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This paper presents a new correlation coefficient measure, which satisfies the requirement of this measure equaling one if and only if two interval neutrosophic sets (INSs) are the same. And an objective weight of INSs is presented to unearth and utilize deeper information that is uncertain. Using the proposed weighted correlation coefficient measure of INSs, a decision-making method is developed, which takes into account the influence of the evaluations’ uncertainty and both the objective and subjective weights.