信息集成算子加权向量的对称性研究

Study on the Symmetry Properties of Weighting Vectors of Information Aggregation Operators

对信息集成算子加权向量的对称性进行了研究.提出了升序加权算术平均(AOWAA)算子和语言AOWAA算子,分别给出了降序加权算术平均(DOWAA)算子和升序加权算术平均(AOWAA)算子、降序加权几何平均(DOWGA)算子和升序加权几何平均(AOWGA)算子、以及语言DOWAA算子和语言AOWAA算子的一个等价条件,并证明了在加权向量是对称的情况下:1)利用DOWAA算子对若干个互补判断矩阵进行集成所得到的群判断矩阵仍为互补判断矩阵;2)利用DOWGA算子对若干个互反判断矩阵进行集成所得到的群判断矩阵仍为互反判断矩阵;3)利用语言DOWAA算子对若干个语言互补判断矩阵进行集成所得到的群判断矩阵仍为语言互补判断矩阵.最后探讨了一些常用加权向量的对称性问题.

In this paper, we investigate the symmetry properties of weighting vectors of information aggregation operators, and present an ascending ordered weighted arithmetic averaging （AOWAA） operator and a linguistic AOWAA operator. We give, respectively, an equivalence condition of the descending ordered weighted arithmetic averaging （DOWAA） operator and ascending ordered weighted arithmetic averaging （AOWAA） operator, descending ordered weighted geometric （DOWGA） operator and ascending ordered weighted geometric （AOWGA） operator, linguistic DOWAA operator and linguistic AOWAA operator. Based on the symmetrical weighting vectors, we show that 1） If all the individual complementary judgment matrices are aggregated by using the DOWAA operator, then their aggregated judgment matrices are also complementary; 2 ） If all the individual reciprocal judgment matrices are aggregated by using the DOWGA operator, then their aggregated judgment matrices are also reciprocal; 3 ） If all the individual linguistic complementary judgment matrices are aggregated by using the linguistic DOWAA operator, then their aggregated judgment matrices are also linguistic complementary. Finally, we discuss the symmetry properties of some common weighting vectors of information aggregation operators.