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