Fⁿ-Hypergroups based on fuzzy hyperoperations and fundamental relations

Article type: Research Article

Authors: Farshi, M. | Davvaz, B.

Affiliations: Department of Mathematics, Yazd University, Yazd, Iran

Note: [] Corresponding author. B. Davvaz, Department of Mathematics, Yazd University, Yazd, Iran. E-mail: davvaz@yazd.ac.ir

Abstract: In this paper, the notion of fuzzy n-hypergroups (Fn-hypergroups) by using the notion of Fn-hyperoperations is introduced and some related properties are investigated. In this regards relationships between Fn-hypergroups and n-hypergroups are considered. Next, some properties of direct product of Fn-hypergroups are presented. We then study the quotient of Fn-hypergroups by a fundamental relation and describe some of their properties.

Keywords: Hyperstructure, hyperoperation, n-hypergroup, $F^n$-hypergroup, fundamental relation

DOI: 10.3233/IFS-130829

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 3, pp. 1453-1464, 2014