I. the origin of species by means of natural selection

Classical Sets and Fuzzy Sets.- Classical and Fuzzy Relations.- Membership Functions.- Defuzzification.- Fuzzy Rule-Based System.- Fuzzy Decision Making.- Applications of Fuzzy Logic.- Fuzzy Logic Projects with Matlab.

Introduction to Fuzzy Logic using MATLAB

Ten years of genetic fuzzy systems: current framework and new trends

Fuzzy inference systems (FIS) are widely used for process simulation or control. They can be designed either from expert knowledge or from data. For complex systems, FIS based on expert knowledge only may suffer from a loss of accuracy. This is the main incentive for using fuzzy rules inferred from data. Designing a FIS from data can be decomposed into two main phases: automatic rule generation and system optimization. Rule generation leads to a basic system with a given space partitioning and the corresponding set of rules. System optimization can be done at various levels. Variable selection can be an overall selection or it can be managed rule by rule. Rule base optimization aims to select the most useful rules and to optimize rule conclusions. Space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters. Structure optimization is of a major importance: selecting variables, reducing the rule base and optimizing the number of fuzzy sets. Over the years, many methods have become available for designing FIS from data. Their efficiency is usually characterized by a numerical performance index. However, for human-computer cooperation another criterion is needed: the rule interpretability. An implicit assumption states that fuzzy rules are by nature easy to be interpreted. This could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts. The paper analyzes the main methods for automatic rule generation and structure optimization. They are grouped into several families and compared according to the rule interpretability criterion. For this purpose, three conditions for a set of rules to be interpretable are defined.

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Designing fuzzy inference systems from data: An interpretability-oriented review

The use of genetic algorithms (GAs) and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature. Authors have focused on various aspects of these randomized techniques, and a whole scale of algorithms have been proposed. We comment on some recent work and describe a new and efficient two-step approach that leads to good results for function approximation, dynamic systems modeling and data classification problems. First, fuzzy clustering is applied to obtain a compact initial rule-based model. Then this model is optimized by a real-coded GA subjected to constraints that maintain the semantic properties of the rules. We consider four examples from the literature: a synthetic nonlinear dynamic systems model, the iris data classification problem, the wine data classification problem, and the dynamic modeling of a diesel engine turbocharger. The obtained results are compared to other recently proposed methods.

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GA-fuzzy modeling and classification: complexity and performance

The author has developed a novel approach to fuzzy modeling from input-output data. Using the basic techniques of soft computing, the method allows supervised approximation of multi-input multi-output (MIMO) systems. Typically, a small number of rules are produced. The learning capacity of FuGeNeSys is considerable, as is shown by the numerous applications developed. The paper gives a significant example of how the fuzzy models developed are generally better than those to be found in literature as concerns simplicity and both approximation and classification capabilities.

M. Russo

Papers

FuGeNeSys-a fuzzy genetic neural system for fuzzy modeling