Characterizations of semisimple ordered semihypergroups in terms of fuzzy hyperideals

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 semihyper- groups 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.