Fuzzy hyperrings and fundamental relation

Issue title: Selected papers from the 4th Iranian Joint Congress On Fuzzy and Intelligent Systems – CFIS2015, 9–11 September 2015

Article type: Research Article

Authors: Nozari, Tahereh^* | Fahimi, Najmeh

Affiliations: Department of mathematics, Golestan university, Gorgan, Iran

Correspondence: [*] Corresponding author. Tahereh Nozari, Department of mathematics, Golestan university, Gorgan, Iran. Tel.: +98 1732254163; Fax: +98 1732245882; E-mail: t.nozari@gu.ac.ir.

Abstract: In this paper we introduce and analyze the fundamental relation on fuzzy hyperrings. This relation is the smallest equivalence relation on a given fuzzy hyperring such that it’s quotient structure is a ring. Then we introduce the notion of a fuzzy complete part of a fuzzy hyperring and we study the relationship between the fundamental relation and fuzzy complete parts of a fuzzy hyperring. Also the commutative fundamental relation is introduced that its quotient structure in this case is a commutative ring. Finally some necessary and sufficient conditions so that this relation be transitive, are determined.

Keywords: Fuzzy hyperring, fundamental relation, fundamental ring, complete part, commutative fundamental relation

DOI: 10.3233/IFS-152045

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 3, pp. 1311-1317, 2016