Fuzzy curve fitting using least square principles

One of the potential advantages of a fuzzy rule base system is its ability to model a nonlinear complex system by using a few simple If...Then fuzzy rules. As the number of such rules increases, we obtain a better modeling capability, although the storage of many such finely tuned fuzzy rules can be expensive. Therefore, there is a need to address the issue of optimally with respect to the number of rules needed to model a complex control system. Alternatively, interpolation of fuzzy rules during system's run time can provide a cheaper and practical solution. Interpolation of sparse fuzzy rules have been studied extensively by Koczy (1996). New fuzzy arithmetic operations, to evaluate fuzzy numbers, have been proposed. The proposal is developed as the standard fuzzy number arithmetic operators do not provide desirable fuzzy arithmetic results when used in fuzzy mathematics. In our case, we have used the new fuzzy arithmetic operators in the context of fuzzy least square curve fitting. The method described here is different from the technique that was proposed by Koczy. It never converts the fuzzy numbers into real numbers by evaluating their supremum and infimum at alpha-cuts, rather, it performs pure fuzzy arithmetic evaluations at a fuzzy numeric level.