一种基于前景理论的毕达哥拉斯犹豫模糊不确定语言ELECTRE多属性决策方法

Method for multi-attribute decision-making with Pythagorean hesitant fuzzy uncertain linguistic ELECTRE based on prospect theory

针对属性权重已知、属性值为毕达哥拉斯犹豫模糊不确定语言变量的多属性决策问题,提出一种前景理论和消去与选择转换法(ELECTRE)相结合的多属性决策方法.首先给出毕达哥拉斯犹豫模糊不确定语言集的定义,包括得分函数、距离测度和运算法则;然后将前景理论引入该决策环境下,构建前景价值矩阵,运用传统ELECTRE法求得一致矩阵和矛盾矩阵,并对其进行转化构建前景优/劣势判断矩阵,进而求得总优/劣势值以确定备选方案的优劣排序;最后通过算例分析验证所提出方法的有效性和可行性,并与该决策环境下的传统ELECTRE法进行对比,表明了该方法的优越性和实用性.

A decision method of integrating the prospect theory with(ELECTRE) is proposed for multi-attribute decision-making, where the attribute weights are known and attribute values are in the form of the Pythagorean hesitant fuzzy uncertain linguistic number. First of all, the definition of the Pythagorean hesitant fuzzy uncertain linguistic set is given, including the scoring function, the distance measure and the algorithm. Then, a prospect value matrix is built by introducing the prospect theory into this decision-making environment, and the traditional ELECTRE method is used to obtain the consistency matrix and the contradiction matrix. The consistency matrix and contradiction matrix are obtained by using the traditional ELECTRE method, and the matrices are converted to construct the prospects superiority/inferiority judgment matrix. Thus, the total superiority/inferiority values are obtained to determine the ranking of alternatives. Finally, a numerical example is provided to illustrate the effectiveness and feasibility of the proposed method. Compared with the traditional ELECTRE method, the superiority and practicability of the proposed method are adequately verified.