Complete Subobjects of Fuzzy Sets Over MV-Algebras

Abstract

A subobjects structure of the category Ω-FSet of Ω-fuzzy sets over a complete MV-algebra $$\Omega = \left( {L,\Lambda , \vee , \otimes , \to } \right)$$ is investigated, where an Ω-fuzzy set is a pair A = (A, δ) such that A is a set and δ: A × A → Ω is a special map. Special subobjects (called complete) of an Ω-fuzzy set A which can be identified with some characteristic morphisms A → Ω* = (L × L, μ) are then investigated. It is proved that some truth-valued morphisms $$_\Omega :\Omega ^ * \to \Omega ^ * , \cap _\Omega , \cup _\Omega :\Omega ^ * \times \Omega ^ * \to \Omega ^ * $$ are characteristic morphisms of complete subobjects.