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On a categorical analysis of Zadeh generalized subsets of sets I

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Categorical Algebra and its Applications

Part of the book series: Lecture Notes in Mathematics ((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.

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

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Authors and Affiliations

  1. Institut de Mathématique, Université Catholique de Louvain, 2, chemin du Cyclotron, B-1348, Louvain-la-Neuve, Belgium

    M. M. Mawanda

Authors
  1. M. M. Mawanda
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Francis Borceux

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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

  • eBook Packages: Springer Book Archive

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