Fuzzy Galois connections on fuzzy sets
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866917749347844096 |
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| author | García, Javier Gutiérrez Lai, Hongliang Shen, Lili |
| author_facet | García, Javier Gutiérrez Lai, Hongliang Shen, Lili |
| contents | In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the readership of fuzzy set theorists, with particular attention paid to fuzzy Galois connections between preordered fuzzy sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_08849 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Fuzzy Galois connections on fuzzy sets García, Javier Gutiérrez Lai, Hongliang Shen, Lili Logic in Computer Science 03B52, 06A15, 06F07, 18B35, 18D20, 18A40 In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the readership of fuzzy set theorists, with particular attention paid to fuzzy Galois connections between preordered fuzzy sets. |
| title | Fuzzy Galois connections on fuzzy sets |
| topic | Logic in Computer Science 03B52, 06A15, 06F07, 18B35, 18D20, 18A40 |
| url | https://arxiv.org/abs/1707.08849 |