  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.
