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Soft Computing for Knowledge Discovery pp 35–66Cite as

Fuzzy Set Theory

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Part of the book series: The Springer International Series in Engineering and Computer Science ((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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Authors and Affiliations

  1. Xerox Research Centre Europe (XRCE), Grenoble Laboratory, 6 chemin de Maupertuis, Meylan, 38240, France

    James G. Shanahan

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  1. James G. Shanahan
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© 2000 Kluwer Academic Publishers

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Shanahan, J.G. (2000). Fuzzy Set Theory. In: Soft Computing for Knowledge Discovery. The Springer International Series in Engineering and Computer Science, vol 570. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4335-0_3

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  • DOI: https://doi.org/10.1007/978-1-4615-4335-0_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6947-9

  • Online ISBN: 978-1-4615-4335-0

  • eBook Packages: Springer Book Archive

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