Department of Mathematics, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, CZ-702 00 Ostrava, e-mail: Jiri.Mockor@osu.cz
Abstract: A subobjects structure of the category $\Omega${-\FSet} of $\Omega$-fuzzy sets over a complete $MV$-algebra $\Omega=(L,\wedge,\vee,\otimes,\rightarrow)$ is investigated, where an $\Omega$-fuzzy set is a pair $ A=(A,\delta)$ such that $A$ is a set and $\delta A\times A\rightarrow\Omega$ is a special map. Special subobjects (called complete) of an $\Omega$-fuzzy set $ A$ which can be identified with some characteristic morphisms $ A\rightarrow\Omega^*=(L\times L,\mu)$ are then investigated. It is proved that some truth-valued morphisms $\neg_{\Omega} \Omega^*\rightarrow\Omega^*,\cap_{\Omega}$, $\cup_{\Omega} \Omega^*\times\Omega^*\rightarrow\Omega^*$ are characteristic morphisms of complete subobjects.
Keywords: fuzzy set over $MV$-lagebra, complete subobjects, subobjects classification
Classification (MSC 2000): 06D15, 18B05, 03E72
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