Abstract:

The operational laws of the intuitionistic trapezoidal fuzzy number are improved, a concept of instuitionistic trapezoidal fuzzy random variable (ITrFRV) is introduced based on the intuitionistic trapezoidal fuzzy number and the trapezoidal fuzzy random variable, and the related properties of an ITrFRV are also proposed and proved. With respect to a problem of multiple attribute decision making (MADM), in which attribute weights are unknown and attribute values are given in terms of intuitionistic trapezoidal fuzzy random variables, considering the decisionmaker’s psychological behavior, an approach for intuitionistic trapezoidal fuzzy random prospect decision making is proposed based on the combination of parameter estimation and score functions. Firstly, by acquiring intuitionistic trapezoidal fuzzy sample information in different periods of the decision making process, the unknown parameters of entire intuitionistic trapezoidal fuzzy populations with a known distribution pattern are estimated, and an intuitionistic trapezoidal fuzzy random matrix is obtained. Secondly, an expectationvariance intuitionistic fuzzy number matrix is constructed, and then the concept of a fuzzy random score function is defined to transform a normalized expectation intuitionistic fuzzy number matrix into a score function matrix. Finally, the prospect theory is utilized to calculate a prospect score function, attribute weights are determined by constructing a grey system theory model, and then a ranking of alternatives are obtained according to comprehensive prospect score values. A practical example is introduced to show the feasibility and effectiveness of the proposed approach.