Identifying a fuzzy model by using the bipartite membership functions

The gradient descent method and genetic algorithms have been widely used to re ne fuzzy models constructed for the given data. This paper approaches from another viewpoint to adjusting the fuzzy model built for the preprocessed data. The membership functions de ned for each premise variable are equally distributed and xed in the transformed domain. To better identify the fuzzy model, either the transformation functions or consequent parts of fuzzy rules or both need to be optimized. Since adjusting a rule to satisfy one pattern may deteriorate the others performance and result in a lengthy tuning process, we then treat each triangular membership function as two disjoint ones such that each fuzzy rule is divided into mutually independent rules. This in turn bene ts the re nement of consequent parts in the fuzzy rules since adjusting a rule will not a ect the others. Not only the simulation results from the proposed model will be demonstrated but also the results from the conventional approaches will be given for comparisons. We use the least squared method to calculate the desired consequent real numbers for the data located in the same region of transformed domain. The conformity of the after-tuned consequent parts in the fuzzy rules with the desired values further veri es the e ectiveness of the presented methodology. c © 2001 Elsevier Science B.V. All rights reserved.