Towards asymmetric uncertainty modeling in designing General Type-2 Fuzzy classifiers for medical diagnosis
Introduction
Many of the real-world problems and applications of artificial intelligence can be represented as classification problems. In this regard, intelligent systems can provide excellent results, for example, in (Jiang et al., 2020), the authors propose an interesting artificial neural network design based on medical experts for medical diagnosis of different diseases. On the other hand (Alneamy et al., 2019) introduce an architecture with fuzzy wavelet layers applied successfully in medical diagnosis. In addition, hybrid approaches like the Adaptive Neuro Fuzzy Inference System (ANFIS), proposed in (Jang, 1993), where fuzzy inference systems and neural networks are combined for first the time, are generating interesting applications as the one proposed in (Avci & Turkoglu, 2009), where an intelligent system based on principle component analysis and ANFIS approach was built for heart diseases. There are also modular approaches as the one proposed in (Liu, Miao, Sun, Song, & Quan, 2016) for performing one-class classification. On the other hand, Support Vector Machines have achieved great results for hydrometeorological monitoring network analysis (Asquith, 2020), Decision Trees can also be used for one-class classification (Itani, Lecron, & Fortemps, 2020) and bagging/boosting modular architectures for spoof fingerprint detection (Agarwal & Chowdary, 2020). However, the kind of intelligent systems that are studied in the present paper are the so called Fuzzy Systems, specifically Type-2 Fuzzy Systems, and the main reason to study this kind of intelligent systems is because they provide us with an uncertainty handling ability that can enable achieving good performance in real-world problems and this is because problems based on real-world data have to deal with many sources of uncertainty. The main goal of the paper is to generate type-2 fuzzy classifiers with a new approach for the estimation of the Footprint of Uncertainty.
As can be observed in Fig. 1 the number of research documents published on Type-2 Fuzzy Logic in the recent years has been steadily growing. Currently there exists an interest in this topic because type-2 fuzzy systems provide better performance than conventional type-1 fuzzy systems, and some examples of successful applications of type-2 fuzzy logic in real-world problems are as follows. In (Castillo et al., 2019) type-2 fuzzy logic was applied for dynamic parameter adaptation in metaheuristics, in (Kim et al., 2018) an interval type-2 fuzzy c-means method was used for achieving classification, and in (Melin et al., 2014) type-2 fuzzy logic was used for the first time for image edge detection. In addition, in (Ontiveros et al., 2020) type-2 fuzzy logic was applied in medical diagnosis, in (Ontiveros-Robles et al., 2018) a comparative study of noise robustness for type-2 fuzzy controllers was presented, and in Sanchez et al., 2015) a method for the formation of type-2 fuzzy sets was presented. In most of these cases, the process of uncertainty handling has played a relevant role in the performance of the presented systems.
However, an interesting study area is uncertainty modeling. In this regard, the FOU (Footprint of Uncertainty) concept plays a relevant role in the performance of type-2 fuzzy systems, as was concluded in (Ontiveros et al., 2020) and (Ontiveros-Robles et al., 2018). However, the FOU cannot have an arbitrary form and this issue needs special attention. There exists very interesting works specifically about modeling type-2 membership functions with the principle of justifiable granularity, for example in (Moreno et al., 2020).
The main contribution of the paper is the proposed alternative way for uncertainty modeling in Generalized Type-2 Fuzzy Classifiers, and this approach consists on modeling Type-2 Membership Functions (Type-2 MFs) through the FOU and a new concept introduced in the present work that is called the COU (Core of Uncertainty). The details about the proposed methodology are explained in the followings sections, and the results of the proposed methodology are systems with an asymmetric uncertainty modeling of uncertainty.
The organization of the present paper is the following: Section 2 summarizes the materials and methods, which consists of the basic concepts and theory about fuzzy logic that are necessary for understanding the proposed methodology, in Section 3 the details about the proposed methodology are presented with an example based on a real-world classification problem, Section 4 reports the experimental results for testing the proposed approach and finally Section 5 offers the conclusion and future works.
Section snippets
Materials and methods
In this section several basic concepts, related to the proposed approach, that form the basis of the proposed methodology are reviewed. Some of them are the mathematical concepts of Type-2 Fuzzy Logic, also the nature-inspired optimization method that is used in the proposed methodology and other important related concepts are presented.
Proposed methodology
Based on the theoretical concepts introduced in Section 2, this section aims at explaining the proposed methodology for the asymmetric modeling of the FOU and its application in classification problems.
The main idea of the section is to provide general and specific details about the design of these generalized type-2 fuzzy classifiers. The flowchart of the proposed methodology can be appreciated in Fig. 7.
As can be observed from Fig. 7, the main idea is to apply the concepts introduced in
Experimental results
To test the performance of the presented approach, some of the most popular datasets in the literature for diagnosis (classification) were used. These datasets are listed in Table 2 with their respective number of attributes, abbreviations, instances and data entropy. The data entropy concept measures the quality of the information and this is why this value is important in this table. In this case, unbalanced data have a lower entropy and balanced data have a higher entropy, and this measure
Conclusion
From the experimental results, it can be concluded that the proposed methodology for uncertainty modeling provides an improvement in the performance of the General Type-2 Fuzzy Classifiers, and this conclusion is based on the comparison with a similar approach, but with symmetric uncertainty (in the primary and secondary membership functions).
The introduction of the concept of the Core of Uncertainty helps us to explain in a better way the general type-2 membership functions for a better
CRediT authorship contribution statement
Emanuel Ontiveros-Robles: Methodology, Software, Validation, Writing - original draft. Oscar Castillo: Formal analysis, Visualization, Writing - review & editing. Patricia Melin: Conceptualization, Investigation, Project administration, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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