Identification of Fuzzy Set-Based Fuzzy Systems by Means of Data Granulation and Genetic Optimization

Abstract

This paper proposes an identification of fuzzy set-based fuzzy systems formed by using respective fuzzy spaces (fuzzy set). This model implements system structure and parameter identification by means of information granulation and genetic algorithms. Information granules are sought as associated collections of objects (data, in particular) drawn together by the criteria of proximity, similarity, or functionality. Information granulation realized with HCM clustering help determine the initial parameters of fuzzy model such as the initial apexes of the membership functions in the premise and the initial values of polynomial functions in the consequence. And the initial parameters are tuned by means of the genetic algorithms and the least square method. To optimally identify the structure and parameters we exploit the consecutive optimization of fuzzy set-based fuzzy model by means of genetic algorithms. An aggregate objective function is constructed in order to strike a sound balance between the approximation and generalization capabilities of the fuzzy model. The experimental part of the studies involves two representative numerical examples.