Abstract
In this paper, soft intersection $$\varGamma $$ -hyperideals of ordered $$\varGamma $$ -semihypergroups over an initial universe $$\mathcal {V}$$ are defined and some properties of them with soft intersection product are obtained. Further, some characterizations of regular and intra-regular ordered $$\varGamma $$ -semihypergroups in terms of soft intersection $$\varGamma $$ -hyperideals are provided. We also introduce the notion of semisimple ordered $$\varGamma $$ -semihypergroups. Finally, we give some characterizations of semisimple ordered $$\varGamma $$ -semihypergroups in terms of soft prime and soft semiprime $$\varGamma $$ -hyperideals.
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