Abstract
This chapter presents the fundamental ideas behind fuzzy set theory. It begins with a review of traditional set theory (commonly referred to as crisp or classical set theory in the fuzzy set literature) and uses this as a backdrop, against which fuzzy sets and a variety of operations on fuzzy sets are introduced. Various justifications and interpretations of fuzzy sets as a form of knowledge granulation are subsequently presented. Different families of fuzzy set aggregation operators are then examined. The original notion of a fuzzy set can be generalised in a number of ways leading to more expressive forms of knowledge representation; the latter part of this chapter presents some of these generalisations, where the original idea of a fuzzy set is generalised in terms of its dimensionality, type of membership value and element characterisation. Finally, fuzzy set elicitation is briefly covered for completeness (Chapter 9 gives more detailed coverage of this topic).
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