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The paper presents a new correlation coefficient measures satisfying the requirement that the correlation coefficient measure equals one if and only if two interval neutrosophic sets (INSs) are same and the weighted correlation coefficient measure of INSs based on the extension of the correlation coefficient measures of intuitionstic fuzzy sets (IFSs). Firstly, an improved correlation coefficient measure, the weighted correlation coefficient measure and their properties for INSs are developed. Secondly, the notion that the weight in the weighted correlation coefficient should be the integrated weight which is the integration of subjective weight and objective weight is put forward. Thirdly, an objective weight of INSs based on entropy is presented to unearth and utilize the deeper uncertainty information. Then, a decision making method is proposed by the use of the weighted correlation coefficient measure of INSs. Specially, this method takes the influence of the evaluations’ uncertainty into consideration and takes both the objective weight and the subjective weight into consideration. Finally, an illustrative example demonstrates the concrete application of the proposed method and the comparison analysis is given

zenodo (cern european organization for nuclear research)

Improved Weighted Correlation Coefficient based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision Making Problems