A novel approach to study ternary semihypergroups in terms of prime soft hyperideals

In this paper, we give the generalized form of soft semihypergroups in ternary structure and have studied it with the help of examples. There are some structures that are not appropriately handled by using the binary operation of the semihypergroup, such as all the sets of non-positive numbers are not closed under binary operation but hold for ternary operation. To deal with this type of problem and handling special type of uncertainty, we study the ternary semihypergroup in terms of prime soft hyperideals. We have introduced prime, strongly prime, semiprime, irreducible and strongly irreducible soft bi-hyperideals in ternary semihypergroups and studied certain properties of these soft bi-hyperideals in ternary semihypergroups. The main advantage of this paper is that we proved that each soft bi-hyperideal of ternary semihypergroup $K$ is strongly prime if it is idempotent and the set of soft bi-hyperideals of $K$ is totally ordered by inclusion.