Relations and homomorphisms of fuzzy hyper BE–subalgebras

Article type: Research Article

Authors: Hamidi, Mohammad^a | Borumand Saeid, Arsham^{b; *}

Affiliations: [a] Department of Mathematics, Payame Noor University (PNU), Tehran, Iran | [b] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Correspondence: [*] Corresponding author. Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +98 34 31322490; E-mail: [email protected].

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.

Keywords: Fuzzy (hyper)BE–subalgebra, (strongly) fuzzy hyper filter, fundamental relation δ^*, (locally) fuzzy homomorphism

DOI: 10.3233/JIFS-151517

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1565-1578, 2016