Abstract: To deal with the problems of too strict requirements for the existing intuitionistic fuzzy dominance relationship, large loss and incomplete utilization of evaluation information, an intuitionistic fuzzy perturbation dominance relationship in line with the characteristics of intuitionistic fuzzy is proposed by using the disturbance degree between intuitionistic fuzzy sets. Then, a perturbation dominance class with lower requirements than the equivalence class is obtained, so as to make greater use of evaluation information. Its related properties are discussed. Next, aiming at the problem that the conditional probability in the existing intuitionistic fuzzy three-way decision method is expressed by real numbers, which leads to the loss of uncertain information, a calculation method of conditional probability expressed by intuitionistic fuzzy numbers is proposed based on the perturbation dominance relationship, and the three-way decision and multi-attribute decision rules are given. Then, an example is given to verify the effectiveness of the method, and the sensitivity of the dominance degree and risk avoidance coefficient is analyzed. 

Key words: three-way decision, intuitionistic fuzzy set, perturbation dominance relationship, multi- attribute decision, degree of intuitionistic fuzzy perturbation, conditional probability