Possibility belief interval-valued soft set and its application in decision making

The aim of this article is to present the concept of restricted union and extended intersection of belief interval-valued soft sets, along with its properties. In addition, we propose the concept of possibility belief interval-valued soft set theory and investigate their properties. For suitability of possible applications, there are seven kinds of operations (e.g., union, intersection, restricted union, extended intersection, complement, soft max-AND, and soft min-OR) on the possibility belief interval-valued soft sets are defined and their basic theoretical are given. Then, we construct two algorithms by using soft max-AND and soft min-OR operations of possibility interval-valued soft sets for fuzzy decision-making problem. Lastly, we introduce an algorithm using a possibility interval-valued soft set to solve the decision-making problems and clarify its applicability by a numerical example.