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Iranian Journal of Fuzzy Systems، جلد ۸، شماره ۵، صفحات ۳۱-۵۸
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| عنوان فارسی |
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| چکیده فارسی مقاله |
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| کلیدواژه‌های فارسی مقاله |
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| عنوان انگلیسی |
ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS |
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| چکیده انگلیسی مقاله |
In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mappings, respectively. It isproved that there are adjunctions between {bf Set} and $LF$-{bf CSLat}$(sqcup)$, between $LF$-{bfPos} and $LF$-{bf CSLat}$(sqcup)$, and between $LF$-{bf Pos} and$LF$-{bf CSLat}$(sqcap)$, that is, {bf Set}$dashv LF$-{bf CSLat}$(sqcup)$, $LF$-{bfPos}$dashv LF$-{bf CSLat}$(sqcup)$, and $LF$-{bf Pos}$dashv$$LF$-{bf CSLat}$(sqcap)$. And a usual mapping $f$ generates thetraditional Zadeh forward powerset operator $f_L^rightarrow$ andthe fuzzy forward powerset operators $widetilde{f}^rightarrow,widetilde{f}_ast^rightarrow, widetilde{f}^{astrightarrow}$defined by the author et al via these adjunctions. Moreover, it is also shownthat all the fuzzy powerset operators mentioned above can be generated by the underlying algebraic theories. |
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| کلیدواژه‌های انگلیسی مقاله |
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| نویسندگان مقاله |
Qi-Ye Zhang |
School of Mathematics and Systems Science, Beihang University, Beijing
100191, China and LMIB of the Ministry of Education, Beijing 100191, China
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| نشانی اینترنتی |
http://ijfs.usb.ac.ir/article_296_80d019c2a46e66b3c7ab1031e2569b3e.pdf |
| فایل مقاله |
اشکال در دسترسی به فایل - ./files/site1/rds_journals/448/article-448-1550075.pdf |
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| زبان مقاله منتشر شده |
en |
| موضوعات مقاله منتشر شده |
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