犹豫模糊环境下基于互补判断矩阵的客观权重获取方法

An Objective Weight Obtain Method Based on Complementary Judgment Matrix in Hesitant Fuzzy Environment

犹豫模糊集是决策者表达不一致性备选方案评估值的有力工具,允许集合中元素的隶属度可以是多个不同的值。基于模糊互补判断矩阵的加型一致性理论,提出了一种属性客观权重的获取方法。首先,定义了两个犹豫模糊元素之间的平均偏差,进而定义了一个新的模糊互补判断矩阵并证明其具有加型一致性;基于此,构建了一致性偏差最大化的属性客观权重优化模型,从而计算得到最优的属性客观权重;并将它应用到模糊多属性决策中,通过实例证明所提方法的可行性和有效性。

Hesitant fuzzy set allows an element in the domain with a set of membership degree between 0 and 1,which is a powerful tool to express the inconsistent alternative assessment value of decision makers.An attribute objective weight obtain method is proposed based on additive consistency theory of fuzzy complementary judgment matrix in this paper.Firstly,the mean variation between two hesitant fuzzy elements and a new fuzzy complementary judgment matrix have been defined and then proved to have additive consistency; Secondly an attribute objective weight optimization model is constructed based on maximizing consistent deviation.Then the optimal attribute objective weight is obtained by computation and applied to multiple attribute decision making.Finally,an example is given to illustrate the feasibility and effectiveness of the proposed method.