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On a categorical analysis of Zadeh generalized subsets of sets I

Part of the Lecture Notes in Mathematics book series (LNM,volume 1348)

Abstract

How can fuzzy sets be viewed as generalized subsets of actual sets? An answer to this question is given via a categorical analysis of the synchronic approach of fuzzy set theory. Starting from an abstract definition of a category with fuzzy subsets, we establish necessary and sufficient conditions on a posst to be that of truth-values for such a category. These conditions justify Zadeh's original choice of the unit segment as a set of truth-values. Some defects concerning universal constructions in a non trivial category with fuzzy subsets are mentioned and a natural best toposophical approximation of such a category is proposed.

Keywords

  • Categorical Analysis
  • Full Subcategory
  • Fuzzy Subset
  • Simple Extension
  • Small Category

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by Projet FDS "Théorie des Topos" C.A.C. 216/1459.

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© 1988 Springer-Verlag

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Mawanda, M.M. (1988). On a categorical analysis of Zadeh generalized subsets of sets I. In: Borceux, F. (eds) Categorical Algebra and its Applications. Lecture Notes in Mathematics, vol 1348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081364

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  • DOI: https://doi.org/10.1007/BFb0081364

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50362-0

  • Online ISBN: 978-3-540-45985-9

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