TY - JOUR
ID - 296
TI - ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET
OPERATORS
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Zhang, Qi-Ye
AD - School of Mathematics and Systems Science, Beihang University, Beijing
100191, China and LMIB of the Ministry of Education, Beijing 100191, China
Y1 - 2011
PY - 2011
VL - 8
IS - 5
SP - 31
EP - 58
KW - Complete residuated lattice
KW - $L$-fuzzy poset
KW - category
KW - Adjunction
KW - Algebraic theory
KW - Powerset theory
KW - Algebraic generation
DO - 10.22111/ijfs.2011.296
N2 - 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.
UR - https://ijfs.usb.ac.ir/article_296.html
L1 - https://ijfs.usb.ac.ir/article_296_80d019c2a46e66b3c7ab1031e2569b3e.pdf
ER -