Abstract
This paper introduces the notion of (locally) fuzzy homomorphism in fuzzy hyper BE-subalgebra and makes a connection between fuzzy BE-algebras and hyper BE-algebras via this notion. Considering the fuzzy homomorphism in fuzzy hyper BE-subalgebra, this study defines some equivalence relations in a way that, under some conditions, are regular or strongly regular and so derives fuzzy BE-algebras by quotient of hyper fuzzy BE-subalgebras. In fact, it tries to introduce some strongly regular relations on any hyper BE-algebras by using the concept of fuzzy hyper BE-subalgebras and fuzzy homomorphism. Moreover, the concept of normal fuzzy homomorphism is defined and some new normal fuzzy homomorphisms are introduced to make better connections between fuzzy BE-algebras and fuzzy hyper BE-subalgebras.
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