Some distances, similarity and entropy measures for interval-valued neutrosophic sets and their relationship

This paper proposes some new distance measures between interval-valued neutrosophic sets (IvNSs) and their similarity measures. Then, some entropy measures of IvNS based on the distances are proposed as the extension of the entropy measures of interval-valued intuitionistic fuzzy sets (IvIFSs). Also, we investigate the relationship between the presented entropy measures and the similarity measures for IvNSs. Finally, the comparison of the new entropy measures with existing entropy measures for IvNSs is given by the numerical and decision-making examples to demonstrate that the proposed new entropy measures for IvNSs are effective and reasonable and more intelligible in representing the degree of fuzziness of IvNSs than the existing ones.