Study on the Symmetry Properties of Weighting Vectors of Information Aggregation Operators
信息集成算子加权向量的对称性研究

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.