Equalizer in the Kleisli category of the $n$-fuzzy powerset monad
In this article, we first consider the $L$-fuzzy powerset monad on a completely distributive lattice $L$. Then for $L=[n]$, we investigate the fuzzy powerset monad on $[n]$ and we introduce simple, subsimple and quasisimple $L$-fuzzy sets. Finally, we provide necessary and sufficient conditions for...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2024-12-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4320_8baa3307efc023dd99e6e6cf076339c8.pdf |
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| author | Seyed Naser Hosseini Yousef Qasemi Nezhad |
| author_facet | Seyed Naser Hosseini Yousef Qasemi Nezhad |
| author_sort | Seyed Naser Hosseini |
| collection | DOAJ |
| description | In this article, we first consider the $L$-fuzzy powerset monad on a completely distributive lattice $L$. Then for $L=[n]$, we investigate the fuzzy powerset monad on $[n]$ and we introduce simple, subsimple and quasisimple $L$-fuzzy sets. Finally, we provide necessary and sufficient conditions for the existence of an equalizer of a given pair of morphisms in the Kleisli category associated to this monad. Several illustrative examples are also provided. |
| format | Article |
| id | doaj-art-42443b0117ad4c9e86b1c11263f12f87 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-42443b0117ad4c9e86b1c11263f12f872025-01-04T19:29:49ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052024-12-01134839910.22103/jmmr.2024.22946.15844320Equalizer in the Kleisli category of the $n$-fuzzy powerset monadSeyed Naser Hosseini0Yousef Qasemi Nezhad1Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, IranDepartment of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, IranIn this article, we first consider the $L$-fuzzy powerset monad on a completely distributive lattice $L$. Then for $L=[n]$, we investigate the fuzzy powerset monad on $[n]$ and we introduce simple, subsimple and quasisimple $L$-fuzzy sets. Finally, we provide necessary and sufficient conditions for the existence of an equalizer of a given pair of morphisms in the Kleisli category associated to this monad. Several illustrative examples are also provided.https://jmmrc.uk.ac.ir/article_4320_8baa3307efc023dd99e6e6cf076339c8.pdf(completely distributive) lattice(simplesubsimplequasisimple) fuzzy setfuzzy powerset functor |
| spellingShingle | Seyed Naser Hosseini Yousef Qasemi Nezhad Equalizer in the Kleisli category of the $n$-fuzzy powerset monad Journal of Mahani Mathematical Research (completely distributive) lattice (simple subsimple quasisimple) fuzzy set fuzzy powerset functor |
| title | Equalizer in the Kleisli category of the $n$-fuzzy powerset monad |
| title_full | Equalizer in the Kleisli category of the $n$-fuzzy powerset monad |
| title_fullStr | Equalizer in the Kleisli category of the $n$-fuzzy powerset monad |
| title_full_unstemmed | Equalizer in the Kleisli category of the $n$-fuzzy powerset monad |
| title_short | Equalizer in the Kleisli category of the $n$-fuzzy powerset monad |
| title_sort | equalizer in the kleisli category of the n fuzzy powerset monad |
| topic | (completely distributive) lattice (simple subsimple quasisimple) fuzzy set fuzzy powerset functor |
| url | https://jmmrc.uk.ac.ir/article_4320_8baa3307efc023dd99e6e6cf076339c8.pdf |
| work_keys_str_mv | AT seyednaserhosseini equalizerinthekleislicategoryofthenfuzzypowersetmonad AT yousefqaseminezhad equalizerinthekleislicategoryofthenfuzzypowersetmonad |