δ-relation on dual hyper K–algebras

Article type: Research Article

Authors: Hamidi, Mohammad^a | Rezaei, Akbar^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: In this paper, we are going to introduce a fundamental relation “δ” on (hyper BE-algebra) dual hyper K-algebra and investigate some properties. We show that quotient of any dual hyper K-algebra via a regular relation is a hyper BE-algebra and this quotient, via any strongly regular relation is a BE-algebra. Furthermore, it shows that “δ” under some condition is transitive and quotient of any weak commutative dual hyper K-algebra via “δ*” is a dual BCK-algebra.

Keywords: (hyper)BE–algebra, hyper K–algebra, fundamental relation

DOI: 10.3233/IFS-151667

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 5, pp. 1889-1900, 2015