A New Approach of Possibility Single-Valued Neutrosophic Set and Its Application in Decision-Making Environment

The single-valued neutrosophic set (SVNS) is a widely known model for dealing with uncertain, conflicting, and indeterminate information. In practice, the SVNSs are very useful tools to be used in solving multi-criteria decision-making (MCDM), but in the process of processing by the three functions of SVNS the evaluation process for this handling disappears. To overcome this deficiency, we present in this work a new approach called possibility single-valued neutrosophic set (PSVNS) that differs from previous approaches. The implementation of this proposed approach in this work is based on giving each of the three functions in SVNS a fuzzy degree ranging between 0 and 1. As a result, firstly, the elementary notion of possibility single neutrosophic set is proposed, and some of its primary properties, i.e., subset, null set, absolute set, and complement are explored, as well as some numerical examples that explain the mechanism of the obtained results. Secondly, the basic set-theoretic operations i.e., such as extended union, the intersection of two PSVNSs, and the complement operation of PSVNS, as well as some relevant properties, are investigated, and numerical examples are provided to illustrate the mechanism behind these results. Lastly, the similarity measure between two PSVNSs is characterized with the help of an example. This technique of similarity measure is successfully used in decision-making to choose the appropriate college.