Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of possibility interval-valued fuzzy soft sets are proposed. Their operations and basic properties are studied which are subset, equal, relative complement, union, intersection, restricted union, extended intersection, “AND”, “OR” and De Morgan Laws. Furthermore, an application of the new approach in decision making based on possibility interval-valued fuzzy soft set is illustrated.