Fuzzy ordered Krasner hyperrings

Issue title: Dedicated to Professor Lotfi A. Zadeh and Fifty Years of Fuzzy Logic

Article type: Research Article

Authors: Davvaz, B.^a | Leoreanu-Fotea, V.^{b; *}

Affiliations: [a] Department of Mathematics, Yazd University, Yazd, Iran | [b] Faculty of Mathematics, Al.I. Cuza University of Iasi, Romania

Correspondence: [*] Corresponding author. V. Leoreanu-Fotea, Faculty of Mathematics, Al.I. Cuza University of Iasi, Romania. Tel.: +40 742 816 969; Fax: +40 232 201 160; E-mail: foteavioleta@gmail.com.

Abstract: An ordered Krasner hyperring is a Krasner hyperring (R, + , ·) besides a partial order relation ≤ that satisfies the monotone conditions. In this paper, we introduce the concept of fuzzy hyperideals, fuzzy quasi-hyperideals and fuzzy bi-hyperideals of an ordered Krasner hyperring and we present some examples in this respect. We give the main theorems which characterize the hyperideals, quasi-hyperideals and bi-hyperideals in terms of fuzzy hyperideals, fuzzy quasi-hyperideals and fuzzy bi-hyperideas, respectively.

Keywords: Hyperring, Krasner hyperring, order, ordered Krasner hyperring, fuzzy set, fuzzy hyperideal, fuzzy quasi-hyperideal, fuzzy bi-hyperideal

DOI: 10.3233/IFS-151716

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 3, pp. 1057-1064, 2015