Intuitionistic fuzzy recommender systems: An effective tool for medical diagnosis

Highlights

• We presented a novel intuitionistic fuzzy recommender system for medical diagnosis.

• New definitions of fuzzy matrices and similarity degrees with theorems were shown.

• A novel intuitionistic fuzzy collaborative filtering method was proposed.

• The proposed algorithm could handle the limitations of the relevant works.

• It had better accuracy than other algorithms in many types of datasets.

Abstract

Medical diagnosis has been being considered as one of the important processes in clinical medicine that determines acquired diseases from some given symptoms. Enhancing the accuracy of diagnosis is the centralized focuses of researchers involving the uses of computerized techniques such as intuitionistic fuzzy sets (IFS) and recommender systems (RS). Based upon the observation that medical data are often imprecise, incomplete and vague so that using the standalone IFS and RS methods may not improve the accuracy of diagnosis, in this paper we consider the integration of IFS and RS into the proposed methodology and present a novel intuitionistic fuzzy recommender systems (IFRS) including: (i) new definitions of single-criterion and multi-criteria IFRS; (ii) new definitions of intuitionistic fuzzy matrix (IFM) and intuitionistic fuzzy composition matrix (IFCM); (iii) proposing intuitionistic fuzzy similarity matrix (IFSM), intuitionistic fuzzy similarity degree (IFSD) and the formulas to predict values on the basis of IFSD; (iv) a novel intuitionistic fuzzy collaborative filtering method so-called IFCF to predict the possible diseases. Experimental results reveal that IFCF obtains better accuracy than the standalone methods of IFS such as De et al., Szmidt and Kacprzyk, Samuel and Balamurugan and RS, e.g. Davis et al. and Hassan and Syed.

Introduction

In this section, we formulate the medical diagnosis problem and give some illustrated examples in Section 1.1. Section 1.2 describes the relevant works using the intuitionistic fuzzy sets for the medical diagnosis problem. Section 1.3 summarizes the limitations of those relevant works, and based on these facts the motivation and ideas of the proposed approach are highlighted in Section 1.4. Section 1.5 demonstrates our contributions in details, and their novelty and significance are discussed in Section 1.6. Lastly, Section 1.7 elaborates the organization of the paper.

Medical diagnosis has been being considered as one of the most important and necessary processes in clinical medicine that determines acquired diseases of patients from given symptoms. According to Kononenko [20], diagnosis commonly relates to the probability or risk of an individual developing a particular state of health over a specific time, based on his or her clinical and non-clinical profile. It is useful to minimize the risk of associated health complications such as osteoporosis, small bowel cancer and increased risk of other autoimmune diseases. Mathematically, its definition is stated as follows.

Definition 1 Medical diagnosis

Given three lists: P = {P₁, …, P_n}, S = {S₁, …, S_m} and D = {D₁, …, D_k} where P is a list of patients, S a list of symptoms and D a list of diseases, respectively. Three values n, m, k ∈ N⁺ are the numbers of patients, symptoms and diseases, respectively. The relation between the patients and the symptoms is characterized by the set- $R_{\mathit{PS}}=\{R^{\mathit{PS}}(P_i\text{,}{S}_j)|\forall i=1\text{,}\dots \text{,}n\text{;}\forall j=1\text{,}\dots \text{,}m\}$ where R^PS(P_i, S_j) shows the level that patient P_i acquires symptom S_j and is represented by either a numeric value or a (intuitionistic) fuzzy value depending on the domain of the problem. Analogously, the relation between the symptoms and the diseases is expressed as $R_{\mathit{SD}}=\{R^{\mathit{SD}}(S_i\text{,}{D}_j)|\forall i=1\text{,}\dots \text{,}m\text{;}\forall j=1\text{,}\dots \text{,}k\}$ where R^SD(S_i, D_j) reflects the possibility that symptom S_i would lead to disease D_j. The medical diagnosis problem aims to determine the relation between the patients and the diseases described by the set- $R_{\mathit{PD}}=\{R^{\mathit{PD}}(P_i\text{,}{D}_j)|\forall i=1\text{,}\dots \text{,}n\text{;}\forall j=1\text{,}\dots \text{,}k\}$ where R^PD(P_i, D_j) is either 0 or 1 showing that patient P_i acquires disease D_j or not. The medical diagnosis problem can be shortly represented by the implication $\{R_{\mathit{PS}}\text{,}{R}_{\mathit{SD}}\}\to R_{\mathit{PD}}$.

Example 1

Consider the dataset in [31] having four patients namely P = {Ram, Mari, Sugu, Somu}, five symptoms S = {Temperature, Headache, Stomach-pain, Cough, Chest-pain} and five diseases D = {Viral-Fever, Malaria, Typhoid, Stomach, Heart}. The relations between the patients – the symptoms and the symptoms – the diseases are illustrated in Table 1, Table 2, respectively.

The relation between the patients and the diseases determined by the medical diagnosis is illustrated in Table 3. Since the domain of the problem is the intuitionistic fuzzy values, this relation is also expressed in this form. The most acquiring disease that the patients suffer is expressed in Table 4, which is converted from Table 3 by a trivial defuzzification method considering the maximal membership degree of disease among all.

Medical diagnosis is considered as an efficient support tool for clinicians to make the right therapeutical decisions especially in the cases that medicine extends its predictive capacities using genetic data [5]. As being observed in Table 3, medical diagnosis could assist the clinicians to enumerate the possible diseases of patients accompanied with certain membership values. Thus, it is convenient for clinicians, who are experts in this field, to quickly diagnose and give proper medicated figures. This fact clearly shows the importance of medical diagnosis in medicine sciences nowadays.

Computerized techniques for medical diagnosis such as fuzzy set, genetic algorithms, neural networks, statistical tools and recommender systems aiming to enhance the accuracy of diagnosis have been being introduced widely [20]. Nonetheless, an important issue in medical diagnosis is that the relations between the patients – the symptoms (R_PS) and the symptoms – the diseases (R_SD) are often vague, imprecise and uncertain. For instance, doctors could faced with patients who are likely to have personal problems and/or mental disorders so that the crucial patients’ signs and symptoms are missing, incomplete and vague even though the supports of patients’ medical histories and physical examination are provided within the diagnosis. Even if information of patients are clearly provided, how to give accurate evaluation to given symptoms/diseases is another challenge requiring well-trained, copious-experienced physicians. These evidences raise the need of using fuzzy set or its extension to model and assist the techniques that improve the accuracy of diagnosis. The definition of fuzzy set is stated below.

Definition 2

A Fuzzy Set (FS) [49] in a non-empty set X is a function

$$\begin{array}{c}\mu :X\to [0\text{,}1]\hfill \\ x\mapsto \mu (x)\text{,}\hfill \end{array}$$

where μ(x) is the membership degree of each element x ∈ X. A fuzzy set can be alternately defined as,

$$A=\{〈x\text{,}\mu (x)〉|x\in X\}\text{.}$$

An extension of FS that is widely applied to the medical prognosis problem is Intuitionistic Fuzzy Set (IFS), which is defined as follows.

Definition 3

An Intuitionistic Fuzzy Set (IFS) [4] in a non-empty set X is,

$$\stackrel{\sim }{A}=\left\{〈x\text{,}{\mu }_{\stackrel{\sim }{A}}(x)\text{,}{\gamma }_{\stackrel{\sim }{A}}(x)〉|x\in X\right\}\text{,}$$

where ${\mu }_{\stackrel{\sim }{A}}(x)$ and ${\gamma }_{\stackrel{\sim }{A}}(x)$ are the membership and non-membership degrees of each element x ∈ X, respectively.

$${\mu }_{\stackrel{\sim }{A}}(x)\text{,}{\gamma }_{\stackrel{\sim }{A}}(x)\in [0\text{,}1]\text{,}\forall x\in X\text{,}$$

$$0⩽{\mu }_{\stackrel{\sim }{A}}(x)+{\gamma }_{\stackrel{\sim }{A}}(x)⩽1\text{,}\forall x\in X\text{.}$$

The intuitionistic fuzzy index of an element showing the non-determinacy is denoted as,

$${\pi }_{\stackrel{\sim }{A}}(x)=1-{\mu }_{\stackrel{\sim }{A}}(x)+{\gamma }_{\stackrel{\sim }{A}}(x)\text{,}\forall x\in X\text{.}$$

When ${\pi }_{\stackrel{\sim }{A}}(x)=0$ for ∀x ∈ X, IFS returns to the FS set of Zadeh.

Some extensions of fuzzy sets are not appropriate for modeling uncertainty in the medical diagnosis such as the rough set [28], rough soft sets [11], [12], [16], intuitionistic fuzzy rough sets [50] and soft rough fuzzy sets & soft fuzzy rough sets [23]. The limitations of these sets, as pointed out by Yao [48], Rodriguez et al. [30], Jafarian and Rezvani [17] and many other authors lie to their intrinsic nature and how they are organized and operated such as (i) The positive and the boundary rules are considered in rough sets and their variants so that in cases of many concepts, the negative rules would be redundant; (ii) The modeling of linguistic information is limited due to the elicitation of single and simple terms that should encompass and express the information provided by the experts regarding the a linguistic variable; (iii) if exact membership degrees cannot be determined due to insufficient information then it is impossible to consider the uncertainty on the membership function. Thus, these types of fuzzy sets could not be used for the application of medical diagnosis.

The first approach for the medical diagnosis problem was drawn from the Sanchez’s notion of medical knowledge [32]. Since then several improvements of the Sanchez’s approach in association with IFS and other advanced fuzzy sets have been introduced. De et al. [9] fuzzified the relations between the patients – the symptoms and the symptoms – the diseases by intuitionistic fuzzy memberships and derived the relation between the patients and the diseases by means of intuitionistic fuzzy relations. The algorithm contains the following steps.

• Calculate the relation between the patients and the diseases by intuitionistic fuzzy relations with the membership and non-membership functions being expressed in Eqs. (7), (8), respectively.

  $${\mu }_{\mathit{PD}}(P_i\text{,}{D}_j)={\displaystyle \underset{l=\overline{1\text{,}m}}{\max }}\left\{\min \{{\mu }_{\mathit{PS}}(P_i\text{,}{S}_l)\text{,}{\mu }_{\mathit{SD}}(S_l\text{,}{D}_j)\}\right\}\text{,}\forall i\in \{1\text{,}\dots \text{,}n\}\text{,}\forall j\in \{1\text{,}\dots \text{,}k\}\text{,}$$

  $${\gamma }_{\mathit{PD}}(P_i\text{,}{D}_j)={\displaystyle \underset{l=\overline{1\text{,}m}}{\min }}\left\{\max \{{\gamma }_{\mathit{PS}}(P_i\text{,}{S}_l)\text{,}{\gamma }_{\mathit{SD}}(S_l\text{,}{D}_j)\}\right\}\text{,}\forall i\in \{1\text{,}\dots \text{,}n\}\text{,}\forall j\in \{1\text{,}\dots \text{,}k\}\text{.}$$

• Perform the defuzzification through the S_PD,

  $$S_{\mathit{PD}}={\mu }_{\mathit{PD}}-{\gamma }_{\mathit{PD}}\times {\pi }_{\mathit{PD}}\text{.}$$

• Determine the most acquiring diseases of patients based on the maximal S_PD and minimal π_PD.

Example 2

Consider the dataset in Example 1. The relation between the patients and the diseases calculated by Eqs. (7), (8) is expressed in Table 5. The S_PD matrix is described in Table 6. Based upon this table, Ram, Sugu and Somu suffer from the Malaria and Mari acquires Stomach the most.

Samuel and Balamurugan [31] improved the method of De et al. [9] by a new technique named intuitionistic fuzzy max–min composition. This method is analogous to that of De et al. [9] except that Steps 2 & 3 are replaced by,

• Compute $W_{\mathit{PD}}=({\mu }_{\mathit{PD}}\text{,}1-{\gamma }_{\mathit{PD}})$.

• For each P_i find ${\max }_j\{\min ({\mu }_{\mathit{PD}}(P_i\text{,}{D}_j)\text{,}1-{\gamma }_{\mathit{PD}}(P_i\text{,}{D}_j))\}$ and conclude the most acquiring diseases.

Example 3

Consider again the dataset in Example 1. The W_PD matrix is shown in Table 7. The reduction of W_PD is presented in Table 8. From this table, Ram, Sugu and Somu suffer from the Malaria and Mari acquires Stomach the most.

Another approach for the medical diagnosis is utilizing the distance functions to calculate the relation between the patients and the diseases from the relations between the patients – the symptoms and the symptoms – the diseases as described in [42], [43], [44], [19], [33]. The general activities of these algorithms are,

• Use the Hamming or Euclidean function to calculate the relation between the patients and the diseases as in Eqs. (10), (11), respectively.

  $$R^{\mathit{PD}}(P_i\text{,}{D}_j)=\frac{1}{2m}{\displaystyle \sum _{l=1}^m}\left(\left|{\mu }_{\mathit{PS}}(P_i\text{,}{S}_l)-{\mu }_{\mathit{SD}}(S_l\text{,}{D}_j)\right|+\left|{\gamma }_{\mathit{PS}}(P_i\text{,}{S}_l)-{\gamma }_{\mathit{SD}}(S_l\text{,}{D}_j)\right|+|{\pi }_{\mathit{PS}}(P_i\text{,}{S}_l)-{\pi }_{\mathit{SD}}(S_l\text{,}{D}_j)|\right)\text{,}$$

  $$R^{\mathit{PD}}(P_i\text{,}{D}_j)={\left(\frac{1}{2m}{\displaystyle \sum _{l=1}^m}\left({\left({\mu }_{\mathit{PS}}(P_i\text{,}{S}_l)-{\mu }_{\mathit{SD}}(S_l\text{,}{D}_j)\right)}^2+{\left({\gamma }_{\mathit{PS}}(P_i\text{,}{S}_l)-{\gamma }_{\mathit{SD}}(S_l\text{,}{D}_j)\right)}^2+{({\pi }_{\mathit{PS}}(P_i\text{,}{S}_l)-{\pi }_{\mathit{SD}}(S_l\text{,}{D}_j))}^2\right)\right)}^{1/2}\text{.}$$

• Conclude the possible diseases of patients based on the minimal distance criterion.

Example 4

Use this method for the dataset in Example 1, we have the relations between the patients and the diseases by the Hamming (Table 9) or Euclidean function (Table 10). The most acquiring diseases of patients are highlighted in bold.

Besides these approaches, some authors have extended them for special cases, e.g. multi-criteria medical diagnosis and the multiple time intervals modeling for the relation between the patients and the symptoms. This requires the deployment on other advanced fuzzy sets such as the type-2 fuzzy sets [26], the interval-valued intuitionistic fuzzy sets [2], fuzzy soft set [25], [47] and intuitionistic fuzzy soft set [1], [21]. The combination of these fuzzy sets with machine learning methods to handle the special cases such as the fuzzy-neural automatic system [27], [24] and the type-2 fuzzy genetic algorithm [45], [14] was also investigated.

Considering the relevant works involving the usage of the IFS set, we clearly recognize that IFS was used mainly for the applications of medical diagnosis among the advanced fuzzy sets. Nonetheless, these works have the following disadvantages.

• The previous works calculate the relation between the patients and the diseases (R_PD) solely from those between the patients – the symptoms (R_PS) and the symptoms – the diseases (R_SD). In some practical cases where the relation between the patients – the symptoms or the symptoms – the diseases is missing, those works could not be performed. This fact is happened in reality since clinicians somehow do not accurately express the values of membership and non-membership degrees of symptoms to diseases or vive versa;

• The information of previous diagnoses of patients could not be utilized. That is to say, a patient has had some records in the patients-diseases databases (R_PD) beforehand. Nevertheless, the calculation of the next records of this patient is made solely on the basis of both R_PS and R_SD. Historic diagnoses of patients are not taken into account so that the accuracy of diagnosis may not be high as a result;

• The determination of the most acquiring disease is dependent from the defuzzification method. For instance, De et al. [9] used S_PD for the defuzzification, Samuel and Balamurugan [31] relied on the reduction matrix from W_PD and Szmidt and Kacprzyk [42], [43], [44], Khatibi and Montazer [19] and Shinoj and John [33] employed the distance functions. Independent determination from the defuzzification method should be investigated for the stable performance of the algorithm.

• Mathematical properties of operations such as the fuzzy implication in De et al. [9], Samuel and Balamurugan [31] and the distance function in Szmidt and Kacprzyk [42], [43], [44], Khatibi and Montazer [19] and Shinoj and John [33] were not discussed in the equivalent articles. Readers could not know the theoretical bases of these operations and why they were selected for the medical diagnosis problem.

From the disadvantages of the previous works, our idea in this article is using the hybrid method between Recommender Systems (RS) and the IFS set to handle them. RS, which are a subclass of decision support systems, can give users information about predictive “rating” or “preference” that they would like to assess an item; thus helping them to choose the appropriate item among numerous possibilities. This kind of expert systems is now commonly popularized in numerous application fields such as books, documents, images, movie, music, shopping and TV programs personalized systems. The mathematical definition of RS is stated below.

Definition 4

Suppose U is a set of all users and I is the set of items in the system. The utility function R is a mapping specified on U₁ ⊂ U and I₁ ⊂ I as follows.

$$\begin{array}{cc}\hfill & R:U_1\times I_1\to P\hfill \\ \hfill & (u_1\text{,}{i}_1)\mapsto R(u_1\text{,}{i}_1)\text{,}\hfill \end{array}$$

where R(u₁, i₁) is a non-negative integer or a real number within a certain range. P is a set of available ratings in the system. Thus, RS is the system that provides two basic functions below.

• Prediction: determine $R(u^{\ast }\text{,}{i}^{\ast })$ for any $(u^{\ast }\text{,}{i}^{\ast })\in (U\text{,}I)⧹(U_1\text{,}{I}_1)$.

• Recommendation: choose i^∗ ∈ I satisfying i^∗ = arg max_i∈IR(u, i) for all u ∈ U.

RS has been applied to the medical diagnosis problem. Davis et al. [8] proposed CARE, a Collaborative Assessment and Recommendation Engine, which relies only on a patient’s medical history in order to predict future diseases risks and combines collaborative filtering methods with clustering to predict each patient’s greatest disease risks based on their own medical history and that of similar patients. An iterative version of CARE so-called ICARE that incorporates ensemble concepts for improved performance was also introduced. These systems required no specialized information and provided predictions for medical conditions of all kinds in a single run. Hassan and Syed [13] employed a collaborative filtering framework that assessed patient risk both by matching new cases to historical records and by matching patient demographics to adverse outcomes so that it could achieve a higher predictive accuracy for both sudden cardiac death and recurrent myocardial infraction than popular classification approaches such as logistic regression and support vector machines. More works on the applications of RS could be referenced in Duan et al. [10], Meisamshabanpoor and Mahdavi [22] and our previous works in [7], [38], [40], [39], [41], [34], [35], [36], [37].

Example 5

Consider the training dataset in Table 11. Taking a simple encoded method by multiplying the membership degree by 10 and adding the non-membership degree to it, we have a crisp training in Table 12.

The method of Hassan and Syed [13] employed a collaborative filtering including the traditional Pearson coefficient to calculate the similarity between users and the k-nearest neighbor approximation function to predict the blank values in Table 12. The results are shown in Table 13. If taking the maximal value among all for a given patient in Table 13 then we can conclude that Ram, Sugu and Somu are suffered from Malaria and Mari acquires Stomach. Analogously, Table 14 shows the results of the method of Davis et al. [8] where Ram is suffered from Malaria, Mari acquires Stomach and Sugu and Somu have Typhoid.

From Example 5, we clearly recognize the following facts:

• RS could be applied to the medical diagnosis. Yet in cases that the relations are expressed by fuzzy memberships as in Table 11, the accuracy of diagnosis in RS is dependent on the encoded method. In the other words, RS is effective with the crisp dataset such as Table 12 but not the fuzzy one, e.g. Table 11;

• The problem of the previous researches about the dependence of the determination of the most acquiring disease from the defuzzification method, e.g. the maximal function in Example 5 still exists;

• RS works only if the training dataset is provided. That is to say, we must have the historic diagnoses of patients for the prediction.

From Sections 1.3 The limitations of the previous works, 1.4 The motivation and ideas and illustrated examples, we clearly recognize that the IFS and RS approaches have their own advantages and disadvantages. Thus, a combination of these approaches in order to combine the advantages and eliminate the disadvantages could handle the mentioned issues. Scanning the literature, we realize that some hybrid methods were also designed for the medical diagnosis problem, to name but a few such as Davis et al. [8] combined collaborative filtering methods with clustering; Kala et al. [18] integrated genetic algorithms with modular neural network; Hosseini et al. [14] joined a type-2 fuzzy logic with genetic algorithm. These evidences show that the combination of groups of methods such as between RS and IFS is a trendy approach for medical diagnosis.

Based upon the observations, our contribution in this paper is a novel intuitionistic fuzzy recommender system (IFRS) for medical diagnosis consisting of the following components:

• The new definitions of single-criterion IFRS (SC-IFRS) and multi-criteria IFRS (MC-IFRS) that extend the definition of RS (Definition 4) taking into account a feature of a user and a characteristic of an item expressed by intuitionistic linguistic labels (See Section 2.1). These definitions are the basis for the deployment of similarity degrees used for the prediction of R^PD(P_i, D_j) (Definition 1);

• The new definitions of intuitionistic fuzzy matrix (IFM), which is a representation of SC-IFRS and MC-IFRS in the matrix format and the intuitionistic fuzzy composition matrix (IFCM) of two IFMs with the intersection/union operation. Some interesting theorems and properties of IFM and IFCM are presented (See Section 2.2);

• Some new similarity degrees of IFMs such as the intuitionistic fuzzy similarity matrix (IFSM) and the intuitionistic fuzzy similarity degree (IFSD). The formulas to predict R^PD(P_i, D_j) on the basis of IFSD accompanied with an interesting theorem is proposed (See Section 2.3);

• From the predicting formulas, a novel intuitionistic fuzzy collaborative filtering method so-called IFCF is presented for the medical diagnosis problem (See Section 2.4);

• The validation of the IFCF method in comparison with the standalone methods of IFS such as De et al. [9], Szmidt and Kacprzyk [44], Samuel and Balamurugan [31] and RS, e.g. Davis et al. [8], Hassan and Syed [13] is made by both a numerical illustration on the dataset in Example 1 and the experiments on benchmark medical diagnosis datasets from UCI Machine Learning Repository in terms of the accuracy of diagnosis (See Section 3).

According to the contributions in Section 1.5 and the limitations of IFS and RS in Sections 1.3 The limitations of the previous works, 1.4 The motivation and ideas, respectively, the novel and the significance of the proposed work are stressed as follows.

• The proposed work is different from the previous ones especially the standalone IFS and RS methods. Specifically, it employs the ideas of both the IFS set and RS in the definitions of SC-IFRS and MC-IFRS, which are the basis to develop some new terms and similarity degrees for the IFCF algorithm. Furthermore, as being observed from Example 1 to 3, the determination of the relation between patients and diseases in the standalone IFS methods is performed by some operations such as the fuzzy implication in De et al. [9], Samuel and Balamurugan [31] and the distance function in Szmidt and Kacprzyk [42], [43], [44]. In the proposed work, this can be done through the intuitionistic fuzzy similarity degree (IFSD) in Section 2.3, which is developed based on SC-IFRS and MC-IFRS. Comparing with the standalone RS methods such as Davis et al. [8] and Hassan and Syed [13], the similarity degree – IFSD in the proposed work is constructed from the light of the IFS set but not by the Pearson coefficient from the hard values such as in Table 12. Additionally, the formulas to predict R^PD(P_i, D_j) are also made according to the membership and non-membership functions but not by the hard values above. These proofs demonstrate the novel of the proposed work;

• The proposed hybrid method could handle the issues of the standalone IFS and RS methods. For instance, the limitations of IFS relating to the missing relations and the historic diagnoses of patients stated in Section 1.3(a) and (b) and the limitations of RS relating to the crisp and training datasets stated in Section 1.4(a) and (c) are solved by the integration of IFS and RS. The deficiency of mathematical properties of operations in Section 1.3(d) is resolved by a number of interesting theorems and properties in Section 2. Lastly, when predicting R^PD(P_i, D_j), users could find a suitable defuzzification method for the determination of the most acquiring disease;

• The proposal of this work is significance in terms of both theory and practice. In the theoretical aspect, the proposed work motivates researching on advanced algorithms of IFS and RS especially the hybrid method between them to enhance the accuracy of the algorithm. Looking for details in Section 1.5, we recognize that the proposed method is constructed on a well-defined mathematical foundation, which is not paid much attention in the previous researches. Thus, this guarantees the further deployment of other advanced methods of both IFS and RS on such the mathematical foundation. In the practical side, the proposed work contributes greatly to the medical diagnosis problem and some extensions and variants of this method could be quickly deployed for other socio-economic problems. This clearly affirms the significance of the proposed work.

The rest of the paper is organized as follows. Section 2 presents the main contribution including the IFRS and its elements stated in Section 1.5. Section 3 validates the proposed approach through a set of experiments involving benchmark medical diagnosis data. Section 4 draws the conclusions and delineates the future research directions.