概率犹豫模糊环境下基于累积前景理论和VIKOR的多属性群决策方法

Multi-attribute Group Decision Making Model Based on Cumulative Prospect Theory and VIKOR in Probabilistic Fuzzy Environment

为解决概率犹豫模糊环境下的多属性群决策的问题,同时考虑到决策者心理行为的不足,例如在面对获利时风险规避,面对损失时风险偏好。提出了一种基于累积前景理论与多准则妥协优化解(VIKOR)法相结合的多属性群决策方法。首先,通过一致性调节方法确定决策者的综合权重;其次利用主客观结合的方法求解属性权重;再者通过累积前景理论完善决策者的心理决策过程,摒弃传统的欧式距离公式,采用坎贝拉距离公式加权,构建正、负理想解矩阵;然后基于VIKOR方法确定备选方案的优劣顺序,最后用数值算例进行了对比分析。结果表明:所提出的方法考虑了决策者的心理偏好,完善了决策者的心理行为,实例验证了所提方法的可行性和有效性。

To solve the multi-attribute group decision making problem in a probabilistic hesitant fuzzy environment,while the process of decision maker s mental behavior is highly subjective and the decision result varies from person to person is taken into account.For example,they are more conservative in case of profit and more willing to take risks in case of loss.A multi-attribute group decision making method based on the combination of cumulative prospect theory and multi-criteria compromise optimization solution(VIKOR)method was proposed.Firstly,the combined weights of decision makers were determined through the consistency adjustment method.Secondly,the attribute weights were solved by the combined subject-objective method.Furthermore,the mental decision process of decision makers was refined by the cumulative prospect theory,the traditional Euclidean distance formula was discarded,the weighted Campbell distance formula was adopted,and the positive and negative ideal solution matrices were constructed.Then the superiority order of alternatives was determined based on the VIKOR method.Finally,a numerical example was presented for comparative analysis.The results show that the method proposed allows the psychological preferences of decision makers to be taken into account,the psychological behavior of decision makers to be refined,and the feasibility and effectiveness of the method proposed to be verified by examples.