Fuzzy set theory

Terry D. Clark, Jennifer M. Larson, John N. Mordeson, Joshua D. Potter, Mark J. Wierman

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter we present the reader with the fundamental concepts of fuzzy set theory. The basic primer on fuzzy set theory remains Zadeh's1965 seminal work. A number of scholars have since discussed several aspects of fuzzy set theory pertinent to the social sciences. Perhaps the best overview is provided by Smithson and Verkuilen (2006). Among the more thoroughly discussed topics are the construction of fuzzy numbers (Smithson and Verkuilen, 2006; Verkuilen, 2005; Bilgic and Turksen, 1995) and fuzzy set operations (Smithson and Verkuilen, 2006). This chapter begins with a discussion of the differences between traditional, crisp sets and fuzzy sets. Set theory provides a systematic way to consider collections of distinct objects. Most fields of mathematics can be understood in terms of sets of abstract objects. To harness the utility of sets as building blocks, we must have a way to precisely specify the elements that are members of a set. The notion of membership in a crisp set is simple: an object either is or is not a member of a set. Fuzzy sets allow the possibility of partial membership. An object may partially be a member of the fuzzy set, another object may be more a member of the set than the first object but still not fully a member. Fuzzy set membership can be partial and relative to other objects, so to fully specify a fuzzy set, it is necessary to not only list the objects that are at least partial members, but also to indicate the extent to which each object is a member of a set. Section 2.2 discusses membership functions and related notation.

Original languageEnglish
Title of host publicationApplying Fuzzy Mathematics to Formal Models in Comparative Politics
Pages29-63
Number of pages35
Volume225
DOIs
StatePublished - 2008

Publication series

NameStudies in Fuzziness and Soft Computing
Volume225
ISSN (Print)14349922

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All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Computational Mathematics

Cite this

Clark, T. D., Larson, J. M., Mordeson, J. N., Potter, J. D., & Wierman, M. J. (2008). Fuzzy set theory. In Applying Fuzzy Mathematics to Formal Models in Comparative Politics (Vol. 225, pp. 29-63). (Studies in Fuzziness and Soft Computing; Vol. 225). https://doi.org/10.1007/978-3-540-77461-7_2