Ranking of Neutrosophic number based on values and ambiguities and its application to linear programming problem

Abstract

The goal of this article is to establish a methodology for ordering of single-valued neutrosophic numbers (SVN-numbers) on the basis of values and ambiguities. First of all, the idea of neutrosophic numbers is discussed, and (α, β, γ)-cut and arithmetic oprations definecd over SVN-numbers are examined. Thereafter,corresponding to each components,the values and ambiguities are defined and using these definitions, the ratio ranking function is constructed. Then, for the stability of the ratio ranking function, some examples are provided for comparing this method with other approaches. Applying this ratio ranking function, neutrosophic linear programming problem(Neu-LPP) converts to the crisp linear programmning problems (CLP-Problems) and solved it by computational lingo method. At last, Neu-LPP is illustrated by two numerical real-life examples