A Novel Fuzzy Approximate Reasoning Method Based on Extended Distance Measure in SISO Fuzzy System

This paper presents an original method of fuzzy approximate reasoning that can open a new direction of research in the uncertainty inference of Artificial Intelligence(AI) and Computational Intelligence(CI). Fuzzy modus ponens (FMP) and fuzzy modus tollens(FMT) are two fundamental and basic models of general fuzzy approximate reasoning in various fuzzy systems. And the reductive property is one of the essential and important properties in the approximate reasoning theory and it is a lot of applications. This paper suggests a kind of extended distance measure (EDM) based approximate reasoning method in the single input single output(SISO) fuzzy system with discrete fuzzy set vectors of different dimensions. The EDM based fuzzy approximate reasoning method is consists of two part, i.e., FMP-EDM and FMT-EDM. The distance measure based fuzzy reasoning method that the dimension of the antecedent discrete fuzzy set is equal to one of the consequent discrete fuzzy set has already solved in other paper. In this paper discrete fuzzy set vectors of different dimensions mean that the dimension of the antecedent discrete fuzzy set differs from one of the consequent discrete fuzzy set in the SISO fuzzy system. That is, this paper is based on EDM. The experimental results highlight that the proposed approximate reasoning method is comparatively clear and effective with respect to the reductive property, and in accordance with human thinking than existing fuzzy reasoning methods.