فهرست نشریات علمی دسترسی آزاد ایران

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.