Classical Sets and Fuzzy Sets
Timothy J. Ross · 2010
In this chapter, the author develops the basic definitions for, properties of, and operations on crisp sets and fuzzy sets. It shows that fuzzy set theory is a mathematically rigorous and comprehensive set theory useful in characterizing concepts with natural ambiguity. It is instructive to introduce fuzzy sets by first reviewing the elements of classical (Crisp) set theory. Mapping is an important concept in relating set-theoretic forms to function-theoretic representations of information. In its most general form it can be used to map elements or subsets in one universe of discourse to elements or sets in another universe. Aside from the difference of set membership being an infinite-valued idea as opposed to a binary-valued quantity, fuzzy sets are handled and treated in the same mathematical form as are crisp sets. The principle of noninteractivity between sets was mentioned and is analogous to the assumption of independence in probability modeling. Controlled Vocabulary Terms fuzzy logic; set theory