Risk decision-making method using interval numbers and its application based on the prospect value with multiple reference points

A multi-attribute risk decision-making problem using interval numbers is studied based on the prospect theory. A decision-making process often involves various reference standards resulting from different decision-making mentalities and contexts. To solve these kinds of decision-making problems, we propose a risk decision-making method with multiple reference points for both static and dynamic situations. First, the guidelines for setting reference points under both static and dynamic conditions are provided based on the nature of the decision-making problem. Second, both expected values and positive ideal points for alternatives are set for the static decision-making strategy, and three reference points are provided for the dynamic strategy, including expected values, positive ideal points, and the development status of alternatives according to the guidelines. Third, characterization techniques used to solve prospect values of decision-making alternatives are proposed for both static and dynamic decision-making problems. Then, a detailed analysis is provided in terms of weighting functions and prospect values. In addition, two optimization models using the attribute weight and multi-stage weight are established by considering the sensitivity of these two weights to the decision-making problem, with the aim of maximizing the differentiation degree of alternatives. On that basis, a ranking analysis is provided for the alternatives. Finally, the proposed method is applied to two cases, including supplier selection of key components for large aircraft and an emergency event, to illustrate the application and feasibility of the method.