(A) fuzzy if-then-else inference method based on interpolation

Abstract

This thesis presents a method for propagating fuzzy concepts through fuzzy IF-THEN-ELSE rules. A fuzzy IF-THEN-ELSE rule consists of a set of fuzzy condition and conclusion pairs of the following type: If $A_1$ then $B_1$ else if $A_2$ then $B_2$ else .............. if $A_n$ then $B_n$ else where $A_i$ is a fuzzy condition and $B_i$ is a fuzzy conclusion. In other words, a fuzzy condition-conclusion pair represents a mapping from the fuzzy concept of the condition part to the fuzzy concept of the conclusion part. Conventionally, vectors are used to define fuzzy concept and matrices are used to define fuzzy mapping between fuzzy condition and conclusion. The approach, however, has some shortcomings: low precision, inconvenience, and more importantly, the violation of 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. We propose a parameterized approach in that every fuzzy concept is described by parameterized standard function, including fuzzy conditions and fuzzy conclusions. A fuzzy IF-THEN-ELSE rule takes parameterized fuzzy concept as input, and produces a standard function with new parameters as output. The new parameters are determined by parameterwise interpolation. That is, each output parameters are determined by interpolating the parameters of the same kind contained in fuzzy conclusions. Obviously, the proposed scheme always satisfies the existing condition property. We also claim that the parameterized approach is much simpler to elicit, and supports higher precision than the counterpart vector approach.