Ternary semihypergroups characterized by fuzzy bi-hyperideals
Abstract
This paper deals with a class of algebraic hyperstruc-Tures called ternary semihypergroups. In this paper, we study ternary semihypergroups in terms of fuzzy bi-hyperideals fuzzyficating some results obtained for bi-hyperideals in ternary semihypergroups [31]. We introduce and study some classes of fuzzy bi-hyperideals that of prime, semiprime, strongly prime, irreducible and strongly irreducible fuzzy bi-hyperideals in ternary semihypergroups and some properties of them are investigated. The space of all strongly prime proper fuzzy bi-hyperideals in a ternary semihypergroup is topolo- gized. We characterize those ternary semihypergroups for which each bi-hyperideal is strongly irreducible and also those ternary semihypergroups in which each bi-hyperideal is strongly prime, in particular, it has been proved that in case of the totally ordered set of fuzzy bi-hyperideals of a semihypergroup H, the notion of irreducible prime fuzzy bi-hyperideals and strongly irreducible prime fuzzy bi- hyperideals coincides.
