H-Max Distance Measure of Bipolar Neutrosophic Sets and an Application to Medical Diagnosis

A single-valued neutrosophic set is one of the advanced fuzzy sets that is capable of handling complex real-world information satisfactorily. A development of single-valued neutrosophic set and fuzzy bipolar set, called a bipolar neutrosophic set, was introduced. Distance measures between fuzzy sets and advanced fuzzy sets are important tools in diagnostics and prediction problems. Sometimes they are defined without considering the condition of the inclusion relation on sets. In decision-making applications, this condition should be required (here it is called the inference of the measure). Moreover, in many cases, a distance measure capable of discriminating between two nearly identical objects is considered an effective measure. Motivated by these observations, in this paper, a new distance measure is proposed in a bipolar neutrosophic environment. Furthermore, an entropy measure is also developed by the similarity between two sets of mutual negation. Finally, an application to medical diagnosis is presented to illustrate the effective applicability of the proposed distance measure, where entropy values are used to characterize noises of different attributes. Keywords: neutrosophic distance; similarity measure; bipolar neutrosophic sets; entropy measure; medical diagnosis