Abstract:  In order to solve the large difference between the results of multi-attribute group decision making, the convergence of measurable functions is studied based on intuitionistic fuzzy measures. Based on the possibility theory and intuitionistic fuzzy set theory, the intuitionistic fuzzy possibility measure is studied, and the boundedness, monotonicity, additivity and intuitionistic fuzzy additive properties of the intuitionistic fuzzy measure are determined. The intuitionistic fuzzy measure is based on the three decision-making rules of receiving decision, delaying decision and rejecting decision. Based on the above research results, the convergence of measurable functions in terms of measure is clarified. It is known that there exists a convergence state of set- valued bizero asymptotically additive set function in measurable space. The example shows that this method can effectively calculate the intuitionistic fuzzy possibility measure of different decisions under different attribute characteristics, and can effectively obtain the best decision scheme, can effectively solve the multi-attribute group decision-making problem with good practicality. 

Key words: intuition, fuzzy measure, measurable, function sequence, by measure, convergence