COMPLETE SUBOBJECTS OF FUZZY SETS OVER MV-ALGEBRAS


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Abstract

A subobjects structure of the category Ω-FSet of Ω-fuzzy sets over a complete MV-algebra Ω = (L, ∧, ∨, ⊗, →) 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 morphismsA → Ω* = (L × L, μ) are then investigated. It is proved that some truth-valued morphisms ¬Ω: Ω* → Ω*, ∩Ω, ∪Ω: Ω* × Ω* → Ω* are characteristic morphisms of complete subobjects.

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