Affiliations: [a]
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, P.R. China | [b]
School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P.R.China |
Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan
Correspondence:
[*]
Corresponding author. Jian Tang, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China. Tel./Fax: +86 0931 8912481; E-mail: [email protected].
Abstract: In this paper, the concept of ordered fuzzy points of ordered semihypergroups is introduced. By using this new concept, we define and study the fuzzy left, right and two-sided hyperideals of an ordered semihypergroup. In particular, we investigate the properties of fuzzy hyperideals generated by ordered fuzzy points of an ordered semihypergroup. Furthermore, we introduce the concepts of prime, semiprime, weakly prime and weakly semiprime fuzzy hyperideals of ordered semihypergroups and establish the relationship between the four classes of fuzzy hyperideals. Finally, we give some characterizations of semisimple ordered semihypergroups in terms of fuzzy hyperideals. Especially, we prove that an ordered semihypergroup S is semisimple if and only if every fuzzy hyperideal of S can be expressed as the intersection of all weakly prime fuzzy hyperideals of S containing it.
Keywords: Ordered semihypergroup, ordered fuzzy point, fuzzy hyperideal, prime (semiprime) fuzzy hyperideal, weakly prime (weakly semiprime) fuzzy hyperideal, semisimple ordered semihypergroup
