Fuzzy points and fuzzy prototypes

Abstract

There has been considerable interest in the nature of fuzzy points and in their relationship to crisp points. This paper describes a very general approach to the characterization of points which treats them as generalized maps from one object to another in a 2-categorical framework. It will be shown that fuzzy points are also amenable to this treatment, and that, if the category (of locales) is assumed to be equipped with a KZ monad, the locales of fuzzy sets exhibit behavior which allows for such useful results as the justification of the Zadeh Extension Principle and the unification of change of base and change of set in fuzzy set theory.