Fuzzy Set Theory

  • James G. Shanahan
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 570)

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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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • James G. Shanahan
    • 1
  1. 1.Xerox Research Centre Europe (XRCE)Grenoble LaboratoryMeylanFrance

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