Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem
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...
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MDPI AG
2018-01-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/7/1/8 |
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doaj-1dd2d7fbf105410ba333f5242ef400e72020-11-24T21:09:32ZengMDPI AGAxioms2075-16802018-01-0171810.3390/axioms7010008axioms7010008Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A TheoremChristian Servin0Gerardo D. Muela1Vladik Kreinovich2Department of Computer Science and Information Technology, El Paso Community College, El Paso, TX 79915, USADepartment of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USADepartment of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USAIn 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.http://www.mdpi.com/2075-1680/7/1/8fuzzy setordered categorycategory of fuzzy sets |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Christian Servin Gerardo D. Muela Vladik Kreinovich |
| spellingShingle |
Christian Servin Gerardo D. Muela Vladik Kreinovich Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem Axioms fuzzy set ordered category category of fuzzy sets |
| author_facet |
Christian Servin Gerardo D. Muela Vladik Kreinovich |
| author_sort |
Christian Servin |
| title |
Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem |
| title_short |
Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem |
| title_full |
Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem |
| title_fullStr |
Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem |
| title_full_unstemmed |
Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem |
| title_sort |
fuzzy analogues of sets and functions can be uniquely determined from the corresponding ordered category: a theorem |
| publisher |
MDPI AG |
| series |
Axioms |
| issn |
2075-1680 |
| publishDate |
2018-01-01 |
| description |
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. |
| topic |
fuzzy set ordered category category of fuzzy sets |
| url |
http://www.mdpi.com/2075-1680/7/1/8 |
| work_keys_str_mv |
AT christianservin fuzzyanaloguesofsetsandfunctionscanbeuniquelydeterminedfromthecorrespondingorderedcategoryatheorem AT gerardodmuela fuzzyanaloguesofsetsandfunctionscanbeuniquelydeterminedfromthecorrespondingorderedcategoryatheorem AT vladikkreinovich fuzzyanaloguesofsetsandfunctionscanbeuniquelydeterminedfromthecorrespondingorderedcategoryatheorem |
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