Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making

The neutrosophic set model is an important tool for dealing with real scientific and engineering applications because it can handle not only incomplete information but also the inconsistent information and indeterminate information which exist commonly in real situations. In this paper, we firstly propose two practical techniques converting an interval neutrosophic set into a fuzzy set and a single-valued neutrosophic set, respectively. Then, we define the interval neutrosophic cross-entropy in two different ways, which are based on extension of fuzzy cross-entropy and single-valued neutrosophic cross-entropy. Additionally, two multicriteria decision-making methods using the interval neutrosophic cross-entropy between an alternative and the ideal alternative are developed in order to determine the order of the alternatives and choose most preferred one(s). Finally, an illustrative example is presented to verify the proposed methods and to demonstrate their effectiveness and practicality.