Computational & Applied Mathematics | 2021
A novel investigation on fuzzy hyperideals in ordered $$*$$-semihypergroups
Abstract
In this paper, we study the ordered $$*$$\n -semihypergroups in terms of fuzzy subsets in detail and define a unary operation $$\\star $$\n on the set of all the fuzzy subsets of an ordered $$*$$\n -semihypergroup. To begin with, we define and study the fuzzy hyperideals of an ordered $$*$$\n -semihypergroup. In particular, we investigate the properties of fuzzy hyperideals generated by ordered fuzzy points of an ordered $$*$$\n -semihypergroup. Furthermore, we introduce the concepts of prime, weakly prime and semiprime fuzzy hyperideals of ordered $$*$$\n -semihypergroups. Especially, the relationships among these three types of fuzzy hyperideals are established. In the sequel, we give some characterizations of intra-regular ordered $$*$$\n -semihypergroups and semisimple ordered $$*$$\n -semihypergroups in terms of fuzzy hyperideals. Especially, we prove that an ordered $$*$$\n -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.