加权犹豫模糊集的向量测度法与决策应用

Vector Measure Method for Weighted Hesitant Fuzzy Sets and Its Application to Decision Making

为了更加客观地描述决策信息,本研究将决策专家的综合权重注入犹豫模糊集,定义了加权犹豫模糊集,同时在新定义条件下设置了一种针对备选方案排序的算法。在每个评价准则上先确定绝对权威专家(绝对权威专家的主客观权重与综合权重相等),并根据绝对权威专家给出的评价信息来计算其余决策专家的综合权重。用平面向量来刻画加权犹豫模糊数,并在此基础上建立了加权犹豫模糊元的实值函数模型、虚值函数模型以及2个加权犹豫模糊元的大小比较规则。结合评价准则的主观权重与利用熵值法计算出的评价准则客观权重来确定其综合权重。用参数调整方案在各评价准则上的得分实值与得分虚值的比例来计算方案的综合决策值。最后采用一个数值算例对文中理论与方法的可行性进行了分析。

In order to describe the decision information more objectively in the multi-criteria group decision making problem of hesitant fuzzy set,the weighted hesitant fuzzy set is defined by injecting the comprehensive weights of decision experts into the hesitant fuzzy set.At the same time,an algorithm for ranking alternatives is set up under the newly defined conditions.In each evaluation criterion,the absolute authoritative experts are determined first(the subjective and objective weights of the absolute authoritative experts are the same as the comprehensive weights),and the comprehensive weights of the other decision-making experts are calculated according to the evaluation information given by the absolute authoritative experts.The weighted hesitant fuzzy number is described by plane vector and the real-valued function model and the virtual-valued function model of the weighted hesitant fuzzy element and the size comparison rule of the two weighted hesitant fuzzy elements are established on this basis.The comprehensive weight is determined by combining the subjective weight of evaluation criterion with the objective weight of evaluation criterion calculated by entropy method.The comprehensive decision value of the scheme is calculated by adjusting the ratio of the real value and the imaginary value of the score on each evaluation criterion.Finally,a numerical example is used to analyze the feasibility of the theory and method.