Abstract
An interval-valued refined neutrosophic set is simply an extension of interval neutrosophic set and refined neutrosophic set which can be used in statistics, game theory, engineering, and experimental science. In this study, we define the cut set and extension principle based on interval-valued refined neutrosophic sets which is a bridge between interval-valued refined neutrosophic sets and crisp sets. Also, we examine the properties of the cut sets and extension principle of interval-valued refined neutrosophic sets. Finally, according to the extension principle of the interval-valued refined neutrosophic sets, we introduce some algebraic operations over the interval-valued refined neutrosophic sets.
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