Extension of the TOPSIS method based on prospect theory and trapezoidal intuitionistic fuzzy numbers for group decision making

Considering the decision maker’s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory (PT) and trapezoidal intuitionistic fuzzy numbers (TrIFNs) for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistic fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers’ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.