Kayihura, A.
Mawanda, MM.
The hypothesis of right regularity of non-zero truth-values of a category C with fuzzy subsets is proved to be equivalent to the fact that surjections in C are exactly C-epimorphisms. C has associative images if and only if the AND-semilattice L of truth-values is a sup-complete lattice which satisfies left distributivity law. As a consequence, L is a sup-distributive lattice when the canonical multiplication on L is commutative. It is proved that any topos of j-sheaves for a Grothendieck topology j on the monoid L* of non-zero truth-values is a good toposophical approximation of C when L* is a j-sheaf. A consequence is that the topos of j-sheaves, where j is the canonical topology is the best toposophical approximation of C. When the monoid L is commutative, the corresponding AND-semilattice is a sup-distributive lattice and L* satisfies a strong properties of density then the sup-operation on left ideals of L* determines a Grothendieck topology (-) on L* such that the category of (-)-separated objects is a good completion of C.
Bibliographic reference |
Kayihura, A. ; Mawanda, MM.. On a Categorical Analysis of Zadeh Generalized Subsets of Sets .2.. In: Fuzzy Sets and Systems, Vol. 51, no. 2, p. 219-226 (1992) |
Permanent URL |
http://hdl.handle.net/2078.1/50127 |