Concepts and fuzzy sets: Misunderstandings, misconceptions, and oversights

  • Authors:

  • Radim Belohlavek;George J. Klir;Harold W. Lewis, III;Eileen C. Way

  • Affiliations:

  • Binghamton University, SUNY, Binghamton, NY 13902, USA;Binghamton University, SUNY, Binghamton, NY 13902, USA;Binghamton University, SUNY, Binghamton, NY 13902, USA;Binghamton University, SUNY, Binghamton, NY 13902, USA

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2009

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Abstract

The psychology of concepts has been undergoing significant changes since the early 1970s, when the classical view of concepts was seriously challenged by convincing experimental evidence that conceptual categories never have sharp boundaries. Some researchers recognized already in the early 1970s that fuzzy set theory and fuzzy logic were potentially suitable for modeling of concepts and obtained encouraging results. This positive attitude abruptly changed in the early 1980s, and since that time fuzzy set theory and fuzzy logic have been portrayed as problematic and unsuitable for representing and dealing with concepts. Our aim in this paper is to identify some of the most notorious claims regarding fuzzy set theory and fuzzy logic that have propagated through the literature on psychology of concepts and to show that they are, by and large, false. We trace the origin and propagation of these claims within the literature in this area. It is shown in detail that these claims are consistently erroneous and that they are based on various misunderstandings, misconceptions, and oversights. The ultimate purpose of this paper is to document these various erroneous claims.