Multiple Attribute Decision Making Based on Neutrosophic Preference Relation

The single-valued neutrosophic set (SVNS) performs well in retrieving indeterminate cognitive information for decision makers to solve problems from the perspective of multiple attribute decision making (MADM). Preference relation is used in decision-making as a fundamental tool for decision makers to express their preference. In this context, the SVNS-based preference relation is one of the most useful extensions in that it quantitatively reflects the preference degree. However, the previous studies have paid little attention to the preference degree between alternatives, making the outcomes of decision making inaccurate. Therefore, it is necessary and meaningful to propose the MADM method with SVNS based on the preference relation which takes into account preference information between alternatives. A neutrosophic preference relation is proposed by means of the full of utilization decision information to combine SVNS with preference relation. With respect to the proposed MADM method, the evaluation decision matrix is provided by decision makers and the weights of attribute are gained by using the entropy of SVNS. Then, the neutrosophic preference relation is utilized to obtain evaluation preference matrix. Finally, through full-order relation formed by aggregating the preference relation, the ranking order of all alternatives is obtained and the most desirable alternative is readily determined. By an illustrative example, the proposed method is validated, and its advantages are analyzed by comparison and contrast with the other methods. This method makes full use of decision makers’ cognitve information and takes into account the preference information between alternatives. The outcomes of decision-making demonstrate that the proposed method has the capacity to handle MADM issues.