Francisco Alfredo Márquez

Increasing Fuzzy Rules Cooperation Based on Evolutionary Adaptive Inference Systems

This article presents a study on the use of parametrized operators in the Inference System of linguistic fuzzy systems adapted by evolutionary algorithms, for achieving better cooperation among fuzzy rules. This approach produces a kind of rule cooperation by means of the inference system, increasing the accuracy of the fuzzy system without losing its interpretability. We study the different alternatives for introducing parameters in the Inference System and analyze their interpretation and how they affect the rest of the components of the fuzzy system. We take into account three applications in order to analyze their accuracy in practice.

Cooperative Evolutionary Learning of Linguistic Fuzzy Rules and Parametric Aggregation Connectors for Mamdani Fuzzy Systems

There are two tasks in the design of linguistic fuzzy models for a concrete application: The derivation of the linguistic rule base and the setup of the inference system and the defuzzification method. Traditionally, the derivation of the linguistic rule base has been considered the most important task, but the use of the appropriate aggregation connectors in the inference system and the defuzzification interface can improve the fuzzy system behavior. In this paper, we take in consideration this idea, we propose an evolutionary learning method to learn a linguistic rule base and the parametric aggregation connectors of the inference and defuzzification in a single step. The aim of this methodology is to make possible a high level of positive synergy between the linguistic rule base and the aggregation connectors, improving the accuracy of the linguistic Mamdani fuzzy systems. Our proposal has shown good results solving three different applications. We introduce a statistical analysis of results for validating the model behavior on the applications used in the experimental study. We must remark that we present an experimental study with a double intention: (a) to compare the behavior of the new approach in comparison with those ones that first learn the rule base and then adapt the connectors, and (b) to analyze the rule bases obtained with fixed aggregation connectors and with the adaptive ones for showing the changes on the consequent rules, changes on labels that produce a better behavior of the linguistic model than the classic ones.

A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systems with adaptive defuzzification

In this paper we propose a multi-objective evolutionary algorithm with a mechanism to improve the interpretability in the sense of complexity for Linguistic Fuzzy Rule based Systems with adaptive defuzzification. The use of parameters in the defuzzification operator introduces a series of values or associated weights to each rule, which improves the accuracy but increases the system complexity and therefore has an effect on the system interpretability. To this end, we use maximizing the accuracy as an usual objective for the evolutionary process, and we define objectives related with interpretability, using three metrics: minimizing the classical number of rules, the number of rules with weights associated and the average number of rules triggered by each example. The proposed method was compared in an experimental study with a single objective accuracy-guided algorithm in two real problems showing that many solutions in the Pareto front dominate those obtained by the single objective-based one.

A Study on the Evolutionary Adaptive Defuzzification Methods in Fuzzy Modeling

Evolutionary Adaptive Defuzzification Methods are a kind of defuzzification methods based on using a parametrical defuzzification expression tuned with evolutionary algorithms. Their goal is to increase the accuracy of the fuzzy system without loosing its interpretability. They induce a kind of rule cooperation in the defuzzification interface. This paper deals with Evolutionary Adaptive Defuzzification Methods. We study their common general expression, the different defuzzification methods that can be obtained from it, their interpretation, and their accuracy. We consider two applications in order to analyze their accuracy in practice. We get some useful results for practical fuzzy systems designed by means of this kind of Intelligent Hybrid System.

A Mechanism to Improve the Interpretability of Linguistic Fuzzy Systems with Adaptive Defuzzification based on the use of a Multi-objective Evolutionary Algorithm

Abstract This paper proposes a mechanism that helps improve the interpretability of linguistic fuzzy ruled based systems with common adaptive defuzzification methods. Adaptive defuzzification significantly improves the system accuracy, but introduces weights associated with each rule of the rule base, decreasing the system interpretability. The suggested mechanism is based on three goals: 1) reducing the number of total rules considering that rule weight close to zero can be removed; 2) reducing the rules with weights coupled because rules with weights close to one do not need the weight, and 3) reducing rules triggered jointly, all of them by using several metrics and a proposed interpretability index. This is performed using a multi-objective evolutionary algorithm, obtaining a set of solutions with different trade-offs between accuracy and interpretability. In addition, it is important to note that adaptive defuzzification and therefore the proposal developed in this work can be used together with othe...

An efficient adaptive fuzzy inference system for complex and high dimensional regression problems in linguistic fuzzy modelling

The use of adaptive connectors as conjunction operators in adaptive fuzzy inference systems is one of the methodologies, also compatible with others, to improve the accuracy of fuzzy rule-based systems by means of local adaptation of the inference process to each rule of the rule base. However, when dealing with such currently challenging issues as high-dimensional regression problems, adapting their parameters becomes difficult due to the exponential rule explosion. In this paper, we propose to address the problem by using a new adaptive conjunction operator. This operator provides considerable advantages in efficiency while maintaining the accuracy. Moreover, it is completed with a multi-objective evolutionary algorithm as a search method due to its efficiency in achieving different balances between complexity and accuracy in the learned fuzzy systems. An in-depth experimental study is performed to show the advantages of the proposal presented, using 17 regression problems of different size and complexity, using different rule bases, analyzing the multi-objective algorithms and Pareto fronts obtained and performing statistical analyses. It confirms its effectiveness in terms of efficiency, but also in terms of accuracy and complexity of the obtained models.

Parallel Distributed Two-Level Evolutionary Multiobjective Methodology for Granularity Learning and Membership Functions Tuning in Linguistic Fuzzy Systems

This paper deals with the learning of the membership functions for Mamdani Fuzzy Systems – the number of labels of the variables and the tuning of them – in order to obtain a set of Linguistic Fuzzy Systems with different trade-offs between accuracy and complexity, through the use of a two-level evolutionary multi-objective algorithm. The presented methodology employs a high level main evolutionary multi-objective heuristic searching the number of labels, and some distributed low level ones, also evolutionary, tuning the membership functions of the candidate variable partitions.

Cooperation between the Inference System and the Rule Base by Using Multiobjective Genetic Algorithms

This paper presents an evolutionary Multiobjective learning model achieving positive synergy between the Inference System and the Rule Base in order to obtain simpler and still accurate linguistic fuzzy models by learning fuzzy inference operators and applying rule selection. The Fuzzy Rule Based Systems obtained in this way, have a better trade-off between interpretability and accuracy in linguistic fuzzy modeling applications.

Rule base and adaptive fuzzy operators cooperative learning of Mamdani fuzzy systems with multi-objective genetic algorithms

In this paper, we present an evolutionary multi-objective learning model achieving cooperation between the rule base and the adaptive fuzzy operators of the inference system in order to obtain simpler, more compact and still accurate linguistic fuzzy models by learning fuzzy inference adaptive operators together with rules. The multi-objective evolutionary algorithm proposed generates a set of fuzzy rule based systems with different trade-offs between interpretability and accuracy, allowing the designers to select the one that involves the most suitable balance for the desired application. We develop an experimental study testing our approach with some variants on nine real-world regression datasets finding the advantages of cooperative compared to sequential models, as well as multi-objective compared with single-objective models. The study is elaborated comparing different approaches by applying non-parametric statistical tests for pair-wise. Results confirm the usefulness of the proposed approach.

Parallel evolutionary multiobjective methodology for granularity and rule base learning in linguistic fuzzy systems

In this paper we present a parallel evolutionary multi-objective methodology for granularity and rule-based learning for Mamdani Fuzzy Systems. The proposed methodology produces a set of solutions with different trade-off between accuracy and interpretability, based on searching the number of labels and the fuzzy rules, and also makes a variable selection. This process is achieved by exploiting present parallel computer systems allowing it to deal with more complex models.