Some remarks on fuzzy powerset operators
The paper remembers some concepts and properties given in a paper before, that is, present the categories \(\mathcal {A-F}\), \(\mathcal E-F\), \(\mathcal {G-F}\) and \(F\)-\({\mathcal S}et\), reconsiders and redefines the fuzzy powerset operators for each one and lists some properties of these. Then, the authors develop some characterizations of isomorphisms in the categories \(\mathcal {E-F}\), \(\mathcal G-F\) and \(\mathcal {A-F}\), by means of the corresponding powerset operators. They present covering properties in relation to fuzzy points, properties about the image of bold fuzzy points, under the injectivity of the forward powerset operator, and an improve of the above characterization of isomorphisms in \(\mathcal A-F\). Finally, they define the complemented backward powerset operator related to a morphism in anyone of the considered ground categories and the corresponding order reversing involution, and some propositions which relate this operator with both forward and backward powerset operators are proved.
scientific article; zbMATH DE number 1758528