Transposition Fⁿ-hypergroups

Article type: Research Article

Authors: Farshi, Mehdi | Davvaz, Bijan | Mirvakili, Saeed

Affiliations: Department of Mathematics, Yazd University, Yazd, Iran | Department of Mathematics, Payame Noor University, Tehran, Iran

Note: [] Corresponding author. Bijan Davvaz, Department of Mathematics, Yazd University, Yazd, Iran. Tel.: +983518122711; Fax: +983518210695; E-mails: [email protected], [email protected]

Abstract: In this paper, the notion of weak transposition Fn-hypergroups as a subclass of fuzzy transposition n-ary hypergroups (transposition Fn-hypergroups) is introduced and several properties are found and examples are presented. We show that transposition Fn-hypergroups are a generalization of F-polygroups, Fn-polygroups and join Fn-spaces. Finally, we prove that the class of Fn-polygroups and faint regular weak transposition Fn-hypergroups coincide.

Keywords: n-hypergroup, $F^n$-polygroup, $F^n$-hypergroup, faint regular, regular, weak transposition

DOI: 10.3233/IFS-141454

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 4, pp. 1677-1685, 2015