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Extended fuzzy BCK-subalgebras. (English) Zbl 1357.06018

Summary: This paper extends the notion of fuzzy BCK-subalgebras to fuzzy hyper BCK-subalgebras and defines an extended fuzzy BCK-subalgebras. This study considers a type of fuzzy hyper BCK-ideals in this hyperstructure and describes the relationship between hyper BCK-ideals and fuzzy hyper BCK-ideals. In fact, it tries to introduce a strongly regular relation on hyper BCK-algebras. Moreover, by using the fuzzy hyper BCK-ideals, it defines a congruence relation on (weak commutative) hyper BCK-algebras that under some conditions is strongly regular and the quotient of any hyper BCK-algebra via this relation is a (hyper BCK-algebra) BCK-algebra.

MSC:

06F35 BCK-algebras, BCI-algebras
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