COPRAS method with neutrosophic sets

Abstract

Interval neutrosophic number (INN), which is descripted by the degree of truth-membership, indeterminacy-membership and falsity-membership of an element, is a powerful information tool with many application areas. The purpose of this study is to develop an extended form of COPRAS (Complex Proportional Assessment) method used for solving the decision making problems in which all the data presented by decision makers is in the form of interval neutrosophic matrix presented by INNs, and the information about criterion weights is partially known or completely unknown. In order to accomplish this goal, a new score function and an accuracy function that consider the decision maker’s risk attitude are defined under a parameter called the risk index to determine the ordering of INNs. Then, based on Maclaurin symmetric mean (MSM) operator that can capture the interrelationships among multi-input arguments, some aggregation operators are defined, such as interval neutrosophic Maclaurin symmetric mean (INMSM) operator and interval neutrosophic weighted Maclaurin symmetric mean (INWMSM) operator. Moreover, some optimization models are established to determine the subjective and objective weights of decision criteria. A numerical problem is solved to demonstrate the effective and feasible structure of the developed method. Then, a sensitive analysis is conducted according to the decision maker’s risk attitude, and the advantages of the developed method are listed. Finally, a comparison analysis is provided to present the relationships among the developed method and existing methods, and some conclusions are given at the end of the study. © Springer Nature Switzerland AG 2019.