Method on the Assessment Level of Experts in Group Decision Making Based on Multi-Granularity Linguistic Judgment Matrices

Regarding assessment level of experts in group decision making based on different granularity linguistic judgment matrices, the linguistic judgment matrices are quantified through constructing transfer function in this paper, the matrices are transformed into the reciprocal matrices with 1-9 scale, furthermore a method to assessment level of experts is proposed based on the theory of mathematical statistics. In this method, through introducing the conception of random error, the conclusion is obtained that the relative error of an element in the consistent matrix submits to normal distribution with mathematical expectation being zero. According to this conclusion, the experts' total departure 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, tests on the ranking and classifications of the experts are done. Finally, an example is used to illustrate the validity and practicality of the method.