Theory of soft sets proposed by Molodtsov as a general framework for reasoning about vague concepts is a powerful mathematical tool for modelling various types of uncertainties. In this paper, we introduce the notions of intersectional soft subsemihypergroup, intersectional soft left (lateral, right) hyperideal of ordered ternary semihypergroups and related properties are investigated. We present characterizations of right weakly regular ordered ternary semihypergroups by means of intersectional hyperideals.