Reasons for a careful design of fuzzy sets

This paper is, basically, a reflection on modeling, starting by asking what happens when the meaning of a predicate P is interpreted by the membership function of a fuzzy set that, labeled P , is designed with the information available to the designer on the use of the predicate in the corresponding universe of discourse. In it, the modification of the meaning that P can suffer by its identification with the membership function of the fuzzy set, is analyzed and discussed. It is argued that what can be done for reaching a least possible modification of the meaning, is just a careful design of the membership function. This reflection is further continued at the level of linguistic variables, fuzzy if-then rules, and rule-based systems. It is concluded that as argued in the case of fuzzy sets, the involved operations in rules and systems should be at least carefully chosen, if not specially designed.