Since its inception in 1965, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, and robotics. Mathematical developments have advanced to a very high standard and are still forthcoming to day. In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques. Since 1992 fuzzy set theory, the theory of neural nets and the area of evolutionary programming have become known under the name of ‘computational intelligence’ or ‘soft computing’. The relationship between these areas has naturally become particularly close. In this review, however, we will focus primarily on fuzzy set theory. Applications of fuzzy set theory to real problems are abound. Some references will be given. To describe even a part of them would certainly exceed the scope of this review. Copyright © 2010 John Wiley & Sons, Inc.

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Fuzzy set theory

Simple Object Access Protocol と,その応用としてのソフトウェアの組み合わせについて (渡邉昭夫教授退任記念号)

Linguistic fuzzy modeling allows us to deal with the modeling of systems by building a linguistic model which is clearly interpretable by human beings. However, since the accuracy and the interpretability of the obtained model are contradictory properties, the necessity of improving the accuracy of the linguistic model arises when complex systems are modeled. To solve this problem, one of the research lines in recent years has led to the objective of giving more accuracy to linguistic fuzzy modeling without losing the interpretability to a high level. In this paper, a new postprocessing approach is proposed to perform an evolutionary lateral tuning of membership functions, with the main aim of obtaining linguistic models with higher levels of accuracy while maintaining good interpretability. To do so, we consider a new rule representation scheme base on the linguistic 2-tuples representation model which allows the lateral variation of the involved labels. Furthermore, the cooperation of the lateral tuning together with fuzzy rule reduction mechanisms is studied in this paper, presenting results on different real applications. The obtained results show the good performance of the proposed approach in high-dimensional problems and its ability to cooperate with methods to remove unnecessary rules.

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A Proposal for the Genetic Lateral Tuning of Linguistic Fuzzy Systems and Its Interaction With Rule Selection

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Seventh ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing

System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by Takagi-Sugeno-Kang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years.

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Interpretability Improvements to Find the Balance Interpretability-Accuracy in Fuzzy Modeling: An Overview

In this paper, the FRIwE method is proposed to identify fuzzy models from examples. Such a method has been developed trying to achieve a double goal:accuracy and interpretability. In order to do that, maximal structure fuzzy rules are firstly obtained based on a method proposed by Castro et al. In a second stage, the conflicts generated by the maximal rules are solved, thus increasing the model accuracy. The resolution of conflicts are carried out by including exceptions in the rules. This strategy has been identified by psychologists with the learning mechanism employed by the human being, thus improving the model interpretability. Besides, in order to improve the interpretability even more, several methods are presented based on reducing and merging rules and exceptions in the model. The exhaustive use of the training examples gives the method a special suitability for problems with small training sets or high dimensionality. Finally, the method is applied to an example in order to analyze the achievement of the goals.

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FRIwE: fuzzy rule identification with exceptions

With identification methods that learn fuzzy rules directly from certainty degrees, we refer to methods that select the most promising rules from the training examples in only one pass. In order to do that, these methods employ a certainty measure to assess the goodness of each rule. This paper aims to analyze in depth the behaviors and features of two different strategies for identifying fuzzy models from certainty degrees, each of both combined with one of two well-known alternatives for measuring the certainty degrees of the rules. With this aim, the advantages and drawbacks of each method are analyzed experimentally by considering the model error when applied to several systems. Besides, the robustness of the results is investigated by applying the methods to noisy data. As a conclusion, a new method combining the best components of the previously considered methods is proposed and its results are analyzed. The achieved performance in accuracy and computational cost shows the benefit of this new method.

Strategies to identify fuzzy rules directly from certainty degrees: a comparison and a proposal

This paper proposes a method to solve the conflicts that arise in the framework of fuzzy model identification with maximal rules (Fuzzy Sets and Systems 101 (1999) 331) where rules are selected as general as possible. This resolution is expressed by including exceptions in the rules, that way achieving a higher model interpretability with respect to other techniques and a more accurate model. Besides, several methods are presented to improve the interpretability, based on compacting the rules and exceptions of the model. Furthermore, in order to reduce the number of conflicts that arise from the maximal rules, a heuristic strategy is proposed to generate those maximal rules. Finally, the method is applied to an example and the results are compared with other identification methods.

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Learning maximal structure fuzzy rules with exceptions

New trends in software development have proposed different interaction mechanisms for software applications. For instance, the Software as a Service (SaaS) model has defined a new delivery and access method, and installation and update processes in the user's computer are not required, software is hosted in a server and can be used over Internet instead. Middleware platforms are required in SaaS frameworks in order to support software services. Currently, web applications are taking full advantages of SaaS benefits, because they can be delivered over Internet and developed according to a service model. However, web applications are still under a maturity process and a low degree of efficiency and reusability are achieved. This paper proposes a web service-based framework according to component software engineering (CBSE), with the aim of developing efficient and reusable web applications. Moreover, web services are the middleware technology that provides full accessibility for this type of components.

Web services and web components

Usually, the rules in a fuzzy model contain in the antecedent a set of propositions each of which restricts a fuzzy variable to a single fuzzy value by means of the predicate equal-to. That way, each rule covers a single fuzzy region of the fuzzy grid. This paper proposes to extent this structure in order to provide more general fuzzy rules, in the sense of covering the input space as much as possible. In order to do this, new predicates are considered and an ant colony optimization algorithm is proposed to learn such fuzzy rules. The obtained fuzzy models provide two benefits: they are described with a lower number of rules and their accuracy improves with the increase in generalization introduced. Some experimental results illustrate these facts

Pablo Carmona

Papers

FRIwE: fuzzy rule identification with exceptions

Strategies to identify fuzzy rules directly from certainty degrees: a comparison and a proposal

Learning maximal structure fuzzy rules with exceptions

Web services and web components

Using Ant Colony Optimization for Learning Maximal Structure Fuzzy Rules