Categorical analysis of logic operators on fuzzy sets (Q1310393)

The connection between fuzzy set theory and topos theory is studied from a categorical point of view. The category \({\mathfrak {Fuz}}\), a subcategory of \({\mathfrak {SetH}}\), is introduced; the concepts of middle object (serving a similar function for \({\mathfrak {SetH}}\) as the subobject classifier in \({\mathfrak {Topos}}\)), \({\mathfrak {WSC}}\) and \({\mathfrak {WTopos}}\) are defined. On this basis the logic operations of fuzzy sets are naturally obtained.