Commensurability of fuzzy membership values in fuzzy rules

Fuzzy rules are often expressed in the form: IF (X is A_X) AND (Y=B_Y) AND ... THEN (Z is C_Z), where X, Y, Z, ... are attribute variables, and A_X, B_Y , C_Z ... are fuzzy sets in the corresponding attribute value domains. When fuzzy sets corresponding to different linguistic terms are combined in the antecedent using fuzzy operators, we are implicitly assuming that these membership functions are commensurate in accordance with their membership values. In most situations, this assumption may not be justified. The author describes an interpretation of fuzzy rules which would suggest a commensurability mapping among the membership functions and the underlying attribute values. This approach will provide us with an insight into the possible equivalence between different attribute values relating to the rule antecedent. Furthermore, the commensurability mapping can help us refine fuzzy rules in a production system by suggesting a realignment of interacting membership functions that can improve the performance of the fuzzy production rules