A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems

The concept of a single valued neutrosophic number (SVN-number) is of importance for quantifying an ill-known quantity and the ranking of SVN-numbers is a very difficult problem in multi-attribute decision making problems. The aim of this paper is to present a methodology for solving multi-attribute decision making problems with SVN-numbers. Therefore, we firstly defined the concepts of cut sets of SVN-numbers and then applied to single valued trapezoidal neutrosophic numbers (SVTN-numbers) and triangular neutrosophic numbers (SVTrN-numbers). Then, we proposed the values and ambiguities of the truth-membership function, indeterminacy-membership function and falsity-membership function for a SVN-numbers and studied some desired properties. Also, we developed a ranking method by using the concept of values and ambiguities, and applied to multi-attribute decision making problems in which the ratings of alternatives on attributes are expressed with SVTN-numbers.