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 (US)
    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

    Fingerprint

    Fuzzy set theory
    Fuzzy Set Theory
    Fuzzy sets
    Fuzzy Sets
    Partial
    Social sciences
    Membership functions
    Set theory
    Object
    Social Sciences
    Set Theory
    Fuzzy numbers
    Membership Function
    Building Blocks
    Notation
    Distinct
    Necessary

    ASJC Scopus subject areas

    • 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

    Fuzzy set theory. / Clark, Terry D.; Larson, Jennifer M.; Mordeson, John N.; Potter, Joshua D.; Wierman, Mark J.

    Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225 2008. p. 29-63 (Studies in Fuzziness and Soft Computing; Vol. 225).

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Clark, TD, Larson, JM, Mordeson, JN, Potter, JD & Wierman, MJ 2008, Fuzzy set theory. in Applying Fuzzy Mathematics to Formal Models in Comparative Politics. vol. 225, Studies in Fuzziness and Soft Computing, vol. 225, pp. 29-63. https://doi.org/10.1007/978-3-540-77461-7_2
    Clark TD, Larson JM, Mordeson JN, Potter JD, Wierman MJ. Fuzzy set theory. In Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225. 2008. p. 29-63. (Studies in Fuzziness and Soft Computing). https://doi.org/10.1007/978-3-540-77461-7_2
    Clark, Terry D. ; Larson, Jennifer M. ; Mordeson, John N. ; Potter, Joshua D. ; Wierman, Mark J. / Fuzzy set theory. Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225 2008. pp. 29-63 (Studies in Fuzziness and Soft Computing).
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