The double contravariant powerset monad in the Goguen category of fuzzy sets

TL;DR

This paper introduces a monad in the Goguen category of fuzzy sets, demonstrating that this category is dually monadic over itself, extending classical set-theoretic concepts to fuzzy set contexts.

Contribution

It constructs a double contravariant powerset monad in the Goguen category, showing the category's self-dual monadic property, a novel extension of set theory to fuzzy sets.

Findings

Established a monad analogous to the powerset monad in fuzzy sets

Proved the Goguen category of fuzzy sets is dually monadic over itself

Extended classical categorical concepts to fuzzy set theory

Abstract

A monad is constructed in the Goguen category of fuzzy sets valued in a unital quantale, which is an analog of the double contravariant powerset monad in the category of sets. With help of this monad it is proved that the Goguen category of fuzzy sets is dually monadic over itself.