A simplified structure evolving method for Mamdani fuzzy system identification and its application to high-dimensional problems

This paper proposes the Simplified Structure Evolving Method (SSEM) for fuzzy system identification, which improves our earlier work on the Structure Evolving Learning Method for fuzzy systems (SELM). The improvement is that SSEM applies a scheme that starts with the simplest fuzzy rule set with only one fuzzy rule (instead of 2n fuzzy rules as in SELM, where n is the number of input variables), whilst retaining all the advantages of SELM. SELM is able to solve the problem of the exponential increase of fuzzy rules, however, it requires a basic fuzzy rule set which is exponential to the number of input variables (2n fuzzy rules) as a starting point. The improvement offered by SSEM enables automatic feature selection and system structure identification, and avoids inefficient rules and inefficient variable involvement for system identification. This improvement enables fuzzy systems to be applicable to problems of any input dimension. Three benchmark examples with high dimension inputs are given to illustrate the advantages of the proposed algorithm.