automatically providing a wide range of specialized and reliable responses to user questions regarding caregiving to individuals facing ASD. ASD is a domain composed of a limited set of general rules (i.e., RBR), extensive specific knowledge through extensive number of cases (i.e., CBR). The proposed system’s Rule and Case Base was developed from different sources (experts, literature, etc.). In the ASD domain, it is also of great importance to forecast the reactions triggered by certain actions of caregivers (suggested automatically by the system). An innovation of the proposed intelligent system is the use of PM to perform the forecasting.

The proposed intelligent system supports and facilitates the daily life of individuals facing ASD through supporting their caregivers by providing specialized, reliable, and professional assistance. Since ASD is a complex and difficult to analyze field, to our knowledge, there has not been developed a similar intelligent information system, thus no comparative study has been conducted.

4 The proposed model

The architecture of the proposed 3-layer model (RBR, CBR, PM) is depicted in Fig. 2. The input includes the initial facts for the inference system, entered by the user. The first and middle layers constitute the tightly sequential processing model, where RBR layer gives enhanced input to the CBR layer. The middle and last layers constitute the embedded processing model, where the PM layer participates in the retrieval part of the CBR by enhancing the result.

Fig. 2

The proposed model

In a more formal way, let FS be the set of given (initial) facts: f₁, …, f_n ∈ FS. Then a subset TRB of RB, the rule base of the RBR component, are triggered: r₁, …, r_m ∈ TRB ⊆ RB. Those rules represent general knowledge provided by domain experts. The triggered rules produce a set AFS of additional facts (i.e., the produced consequents of r₁, …, r_m): af₁, …, af_m ∈ AFS, that further describe/enhance the input. The enhanced input set EFS = FS ∪ AFS, which is derived during this first step, is then used as input to the CBR layer that retrieves from CB = {c_i | c_i = (c_i1, … c_ip)}, the case base of CBR layer, a set RCB of the most relevant stored cases: c₁, …, c_t ∈ RCB ⊆ CB.

The retrieval of the cases is achieved by using proper similarity measures sim(c_ik,c_jk), depending on the attribute type. The final similarity between cases c_i and c_j is calculated by using the weighted sum of the similarities between the attributes of the cases: final_sim(c_i,c_j) = $\sum_{s=1}^{p}{w}_{s}*sim({c}_{is},{c}_{js})$, where w_s denotes the weight of attribute s, which represents the importance of the attribute. Weights can be defined by decision-makers or by experts based on the specific problem characteristics.

The retrieved cases are decomposed into “attribute-value” facts. For example, if c_j is a retrieved case, then p facts are produced: fc_j1, fc_j2, …, fc_jp. Those facts, of all retrieved cases, constitute the retrieved facts set RFS = {c_jk, k = 1, p | c_j ∈ RCB}. After that, a set IN, which includes the given (initial) facts, the additional facts produced by the RBR component, and the facts produced from the retrieved cases, i.e. IN = FS ∪ AFS ∪ RFS, is produced. IN is fed to the PM layer.

PM is a process model, in the form of a Petri net N = (P,T,F), which is extracted during a preprocessing phase, by applying a process mining algorithm to the CB of the CBR layer. To this end, the Case Base Scheme of the CBR layer should be properly designed. Each case should be considered as or be transformed to an instance of a process. Thus, a subset of the attributes of a case should be properly organized to represent the events that constitute a process. The places in N represent value assignments to attributes of the problem. The facts in IN are fed to N, where new places are activated, that is new facts become true. So, the output of the last PM layer is a set of potential future facts: PFS = {ff₁, …, ff_r}, where for each ff_i there is a transition t_i so that (t_i, ff_i) ∈ F, and t_i is a fired transition. So, PFS includes potential future facts, which are justified by the current ones.

Summarizing the above, the sequential model retrieves the most relevant past cases by using similarity measures and reaches the (revised) output cases. The retrieved cases-processes are selected based on their similarity with the input case-process which, however, is usually described by the user taking into consideration only its first states. This is imposed by the nature of the real-life problems formed as a CBR model, i.e., the user needs to tackle a problem (case) he/she is facing, therefore only the basic characteristics (attributes) of the problem along with its first states are known.

The embedded model is responsible for the enrichment of the reasoner’s output, as a response to a user query, with the addition of possible future states of the input case. The key idea is to represent a case as an instance of a process, which is true in many real-life domains. Therefore, given the first states of a case, a process model can predict its possible future states (transitions). The embedded model of the proposed hybrid reasoner is based on a process model built during a preprocessing phase by process mining algorithms applied to the cases stored in the case base. The enrichment of the retrieved cases is achieved by following paths of enabled transitions from the start to the end of the Petri net.

5 Hybrid reasoning example

In this section, the reasoning process of the proposed hybrid model is demonstrated by the following example. Suppose that the set of stored cases (CB) is the one presented in the following Table 2. There are four attributes in each case: a numeric one (num_att), a categorical one (char_att), a categorical one (ontol_att) whose values are taken from the ontology shown in Fig. 3, a multivalued one (multi_att), and the attribute representing the action(s) taken (output).

Table 2 Example case base

Fig. 3

Example ontology

Also, suppose that RB = {r₁, r₂}, where.

• r₁: if char_att is s2 then ontol_att is n4

• r₂: if char_att is s1 then ontol_att is n2

Finally, suppose that the process model (PM layer) is represented by the Petri net diagram shown in Fig. 4.

Fig. 4

Example process model

To illustrate the reasoning process, let suppose that the input fact set to the proposed hybrid reasoner is FS = {f₁, f₂, f₃,f₄}, where

• f₁: num_att is 11

• f₂: char_att is s2

• f₃: multi_att is v3

• f₄: multi_att is v7

Then, rule r₁ is triggered, since its antecedent is true because of f₂. Therefore, the output of the RBR layer is the fact (conclusion):

af₁: ontol_att is n4

Afterwards, the CBR component checks the similarity of the input (f₁, f₂, f₃,f₄,af₁) with each one of the stored cases presented in Table 1. Consider the comparison of the input to the case with case_id = c4. It is calculated by comparing the corresponding values of each one of the four attributes.

First, to compare f₁ with the corresponding value of the numeric attribute num_att, i.e., 11 with 20, we calculate the normalized similarity (Eq. 1 in subSect. 2.2) as: 1-(|20–11|/(25–5)) = 0.55, since the minimum value of num_att is 5 while its maximum value is 25.

Then, to compare f₂ with the corresponding value of the categorical attribute char_att, i.e., s₂ with s₁, we calculate the Eskin similarity measure (Eq. 2 in subSect. 2.2) as: 3²/(3² + 2) = 0.82, since the attribute char_att accepts 3 different values (s₁, s₂, s₂).

Next, to compare af₁ with the corresponding value of the attribute ontol_att, i.e., n4 with n3, we calculate the similarity measure of Eq. 4 in subSect. 2.2 based on the given ontology as: 1-(1/3) x avg((3–3)/4, (4–3)/4) x (1/(4 + 4)) = 0.99, since i) the nearest common father node of n3 and n4 is n3 (level 3), ii) the length of the maximum path from root to leaf that contains n4 is 4, iii) the length of the maximum path from root to leaf that contains n3 is 4, iv) the length of the directed path connecting n4 and n3 is 1.

Finally, to compare f₃ with the corresponding values of the multivalued attribute multi_att, i.e., v₃, v₇ with v₆, v₇, v₈, we calculate the Jaccard similarity (Eq. 3 in subSect. 2.2) as: a/(a + b + c) = 1/(1 + 2 + 1) = 0.25, since i) the number of common items in both sets is a = 1, ii) the number of items that appear exclusively in the first set is b = 2, iii) the number of items that appear exclusively in the second set is c = 1.

To calculate the final similarity, we calculate the weighted average of the similarities of each attribute. In this example, we assume that all attributes are equally significant, thus the final similarity is their average: (0.55 + 0.82 + 0.99 + 0.25) /4 = 0.65.

Similarly, we calculate the similarity with the other cases and the CBR layer outputs the two most similar to the input cases, i.e., those with case_id = c2 and case_id = c5 and output values o₂ and o₅ respectively.

Continuing, the PM layer will also output the o₃ action, given that after applying o₅ action to the Petri net, the n3 concept will be true, based on the path of enabled transitions o₅ → t₁ → n3 → t₂ → o₃.

As mentioned earlier, in the proposed hybrid architecture, as well as in the example presented here, CBR is the primary component for inference. The RBR component is used to enhance the input case and the PM component is used to generate additional output values based on temporal data. To underscore the importance of the full hybrid architecture, we can examine the example above, considering the impact if one of the components were missing.

For instance, if the RBR component, which represents general domain knowledge, were not used, the input case would not be enhanced with the values for the attribute ontol_att. Without this enhancement, the CBR component would deduce that case 1 is more similar to the input case than case 2, so the system would produce as output the value o1 instead of o2.

On the other hand, if the PM component, that represents temporal data and transitions extracted from the cases, were absent, the additional output value o3 would not be generated.

6 Architecture and workflow of pavefs

The proposed hybrid reasoner is used to develop PAVEFS,² an intelligent information system for the diagnosis and care of individuals facing autism spectrum disorders (ASD). PAVEFS is based on both scientific knowledge and good practices concerning ASD, acquired from many experts and caregivers of various specializations. PAVEFS aims at the creation of an extended basis of specialized and reliable information relevant to care procedures of individuals with ASD.

Since the proposed hybrid reasoner is built into the PAVEFS system, a standalone experimental application is developed that can be used to apply the proposed hybrid reasoner to any domain. The application is freely available through the link: https://aigroup.ceid.upatras.gr/hybrid. Also, a publicly available github folder (https://github.com/kkovas12/hybrid-pavefs) has been created including the code of this application.

The system’s architecture is mainly based on users’ (specialized/experts, analysts/investigators, regular and advanced end users) access (both information and responses to queries) through PC, laptop, smart phones, tablets, VoiP, IVR, smart TVs, Fax, OCR. A specially designed form facilitates experts to introduce rules/exceptions and cases concerning both behaviors and care procedures to the system’s knowledge base, while users insert profiles and then submit questions (queries), also through a specially designed form. In general, taking into consideration the profile of an individual facing ASD, as well as the characteristics of her/his specific behaviors described in the question, the system searches in the knowledge base for similar cases. Finally, after processing similar cases, the system returns both the similar cases along with certain successful interventions per behavior and possible future reactions to the suggested interventions.

The antecedents/consequences of rules, the various attributes of cases, the places of the process model, the user profiles as well as the user queries, borrow values from a common dictionary of terms that form an ASD Ontology presented in [51]. The ASD Ontology is a hierarchical tree of concepts relevant to autism, aiming to cover all the necessary terms needed to represent both rules (conditions and conclusions), cases (specific events and the way they are confronted) and the process model (behaviors and interventions). This hierarchy connects more general terms with their more specific sub-categories. In terms of a graph, the ASD ontology allows to compare two terms calculating their similarity based on their distance in the graph, as it is presented in subSect. 6.2.

The ontology tree consists of classes, subclasses, subsubclasses and nodes, thus its depth is 4. The ASD Ontology includes six (6) basic classes (Age, Antecedents, Binaries, Description of Event, Outcome and Profile Information). For instance, the fifth class “Outcome” consists of four subclasses (Person, Response, Restrictions, and Risks). The “Person” subclass includes four nodes while “Response” subclass contains nine subsubclasses and eighteen nodes, referring to all the possible responses in the ASD.

The use of ASD Ontology supports a friendly user interface (detailed definitions are assigned to each node/term of the ontology), while the size and the depth of the ontology tree do not affect time complexity. The ASD Ontology is maintained as an OWL file. The OWL ontology is used only as a hierarchy of terms, thus there is no need to utilize some advanced inference engine that would affect the performance of the system.”

The ASD ontology is accessed each time a query is inserted by the user and a number of cases are retrieved as a response to this query. Thus, the key idea behind the reasoning system of PAVEFS is, given some problematic behavior(s), to trigger the related rules and then to retrieve the most similar cases, in order to automatically adapt the corrective responses that were used in such cases and to suggest suitable interventions. Also, the PM layer suggests possible reactions to the suggested interventions, based on the given process model.

6.1 The RBR layer of PAVEFS

The stored rules concern characteristics of profiles. behaviors, context, reactions to specific stimuli/conditions and restoration procedures. The RBR layer in PAVEFS is mainly used to enhance input with additional information, in order to support the detection of similar stored cases so that to output response actions.

The PAVEFS' RB includes rules originated by the experts’ team and by scientific studies on the confrontment of autistic behaviors. Rules are related to terms of the ASD ontology, and whenever an expert creates a new rule, she/he has to navigate through the ASD ontology and select specific terms for the antecedents/consequences of the rule.

Since interventions to specific ASD behaviors are highly personalized, there are not a lot of rules in PAVEFS’s RB. However, testing the set of rules was a crucial task in order to detect interconnections and cycles/loops. To support testing, an RDF graph is generated in order to visualize RB. The nodes of the RDF graph represent either whole rules or antecedents/consequences of a rule as terms of the ASD ontology. The edges of this RDF graph represent either an “is an antecedent” or an “is a consequence” relation between a rule and a term (nodes). The “Visual Browser” application is used to visualize the generated RDF graph. Figure 5 displays a part of the RDF graph with a few rules (orange nodes) and terms of the ontology (blue nodes). The green edges represent the “is an antecedent” relation and the purple ones the “is a consequence” relation.

Fig. 5

Part of the rules RDF graph

Testing RB is supported by detecting the nodes that are included in both “is an antecedent” and “is a consequence” relations, since they could potentially lead to cycles or chained rule triggers. Then, nodes with only adjacent green edges (always conditions) or only adjacent purple ones are removed. This process results in a simplified graph, where only a part of the initial terms is present, i.e., those that had been used both as antecedents and consequences.

Exceptions can be added to rules of PAVEFS’s RB, in order to allow experts to express exceptions in firing a rule. Exceptions can also be added to personalized rules (dedicated to a certain individual) by end users, as a result of an assessment of the proposed by PAVEFS interventions. Thus, exceptions added to rules can cause specific rules not to trigger or to remove part of their consequences or even to transform some of their consequences.

The inference engine of PAVEFS’s RBR layer also use the ASD ontology in order to fire rules. More specifically, in order to check the existence of an antecedent of a rule, the inference engine checks also the existence of its very closed terms with respect to the ASD ontology, based on a user defined threshold. Thus, a rule can be triggered not only when its antecedents hold, but also if some adequately similar terms hold.

Therefore, PAVEFS’s RBR layer enhances the input knowledge by populating it with additional facts provided by the consequences of fired rules, while exceptions may be also triggered as well modifying these consequences.

6.2 The CBR layer of PAVEFS

The Case Based reasoner is the main component of the proposed model. Given an input, after it is enhanced by the RBR layer, the CBR layer detects the most relevant cases from the stored ones in PAVEFS’s knowledge base.

In PAVEFS, a case includes all the relevant information regarding an autism related incident. The attributes of a case can be grouped into those that refer to: Individual's Profile and History, Event Environment and Involved People, Antecedents, Behaviors, Response Actions, and Risks. The stored cases represent autism related incidents and how they were resolved by specific response actions. CB is populated either by experts or by users (see Fig. 6 for case insertion interface).

Fig. 6

User interface concerning adding a new case

Most of the stored cases (about 3.000) were initially set by experts in various fields concerning caring people with ASD (see Sect. 7) after processing real incidents characterized as good practices. Although the recorded data are anonymized, the consent of those that hold parental responsibility for the data subjects is given by a clear, specific, informed, and unambiguous statement that signifies agreement to the processing of personal data relating to incidents.

Also, there are cases directly inserted in CB, upon users’ prompt, as incidents describing user queries and their corresponding system response, after being approved by the experts. Therefore, as CB is growing the system is becoming more accurate.

A case also includes temporal data since data of up to three sequential behavior-response time periods can be inserted in a case (see Fig. 7 for corresponding user interface). Thus, it is possible to represent how the behaviors changed after specific response actions. There are many incidents where, after an initial response about a specific behavior, the behavior itself or some parameters of it were modified, or another one was added. Temporal data help to represent such kinds of relations and to match similar cases. Also, temporal data form the basis of the Process Mining layer, presented later.

Fig. 7

User interface concerning the input of behaviors over three periods

Given the large number of different attributes that represent a case and the fact that each case may contain multiple parallel and sequential sets of behaviors, the comparison between two different cases, i.e., to calculate a representative overall similarity measure, was one of the most challenging and complicated parts of the system. It required a lot of fine tuning to achieve optimal results.

In order to calculate an overall similarity measure, during comparing two cases, most of the attributes of a case are taken into account. Some attributes of a case are not considered, such as the names of the individuals or experts and the date of the event. For each one of the attributes considered, a different method is used to get similarity, based on its type (as presented in Sect. 2.2).

To describe the behaviors exhibited by an individual during an incident, the experts can select attributes for up to five specific behaviors for each one of the three behavior-response time periods. Most of the attributes taken into consideration in calculating case similarity concern the representation of behaviors. Each specific behavior is represented by 28 attributes organized to three groups: Antecedent, Description of Event, Outcome.

There are seven categorical attributes that take as value a single term from the PAVEFS ontology. For three out of seven attributes, similarity is calculated by using expert defined similarity tables that store the similarity for each different pair of attribute values. For the rest four attributes, similarity is obtained based on the distance of the terms in the PAVEFS Ontology. More specifically, we use the distance presented in [15]. For each such a categorical attribute, there is a corresponding part of the PAVEFS ontology that represents the terms used as its values. Ontology over an attribute c_i is a directed acyclic tree Tc_i = (N, E), where N is the set of nodes and E is the set of edges such that every e_i ∈ E is an ordered pair (n_k, n_l), and n_k, n_l ∈ N. Every node n_i ∈ N represents a possible attribute value. The dissimilarity between any two terms/values is represented by the distance between the corresponding nodes of the tree structure, as it is presented in subSect. 2.2.

Also, there are ten attributes that accept binary values (TRUE/FALSE). Similarity for these attributes is set to 1, if they matched, and to 0 otherwise.

Finally, there are eleven multivalued attributes: five attributes accept up to two values, four attributes accept up to three values, two attributes accept up to four values. To compare similarity for these attributes, similarity measures for sets are exploited. Such measures are based on the following parameters to calculate a similarity value between two sets:

• a: the number of elements that are present in both sets

• n₁: the number of elements in the first set

• n₂: the number of elements in the second set

• b: the number of elements present in set1 but not in set2 (b = n₁-a)

• c: the number of elements present in set2 but not in set1 (c = n₂-a)

• d: the number of elements that are not present in either set

In order to calculate the above parameters, the distance of the terms in the ontology is also taken into account. For each multivalued attribute, there is an associated user defined threshold that indicates how close in the ontology two terms/values should be in order to be considered.

In PAVEFS, the implemented similarity measures are the following: JACCARD [14, 52] SORENSEN-DICE [53,54,55], OTSUKA-OCHIAI [56], BRAUN-BLANQUET [57], SIMPSON [58, 59], SOKAL & SNEATH [60], KULCZYNSKI2 [61], MATCHING [62, 63], RUSSELL [64], HAMANN [65], SNEATH [66], ROGERS &TANIMOTO [67]. For each individual attribute of a case, the most suitable similarity measure from the above is selected, based on extended testing during developing PAVEFS.

Since a case can include up to five specific behaviors for each one of the three behavior-response time periods, in order to calculate the overall similarity, a best match of different period is detected in a first phase, based on the behaviors of each period. For example, the behaviors of the first period of the first case may have higher similarity with the behaviors of the second period of the second case. All the possible combinations of periods are considered and the one that produces the higher similarity score is selected. We favor the combinations that match in more periods. For example, if a combination only finds similarity in one of the three periods, the similarity score would be multiplied by 0.8. Then, the selected combination is used to calculate the similarity for attributes representing behaviors. For each matching period, two sets (set₁ and set₂) up to five behaviors are compared. If there are identical behaviors across the two sets, they are compared based on the corresponding 28 attributes. Then, those behaviors are removed from the two sets and the remaining behaviors are checked based on their distance in the ASD ontology. Finally, the matched behaviors are compared based on the corresponding 28 attributes.

The following pseudocode describes the procedure:

Finally, variables a, b, c, and d are used to calculate a single similarity value for the Behaviors based on the above multivalued set metrics. This procedure is repeated for each matching period and then we take a weighted average (we assume that behaviors in the later periods are more important). This way we reach a single similarity value for the behaviors of the two cases, and we combine it with the previous similarity values (e.g., Risk History, Diagnoses) using again a weighted average. All weights used have been determined in cooperation with domain experts after trial-and-error iterative processes.

Apart from the above 28 fields that represent behaviors, there are also 6 attributes that represent the time of the event and the involved individual. Three of them are numerical, one is categorical and two are multivalued. More specifically, there are three numerical attributes concerning the age of the individual, the time of the day the event happened (0–24), and its duration (as it is resulted in milliseconds by the exact Start–End time). For all these fields, the normalized distance is used.

Moreover, there is a categorical attribute representing the gender of the involved individual. Similarity is calculated by using an expert defined similarity table that stores the similarity for each one of the four different pairs of attribute values.

Finally, there are two multivalued attributes that represent Risk History and Diagnosis data. In each one of them, up to five values can be inserted. Similarity is calculated as described above. The distance of the terms in the ontology is also considered. For each multivalued attribute, there is an associated user defined threshold that indicates how close in the ontology two terms/values should be to be considered as similar.

Finally, after calculating similarity for each one of the 37 attributes, the weighted average is used to calculate the overall similarity: for each attribute a there is a corresponding weight representing its importance. The weights were determined after an initial evaluation phase by experts and subsequently after extended trial tests, in order to optimize the result, thus for two cases i,j:

Overall Similarity(i,j) = $\sum_{a=1}^{n} ({ SIMILARITY}_{ij} \times {WEIGHT}_{a })$

Thus, the CBR Layer will match the enhanced input to the most similar previous cases in the Case Base and produce revised interventions for each behavior, which are fed to the final PM layer of the hybrid system.

Regarding the temporal data represented by the subsequent transitions of behaviors of the involved individual over up to three periods, they are used to identify patterns of behaviors-responses that happen concurrently or subsequently (see next subSect. 6.3).

6.3 The PM layer of PAVEFS

The PM Layer of PAVEFS is based on a process model built during a preprocessing phase based on the cases stored in the Case Base of the CBR Layer. It is built by using a process mining algorithm designed specifically for the PAVEFS, however any other process mining algorithm can be used instead [68]. The process model is built based on selected cases of the Case Base, which were inserted by very experienced experts in the field of ASD care.

The representation of a case as an instance of a process is based on the temporal data included in the case, as described above. A case can include a set of behavior-intervention pairs for each of up to three different sequential time periods. The first period includes the initial behavior- intervention pair(s), while the other two time periods include behavior- intervention pair(s) representing how the behaviors changed after specific response actions. In caring people with ASD, it is usual that after an initial response concerning an initial behavior either this behavior itself or some of its parameters are changed or a new behavior is triggered because of this response.

Thus, a behavior and its corresponding responses can be represented by transitions in a Petri net diagram while a behavior-intervention pair is represented by a workflow trace. Workflow traces are also used to represent the different sequential time periods, i.e., changes of behaviors because of certain responses through time.

6.4 Pavefs architecture

The architecture of PAVEFS is actually the one presented in Fig. 2, a 3-layer hybrid CBR-RBR-PM reasoner, where the cased based reasoner is the main component, with the most crucial role. Also, a rule-based reasoner utilizes rules provided by the experts to enhance the knowledge in the case base by populating it with additional values. Rules also include specific exceptions, provided both by the experts and extracted from the history of stored cases. CBR layer outputs the most similar cases to the ASD problem at hand, whereas PM outputs possible future consequences of the actions suggested by the most relevant extracted cases.

Java programming language is used for the core mechanisms of the PAVEFS hybrid system. The back end is based on the Yii framework (PHP), while data (users, cases, rules, etc.) are stored in a MYSQL database instance. PHP, HTML and Javascript are used for the front-end.

The following example demonstrates the reasoning process of PAVEFS system based on the proposed hybrid model. The example is simplified, in the sense that only a small subset of features is included as shown in Table 3, since there is a large number of features needed to represent a case in the PAVEFS system.

Table 3 Selected features

Note, that each case corresponds to a description of an event concerning certain behaviors exhibited by an individual in autistic spectrum during an incident along with certain successful interventions for these behaviors. The “Age”, “Diagnosis” and “Risk Factor” features refer to the individual in autistic spectrum that was involved in the incident and would be drawn from her profile record. The features “Specific Triggers”, “Behavior” and “SuggestedResponse” describe the behavior.

The feature “SuggestedResponse” stores the successful response to the “Behavior”, during the incident. Finally, the feature “BehaviourPrediction” holds the possible future reactions to the “SuggestedResponse”. The feature “BehaviourPrediction” is not included in the stored cases, and it is filled by the Process Model. In Table 3, the individual features, their value type, as well as weight values that represent their significance when comparing cases, are shown.

The values of “Behavior” and “BehaviorPrediction” are taken by the branch of the ASD Ontology shown in Fig. 8.

Fig. 8

Part of the ASD ontology

We consider the simplified stored cases shown in Table 4, that are used in the CBR component of the PAVEFS system:

Table 4 Simplified cases

We also consider the set of Rules shown in Table 5, which are provided by Experts and concern general knowledge about the domain and suggested responses:

Table 5 Selected rules

Finally, we consider the part of the PAVEFS Process Model, shown as a PetriNet in Fig. 9. It has previously been trained to identify patterns of Behaviors and Responses.

Fig. 9

Part of PAVEFS process model

The reasoning procedure starts inserting the input incident to the system. As an example, we consider the following input incident:

• AGE = 10

• DIAGNOSIS = Autistic Disorder

• RISK FACTOR = Communication Difficulties

• SPECIFIC TRIGGERS = Change in Environment

• INITIAL BEHAVIOR = Self-Injurious Behavior

The first step of the inference procedure is to run the RBR component, using the rules shown in Table 4. The conditions of rule R3 are met, so the rule is triggered, and the input is updated with:

SUGGESTED RESPONSE = Functional Assessment

Then, the CBR component is executed, and it compares the input against all the cases shown in Table 3. The case with the highest match is case C1. The similarity is estimated using the corresponding similarities for the five features: For “Age”, assuming a valid range for age of 5 to 55, the similarity is calculated as 1-(|10–15|/(55–5)) = 0.9. For “Diagnosis” and “RiskFactor”, since C1 has the same values as the input, we assume a similarity value of one. For “SpecificTriggers”, we use the Jaccard formula and we have one common value between the two sets, so the similarity is calculated as a/(a + b + c) = 1/(1 + 1 + 0) = 0.5. Finally, for “Behavior” we use the distance of the corresponding nodes (Hair Pulling, Self-Injurious Behavior) in the Ontology as: 1-(1/3) × avg((3–3)/3, (4–3)/3) × (1/(3 + 3)) = 0.99, since (i) the nearest common father node is of level 3, (ii) the length of the maximum path from root to leaf that contains the first node is 3, (iii) the length of the maximum path from root to leaf that contains the second node is 3, (iv) the length of the directed path connecting the two nodes is 1. Finally, we combine the individual similarity values using the weights, so we get the final similarity value as (0.1 × 0.9) + (0.2 × 1,0) + (0.2 × 1,0) + (0.2 × 0,5) + (0.3 × 0.99) = 0.89. Thus, the output of the PAVEFS system is the value of “SuggestedResponse” of case C1:

SUGGESTED RESPONSE = Interruption and redirection

Finally, the Process Model is used and there is a path of enabled transitions (t1- > t2- > t3), which predicts a possible respond behavior:

BEHAVIOUR PREDICTION = Shouting

Although the PAVEFS system can be freely accessed (http://pavefs-cms.upatras.gr/user/auth/login) a publicly available github folder (https://github.com/kkovas12/hybrid-pavefs) has been created including three (3) certain queries to PAVEFS, in the format that the UI of PAVEFS uses, along with the corresponding suggested interventions and similar cases.

7 Model evaluation

The evaluation of the proposed hybrid reasoning model is performed through the evaluation of the PAVEFS system. During Beta Testing, accuracy is tested, along with functionality and reliability.

The evaluation process for testing accuracy was performed as follows:

• 1. A group of 42 experts in supporting people with ASD was formed, consisting of 14 psychologists, 1 psychologist & music therapist, 12 special needs caregivers, 3 pediatric psychiatrists, 3 ergo therapists, 3 logo therapists, 3 mental health social workers, 3 special needs gymnastics. All the experts had an extensive experience in caring people with ASD within Homes for Semi-independent Living as well as Day Centers in Greece (35 experts) and in UK (7 experts).

• 2. Experts were asked to enter queries to PAVEFS as regular users. Each query refers to a real case where certain behaviors of a specific individual with ASD should be handled. 358 queries based on real incidents entered into PAVEFS.

• 3. Experts were asked to evaluate the proposed interventions returned by PAVEFS as (i) Fully Accepted (all the proposed interventions are proper to handle the incident), (ii) Partially Accepted (most of the proposed interventions are proper to handle the incident), (iii) Problematic (most of the proposed interventions are not proper to handle the incident), (iv) No Response (there is no proposed interventions at all).

Experimental results demonstrated that 61% of the proposed interventions were Fully Accepted, 21% were Partially Accepted, 10% were stated as Problematic, while 8% of the queries remained without a response by PAVEFS because there was no relevant knowledge available in the knowledge base.

Given that 8% of queries remained without response by PAVEFS, due to lack of corresponding knowledge, the system was successful in 82 out of 92 of queries (82/92), which calculates in 89,13%.

Note that, after the evaluation phase, the Case Base of PAVEFS was enriched with proper cases in order to propose interventions for the 8% of the queries that initially had no response. Also, for the incidents to which the system responded problematically (10% of the queries), the corresponding cases were detected and corrected by the experts.

8 Conclusions

RBR and CBR have been widely used together in systems with quite successful results. In the proposed 3-layer model apart from RBR and CBR, PM is also combined. The approach presented in this paper, is a mixture of tightly sequential (RBR-CBR) and embedded processing (CBR-PM) coupling models. CBR is the primary component in the embedded processing (sub)model, whereas PM is embedded in the “retrieve” phase of CBR. CBR is also the basic component of the whole model.

We investigated the application of the proposed hybrid reasoning model to the diagnosis and care of individuals facing autism spectrum disorders (ASD), developing the PAVEFS system. The evaluation of PAVEFS, and hence of the proposed hybrid reasoning model, is also presented.

The proposed hybrid reasoning model is effective in reasoning about domains including both a limited set of general rules and extensive specific knowledge that can be formed as a sequence of actions-reactions. In such domains, it is also of great importance to forecast the reactions triggered after the user follows the consequences derived automatically by a reasoner.

Autism Spectrum Disorders is exactly such a domain. What makes autism challenging for services is that the range and level of function is so variable (although core features are similar in all) and thus the service needs range across every type and place of service provision available [69].

Actually, no single intervention had a positive effect for all child and family outcomes of interest.

Within a biopsychosocial model of disability, the challenges to learning and participation experienced by autistic children are seen to arise from a combination of factors related to the individual (i.e. body structures and functions) and the environment (e.g. a lack of universal design, how supports are delivered) [70].

The RBR layer of PAVEFS consists of a limited set of rules (see subSect. 6.1) while the CBR layer of PAVEFS consists of a great number of cases (see subSect. 6.2). Also, it is crucial, while caring for people with ASD, to forecast how the behaviors will be changed after specific response actions. The PM layer of PAVEFS is used in order to take into consideration possible future behaviors triggered because of current interventions recommended by PAVEFS (see subSect. 6.3).

There are also similar to ASD domains, such as caring for people with dementia or drug addiction. In general, the health sector is a domain where progressively hybrid reasoning systems are applied. As the objective of e-health is inter alia the improvement of prevention, diagnosis, treatment, and the provision of better health management hybrid systems, contribution to this end is undoubtedly valuable to the improvement of the quality of life for the patients.

By applying the proposed hybrid reasoning model to the PAVEFS system, a system for handling ASD cases, seems that the proposed model is effective in reasoning about domains with a limited set of general rules and an extensive subdomain of specific knowledge that can be formed as a sequence of actions-reactions.

The future challenges of the research team are: (i) to expand the application of the proposed hybrid reasoning model to other e-health systems, in order to contribute to the provision of better service quality and to increase the performance and effectiveness in the public health sector and (ii) to test and adjust the proposed hybrid reasoning model to other sectors that require systematic analysis of complex data and personalized interventions for decision making.