@article {
author = {Zhang, Qi-Ye},
title = {ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET
OPERATORS},
journal = {Iranian Journal of Fuzzy Systems},
volume = {8},
number = {5},
pages = {31-58},
year = {2011},
publisher = {University of Sistan and Baluchestan},
issn = {1735-0654},
eissn = {2676-4334},
doi = {10.22111/ijfs.2011.296},
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 $\widetilde{f}^\rightarrow,\widetilde{f}_\ast^\rightarrow, \widetilde{f}^{\ast\rightarrow}$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.},
keywords = {Complete residuated lattice,$L$-fuzzy poset,category,Adjunction,Algebraic theory,Powerset theory,Algebraic generation},
url = {https://ijfs.usb.ac.ir/article_296.html},
eprint = {https://ijfs.usb.ac.ir/article_296_80d019c2a46e66b3c7ab1031e2569b3e.pdf}
}