Fuzzy Interpolative Reasoning Based on Geometric Similarity

The composition rule of inference(CRI)that is used widely in fuzzy reasoning demands that rule base is dense. But when rule base is sparse ,we cannot get any reasoning result by traditional CRI method for an observation is in the gap between two neighboring antecedents. Hence Koczy and Hirota first proposed KH linear interpolative reasoning method. But its consequence does not always keep convexity and normality. Several various conceptually different methods have been proposed in the last past years for interpolating between sparse fuzzy rules which have different characteristics. However,they are rather complicated from a practical point of view. Koczy et al further proposed an improved KH interpolative reasoning method. Although it can keep the convexity and normality of the reasoning result, the effect of its reasoning result is not satisfied. In this paper we propose an interpolative reasoning method based on geometric similarity that can keep the convexity and normality of the reasoning result better and by which reasoning is simple,effect of reasoning is better. It devotes a useful tool for fuzzy reasoning in intelligent systems.