Antonio Peregrín

Applicability of the fuzzy operators in the design of fuzzy logic controllers

A study of the different roles played by the fuzzy operators in fuzzy control is developed in this paper. The behavior of a very large amount of fuzzy operators is analyzed and a comparison of the accuracy of many fuzzy logic controllers designed by means of these operators is carried out. In order to do that, a comparison methodology is defined and two fuzzy control applications are selected, the Inverted Pendulum problem and the fuzzy modeling of the real curve Y = X.

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.

Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic

Abstract This paper deals with the design of stable rule-based fuzzy control systems. Interval analysis is applied to design a stable fuzzy Takagi–Sugeno–Kang controller using a robust condition to ensure the stability. The presented methodology starts with a state model of the plant, finds a candidate fuzzy controller and uses an interval arithmetic algorithm to verify the stability of closed-loop fuzzy model. It is important to emphasize the generality of the presented methodology for fuzzy controller synthesis since there are no constraints in the state vector nor in the control vector. This methodology can also be used with nonlinear plant models. In previous works we showed the applicability of the interval analysis to design a controller that ensures the stability of first order nonlinear system. In this paper, we extend the analysis and the synthesis of stable fuzzy control system to the multivariable case. An example with a fuzzy controller for a nonlinear system is presented to illustrate the design procedure.

Efficient Distributed Genetic Algorithm for Rule extraction

This paper presents an Efficient Distributed Genetic Algorithm for classification Rule extraction in data mining (EDGAR), which promotes a new method of data distribution in computer networks. This is done by spatial partitioning of the population into several semi-isolated nodes, each evolving in parallel and possibly exploring different regions of the search space. The presented algorithm shows some advantages when compared with other distributed algorithms proposed in the specific literature. In this way, some results are presented showing significant learning rate speedup without compromising the accuracy.

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.

Searching for basic properties obtaining robust implication operators in fuzzy control

Abstract This paper deals with the problem of searching basic properties for robust implication operators in fuzzy control. We use the word “robust” in the sense of good average behavior in different applications and in combination with different defuzzification methods. We study the behavior of the two main families of implication operators in the fuzzy control inference process. These two families are composed by those operators that extend the boolean implication (implication functions) and those ones that extend the boolean conjunction (t-norms and force-implications). In order to develop the comparative study, we will build different fuzzy controllers by means of these implication operators and will apply them to the fuzzy modeling of the real function Y=X and two three-dimensional surfaces. We analyze whether one of these two properties, extension of the boolean implication and extension of the boolean conjunction, is sufficient for obtaining a good implication operator or whether some complementary properties are necessary. Next, we analyze whether we can get basic properties for good implication operators, presenting three basic properties for the so-called robust implication operators.

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.