An application of the theory of categorical many-valued partial orders to sets with fuzzy equalities

A recently proposed theory of categorical many-valued partial orders suggests a new approach fuzzy equality-based fuzzy partial orders. The present study applies the theory to the category GL- SET of global L-valued sets for a fixed strictly two-sided, commutative quantale L . a special global L-valued set Q, we construct a partially ordered Q-monoidal relation system YG, containing an Q-monoidal relation system, on GL- SET and formulate fuzzy equality based fuzzy partial orders on sets as YG-partial orders on global L-valued sets in this paper. It is then shown that the category of fuzzy equality-based fuzzy partially ordered sets can presented as the category of YG-partially ordered global L-valued sets. Furthermore, we explicit characterizations of the Kleisli and Eilenberg-Moore categories of the Q-monoidal power object monad associated with