Regular and intra-regular semihypergroups in terms of soft union hyperideals

Article type: Research Article

Authors: Naz, Shafaq^{a; *} | Shabir, Muhammad^b

Affiliations: [a] Department of Mathematics, University of Gujrat, Gujrat, Pakistan | [b] Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Correspondence: [*] Corresponding author. Shafaq Naz, Department of Mathematics, University of Gujrat, Gujrat, Pakistan. Tel.: +92 3344618437; E-mail: [email protected].

Abstract: This paper deals with a particular class of hyperstructures called semihypergroups, which is a generalization of semigroups. We introduce the notions of SU-qausi hyperideal, SU-bi-hyperideal, SU-generalized bi-hyperideal, SU-interior hyperideal and discuss several properties of these hyperideals. We also characterize regular and intra-regular semihypergroups by the properties of their SU-hyperideals.

Keywords: SU-subsemihypergroup, SU-quasi-hyperideal, SU-bi-hyperideal, SU-generalizedbi-hyperideal, SU-interior hyperideal, regular semihypergroup and intra-regular semihypergroup

DOI: 10.3233/JIFS-15331

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 6, pp. 4119-4134, 2017