基于语言判断矩阵的群决策逆判问题研究

针对基于语言判断矩阵的群决策逆判问题，通过对语言判断矩阵进行“量化”，将其转化成为互反判断矩阵，进而提出了一种依据数理统计理论的分析方法．该方法通过引进随机误差的概念，得出了一致性判断矩阵中元素的相对误差服从均值为零的正态分布的结论，进一步依据这一结论，根据各评判专家所提供的判断矩阵对专家们进行反判，即通过计算各专家的偏离度，对专家们进行排序，并且根据假设检验理论对排序进行检验、对专家们进行分类、最后用一个算例说明了该方法的有效性和实用性．

Study on the adverse judgment problem for group decision making based on linguistic judgment matrices

Pointing at the adverse judgment problem for group decision making based on linguistic judgment matrices, through the quantization of the linguistic judgment matrices, this paper proposes an adverse judgment method based on the theory of mathematical statistics. In this method, by introducing the conception of random error, it is obtained the conclusion that the relative error of an element in the consistent matrix obeys the normal distribution with zero mean. According to this conclusion, the experts' variance is calculated to help the decision maker to judge the level of the experts adversely and to make ranking of the experts. By the hypothesis test theory, the tests on the ranking and the classifications of the experts are done. Finally, an example is used to illustrate the use of the method.