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Complete Subobjects of Fuzzy Sets Over MV-Algebras

Authors:	Jiří Močkoř

Institution:	(1) Department of Mathematics, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, CZ-702 00 Ostrava, España

Abstract:	A subobjects structure of the category -FSet of -fuzzy sets over a complete MV-algebra $\Omega = \left( {L,\Lambda , \vee , \otimes , \to } \right)$ is investigated, where an -fuzzy set is a pair A = (A, ) such that A is a set and : A × A is a special map. Special subobjects (called complete) of an -fuzzy set A which can be identified with some characteristic morphisms A ^* = (L × L, ) 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.

Keywords:	fuzzy set over MV-algebra complete subobjects subobjects classification
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