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

Abstract

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