A non-controversial definition of fuzzy sets

  • Authors:
  • Jaroslav Ramík;Milan Vlach

  • Affiliations:
  • Institute for Research and Applications of Fuzzy Modelling, University of Ostrava, Czech Republic;Institute of Information Theory and Automation, Praha, Czech Republic

  • Venue:
  • Transactions on Rough Sets II
  • Year:
  • 2005

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Abstract

Already in the early stages of the development of fuzzy set theory, it has been recognized that fuzzy sets can be defined and represented in several different ways. In this paper we first define fuzzy sets within the classical set theory by suitable nested families of sets, and then we discuss how this definition is related to the usual definition by membership functions.