**2 Set Theory—Classical And Fuzzy Sets**

*Timothy J. Ross University of New Mexico*

**2.1 Introduction**

Fuzzy set theory is developed here by comparing the precepts and operations of fuzzy sets with those of classical set theory. Fuzzy sets will be seen to contain the vast majority of the definitions, precepts, and axioms that define classical sets. In fact, very few differences exist between the two set theories. Fuzzy set theory is actually a fundamentally broader theory than current classical set theory, in that it considers an infinite number of “degrees of membership” in a set other than the canonical values of 0 and 1 apparent in classical set theory. In this sense, one could argue that classical sets are a limited form of fuzzy sets. Hence, it ...