基于广义犹豫三角模糊幂均算子的MADM方法

An approach to multiple attribute decision making on the basis of hesitant triangular fuzzy power average operator

针对以犹豫三角模糊元(HTFE)为输入的多属性决策(MADM)问题,首先,给出犹豫三角模糊集距离的定义,并基于此提出犹豫三角模糊幂均(HTFPA)算子的概念;其次,为了能够有效地弱化与整体信息偏差较大的评估值对决策结果的影响,提出广义犹豫三角模糊幂均(GHTFPA)算子,并讨探其相关性质;再次,通过构建基于最小绝对偏差法的非线性规划模型,以合理地获取广义犹豫三角模糊幂均参数;最后,针对各属性之间均存在交互关联关系且权重信息完全未知的MADM问题,提出基于广义犹豫三角模糊幂均算子的MADM方法.案例和对比分析表明,所提出的方法是可行且合理的.

In terms of the multiple attribute decision making（MADM） problems under hesitant triangular fuzzy environment, the distance measure for the hesitant triangular fuzzy sets is first introduced, and then the concept of the hesitant triangular fuzzy power average（HTFPA） is proposed. In order to effectively alleviate the influence of these ＂false＂ or ＂biased＂ arguments on the final decision-making result, the generalized hesitant triangular fuzzy power average（GHTFPA） is introduced and its related properties are also investigated. Then, a nonlinear programming model is constructed on the basis of the least absolute deviation method to reasonably attain the parameter of the GHTFPA operator.Furthermore, a novel approach, with respect to the MADM problem in which there are interactions among attributes and the attribute weights are unknown, is provided by utilizing the GHTFPA operator. Finally, a numerical example and a comparison are provided to illustrate the feasibility and rationality of the proposed approach.