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W2172129871 abstract "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." @default.
W2172129871 created "2016-06-24" @default.
W2172129871 creator A5078663034 @default.
W2172129871 date "2011-10-06" @default.
W2172129871 modified "2023-09-22" @default.
W2172129871 title "ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS" @default.
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W2172129871 doi "https://doi.org/10.22111/ijfs.2011.296" @default.
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