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

1
Department of Computer Science and Information Technology, El Paso Community College, El Paso, TX 79915, USA
2
Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
All the authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 9 August 2017 / Revised: 2 January 2018 / Accepted: 9 January 2018 / Published: 23 January 2018
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
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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. View Full-Text
Keywords: fuzzy set; ordered category; category of fuzzy sets fuzzy set; ordered category; category of fuzzy sets
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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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.

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