A Method for Propagating Fuzzy Concepts throuth Fuzzy IF-THEN-ELSE Rules

Abstract

This paper presents a method for propagating fuzzy conepts through fuzzy IF-THIN-ELSE rules. A fuzzy IF-THEN ELSE rule consists of a set of fuzzy condition and conclusion pairs. These pairs assumed to contain informations about a fuzzy mapping from fuzzy concepts of condition parts to the fuzzy concepts of conclusion parts.

Conventionally, vectors are used to define fuzzy concepts and matrics are used to define a fuzzy mapping between fuzzy conditions and conclusion. This approach, however, does not satisfy the existing condition property, i.e., when a fuzzy input data exactly matches to a fuzzy condition, fuzzy output data should be mapped to a corresponding fuzzy conclusion.

Alternatively, we proposed a parameterized approach in which every fuzzy concept is described by a parameterized standard function, including fuzzy conditions and fuzzy conclusions. A fuzzy IF-THEN ELSE rule takes the parameterized fuzzy concept as an input, and produces a standard function with new parameters as an output. New parameters are determined by a parameterwise interpolation. That is, each output parameters are determined by interpolating parameters of the same class contained in fuzzy conclusions. Obviously, the proposed scheme always satisfies the existing condition property.