Relations and homomorphisms of fuzzy hyper BE –subalgebras

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.