A natural interpretation of fuzzy sets and fuzzy relations (Q698758)

The author presents a new interpretation of fuzzy sets and fuzzy relations (such as reflexive, symmetric, transitive, etc.) in a cumulative Heyting-valued model for intuitionistic set theory. This interpretation is claimed to be natural, since the definitions and basic properties are almost the same as those concerning crisp sets. The canonical embedding of the class of all sets into the model becomes one of the key issues. In view of this, the author distinguishes between generalized fuzzy sets, fuzzy subsets of crisp sets, and membership functions of fuzzy sets on crisp sets.