An improvement to Koczy´s interpolative reasoning method based on Taylor progression

In the sparse fuzzy rules, the reasoning consequence cannot be obtained by the traditional fuzzy reasoning method. To tackle this problem, Koczy and Hirota have proposed a linear interpolative reasoning method. This method resolved the problem of how to derive the reasoning consequence in the sparse fuzzy rules, but the reasoning consequences by this method sometimes become abnormal fuzzy sets [Y. Shi et al., 1995; Y. Shi & M. Mizumoto, 1997]. In order to guarantee "if fuzzy rules A₁≥B₁, A₂≥B₂ and the observation A* are defined by triangular membership functions, then the interpolated conclusion B* is linearity and convexity", we shall propose the interpolative method based on Taylor progression.