Abstract — This paper proposes an automaticfuzzy system design method that uses a Genetic Algorithm and integrates three design stages; our method determines membership functions, the number of fuzzy rules, and the ruleconsequent parameters at the same time. Because these design stages may not be independent, it is important to consider them simultaneously to obtain optimal fuzzy systems. The method includes a genetic algorithm and a penalty strategy that favors systems with fewer rules. The proposed method is applied to the classic inverted pendulum control problem and has been shown to be practical through a comparison with another method. 1 1

Nowadays Fuzzy Logic Controllers have been succesfully applied to a wide range of engineering control processes. Several tasks have to be performed in order to design an intelligent control system of this kind for a concrete application. One of the most important and difficult ones is the extraction of the expert known knowledge of the controlled system. The aim of this paper is to present an evolutionary process based on genetic algorithms and evolution strategies for learning the Fuzzy Logic Controller Knowledge Base from examples in three different stages. The process allows us to generate two different kinds of Knowledge Bases, descriptive and approximative ones, depending on the scope of the fuzzy sets giving meaning to the fuzzy control rule linguistic terms, taking preliminary linguistic variable

The extraction of easily interpretable knowledge from the large amount of data measured in experiments is well desirable. This paper proposes a method to achieve this. A fuzzy rule system is first generated and optimized using evolution strategies. This fuzzy system is then converted to an RBF neural network to refine the obtained knowledge. In order to extract understandable fuzzy rules from the trained RBF network, a neural network regularization technique called adaptive weight sharing is developed. Simulation results on the Mackey-Glass system show that the proposed approach to knowledge extraction is effective and practical.

Abstract — Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC Q). Flexibility, completeness and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of the input variables increases. However, the completeness and consistency conditions are often violated if a fuzzy system is generated from data collected from real world applications. In an attempt to develop FC Q fuzzy systems, a systematic design paradigm is proposed using evolution strategies. The structure of the fuzzy rules, which determines the compactness of the fuzzy systems, is evolved along with the parameters of the fuzzy systems. Special attention has been paid to the completeness and consistency of the rule base. The completeness is guaranteed by checking the completeness of the fuzzy partitioning of input variables and the completeness of the rule structure. An index of inconsistency is suggested with the help of a fuzzy similarity measure, which can prevent the algorithm from generating rules that seriously contradict with each other or with the heuristic knowledge. In addition, soft T-norm and BADD defuzzification are introduced and optimized to increase the flexibility of the fuzzy system. The proposed approach is applied to the design of distance controller for cars. It is verified that a FC Q fuzzy system works very well both for training and test driving situations, especially when the training data are insufficient. Index Terms—Compactness, completeness, consistency, evolution strategies, flexibility, fuzzy rule systems.

This paper concerns the learning of basic behaviors in an autonomous robot. It presents a method to adapt basic reactive behaviors using a genetic algorithm. Behaviors are implemented as fuzzy controllers and the genetic algorithm is used to evolve their rules. These rules will be formulated in a fuzzy way using prefixed linguistic labels. In order to test the rules obtained in each generation of the genetic evolution process, a real robot has been used. Numerical results from the evolution rate of the different experiments, as well as an example of the fuzzy rules obtained, are presented and discussed. 1998 Elsevier Science B.V. All rights reserved.

. This paper is concerned with the learning of basic behaviors in autonomous robots. In this way, we present a method for the adaptation of basic reactive behaviors implemented as fuzzy controllers applying a genetic algorithm to the evolution of the fuzzy rule system. In this sense, we show our experiments in the evolution of control rules based on symbolic concepts represented as linguistic labels. The rules will be formulated in a fuzzy way and in order to test the rules obtained in each generation of the genetic algorithm a real robot has been used. The individual with the best performance is chosen to generate a new population: the elite strategy. All the new individuals were tested in the same real environment. In conclusion, the individuals of the last generation offer a set of rules that provides better performance than the ones designed by a non-expert designer. Key Words. Autonomous robots, fuzzy, genetic algorithm, learning. 1 Introduction Artificial Life has been defined a...

This study investigates the use of Genetic Algorithms (GAs) to the design and implementation of Fuzzy Logic Controllers (FLC). Generally, the design of FLC involves determination of the structure of the rules, and membership function parameters. In this paper we presents a methodology for simultaneously design membership functions and rule sets for them. Most techniques treat these parts separately, which may result in a suboptimal solution, because the design parts are mutually dependent. We also proposed a new approach for optimum coding of fuzzy controllers via GAs. It is important to note that not only the number of parameters needed to optimize the system is considerably reduced compared with other approaches, but also that the performance of the hybrid system is improved. 1. Introduction Fuzzy sets were introduced by Zadeh [ZAD65] as a means of representing and manipulating data that was not precise, but rather fuzzy. When the ideas of fuzzy logic are applied to control, it is g...

Abstract: Following the wide spread usage of Fuzzy Systems, Rule Reduction has emerged as one of the most important areas of research in the field of Fuzzy Control. Many rule reduction methods have been proposed in the literature and can be broadly classified into Lossless or Lossy with respect to the inference, based on whether the outputs of the original and the reduced rule bases are identical or not. In a typical Multi-Input-Single-Output fuzzy system the number of rules far exceeds the number of fuzzy sets defined on the output domain. This suggests that the rule base can be partitioned into sets of rules, each set being mapped to a single consequent fuzzy set. In this paper, we investigate the conditions on the inference operators employed in a fuzzy system that enable “lossless ” merging of rules with identical consequents. After briefly surveying the many techniques that have been proposed towards reducing the number of rules, we propose a general framework for Inference in Fuzzy Systems and then propose some sufficiency conditions on this general framework that give us a class of Fuzzy Systems that allow lossless rule reduction of the type mentioned above. We then explore these conditions in the setting of Fuzzy Logic. We find that R- and S-implications play a very critical role. We give examples from the above class of Fuzzy Systems. In this study we apply the above technique only on rules whose antecedents and consequents are fuzzy sets.

In this paper the integration of Fuzzy Logic and Genetic Algorithms is discussed. Some potencial Genetic Algorithms applications to fuzzy logic based systems are presented: the generation of the structure of fuzzy IF-THEN rules, the tuning of a fuzzy rules base, and the fuzzy classifier systems. 1 Introduction "Soft Computing is concerned with modes of computing in which precision is traded for tractability, robustness and ease of implementation" [Zad92]. As is known, Soft Computing contains Fuzzy Logic and Genetic Algorithms among its components. From a very broad point of view a Fuzzy System (FS) is any Fuzzy Logic Based System. Fuzzy Logic (FL) can be used either as the basis for the representation of divers forms of knowledge systems, or to model the interactions and relationships among the system variables. Fuzzy logic control systems (FLCS) can be seen as a special case of this more general class of FS. Genetic Algorithms (GA) are search algorithms that use operations found in n...

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