Fuzzy system design through fuzzy clustering and optimal predefuzzification

An approach to the design of fuzzy systems, assuming that the system specification is given in terms of a large number of sample I/O (input/output) pairs, that consists of two stages of processing is presented. First, K fuzzy relation patches are obtained by using a fuzzy clustering technique in the input-output joint universe of discourse. The number K of fuzzy clusters is selected and justified based on some cluster validity measure. Each fuzzy relation patch thus discovered then constitutes a fuzzy rule in the proposed system. Second, as in the case of the Takagi-Sugeno fuzzy model, a function is associated with each rule that can be regarded as a predefuzzifier for that rule. Each of these functions is obtained in an optimal way, so that an appropriately defined object function is minimized. An example is included to illustrate the approach