基于参数估计与记分函数联合的直觉梯形模糊随机前景决策方法

完善直觉梯形模糊数的算术运算,在直觉梯形模糊数及梯形模糊随机变量的基础上,定义直觉梯形模糊随机变量(instuitionistic trapezoidal fuzzy random variable, ITrFRV),探讨并证明ITrFRV的相关性质。针对具有ITrFRV且属性权重未知的模糊随机多属性决策问题,考虑决策者心理行为特征,提出基于参数估计与记分函数联合的直觉梯形模糊随机多属性决策前景决策方法。该方法首先获取决策子周期内的直觉梯形模糊样本信息,估计分布类型已知的直觉梯形模糊总体的未知参数,以获取直觉梯形模糊随机决策矩阵;其次,构造带有方差的期望直觉模糊数矩阵,定义模糊随机记分函数,将规范化的期望直觉模糊数矩阵转化为记分函数矩阵;最后,利用前景理论计算前景记分函数,进而基于灰色系统理论求解属性权重,获取综合前景记分值,由此进行方案比选。案例表明本文方法的可行性及有效性。

Approach for intuitionistic trapezoidal fuzzy random prospect decision making based on the combination of parameter estimation and score functions

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.