Preprint Article Version 1 This version not peer reviewed

Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem

Version 1 : Received: 9 August 2017 / Approved: 9 August 2017 / Online: 9 August 2017 (06:39:47 CEST)

A peer-reviewed article of this Preprint also exists.

Servin, C.; Muela, G.D.; Kreinovich, V. Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem. Axioms 2018, 7, 8. Servin, C.; Muela, G.D.; Kreinovich, V. Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem. Axioms 2018, 7, 8.

Journal reference: Axioms 2018, 7, 8
DOI: 10.3390/axioms7010008

Abstract

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

Subject Areas

fuzzy set; ordered category; category of fuzzysets

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