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The concept of generalized interval-valued vague soft set is introduced along with its operations of intersection and union. An application of generalized interval-valued vague soft sets in decision making with respect to degree of preference is illustrated.

Molodtsov has introduced the concept of soft sets and the application of soft sets in decision making and medical diagnosis problems. The basic properties of vague soft sets are presented. In this paper, we introduce the concept of interval-valued vague soft sets which are an extension of the soft set and its operations such as equality, subset, intersection, union, AND operation, OR operation, complement, and null while further studying some properties. We give examples for these concepts, and we give a number of applications on interval-valued vague soft sets.

The concept of possibility interval-valued vague soft set is introduced along with its operations of subset, intersection and union. An application of possibility interval-valued vague soft sets in decision making with respect to degree of preference is then illustrated.