Affiliations: Department of Electrical Engineering, The University
of Suwon, San 2-2, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743,
South Korea | Department of Electrical and Computer Engineering,
University of Alberta, Edmonton, AB T6G 2G6, Canada | Systems Research Institute, Polish Academy of
Sciences, Warsaw, Poland
Abstract: In this study, we introduce a new category of fuzzy inference
systems based on data (information) granulation and show their applications to
the identification of complex and usually nonlinear systems. Information
granules are treated as collections of objects (data, in particular) brought
together by the criteria of proximity, similarity, or functionality. The formal
framework of information granulation along with the information granules
themselves become an important design feature of fuzzy models, which in essence
are geared towards capturing relationship between information granules rather
than plain numeric data. The key characteristics of experimental data being
used in the construction of the fuzzy model are carefully reflected by fuzzy
rules formed therein. Information granulation realized with the aid of Hard
C-Means (HCM) clustering helps determine the initial values of the parameters
of the fuzzy models. This in particular concerns such important components of
the rules as the initial apexes of the membership functions standing in the
premise part of the fuzzy rules and the initial values of the polynomial
functions present in their consequence part. The initial values of the
parameters are tuned effectively with the aid of the genetic algorithms (GAs)
and the least square method (LSM). An aggregate objective function is
constructed in order to strike a sound balance between the approximation and
generalization capabilities of the fuzzy model. The model is evaluated with the
use of numerical experimentation and contrasted with the quality of some
"conventional" fuzzy models already encountered in the literature.
Keywords: Information Granulation (IG), Fuzzy Inference System (FIS), Genetic Algorithms (GAs), Hard C-Means (HCM) clustering, least square method, design procedure
