Fuzzy Interpolative Reasoning Method Based on Spline

Abstract

When rule base is sparse, we cannot get any reasoning result by traditional fuzzy reasoning method for an observation is in the gap between two neighboring antecedences. Fuzzy reasoning is really equal to an interpolation. For reasoning only considers two neighbor- ring rules, classical KH linear interpolative reasoning method is partial and its consequence does not always keep convexity and normality. So this paper presents a non-linear fuzzy interpolative method based on spline. And it is extended to handle the multidimensional variables fuzzy reasoning. Reasoning is simple by the method; moreover it can keep the convexity and normality of the reasoning consequence.