On a theory of equivalent fuzzy logic advisors

A fuzzy logic advisor (FLA) is the interconnection of three subsystems: encoder, fuzzy logic system, and decoder. It is very useful for making social judgments, and provides a nonlinear mapping of the indicators of a social judgment into a linguistic level of that judgment. A cooperative environment is needed to design the fuzzy logic system within the FLA, and this is done by means of surveys. After defining the notion of equivalent FLAs, this paper provides a theoretical answer to the following question: under what conditions will two (or more) FLAs, that have been designed for the same social judgment, be equivalent? It answers the question with conditions that are both necessary and sufficient. These conditions lead to an equivalency diagram and a practical test to establish equivalence of two (or more) FLAs