Fuzzy logic: review of recent concerns

Concerns about the foundations of fuzzy logic could effectively be responded to positively in that is there is logic in fuzzy logic in the narrow sense as indicated by Zadeh. In order to explain the fundamentals of fuzzy logic, we present a systematic development of classical as well as fuzzy logics. This is done first separating the notions of membership assignment of elements to sets and truth assignment to propositions. Next we discuss the formation of truth tables for both the classical and fuzzy logic theories. Then we consider the derivation of canonical forms for the basic combination of concepts. Under various axiomatic assumptions, it can be shown that there are various categories of fuzzy logics as well as classical logic within the same framework.