Group decision making problem is considered for a class of bounded cooperation mechanism in this paper. Cooperation relation between any two decision makers is vaguely classified by cooperation function with two thresholds. Power index of decision makers is measured by fuzzy measure. Nonlinear programming entropy model of cooperation group decision making is constructed to aggregate power index of decision maker set and solved by maximum entropy principle. Integrated evaluation values of optional schemes are calculated by the way of Choquet fuzzy integral. All optional schemes are ordered and optimal scheme is chosen. At last, one numerical example is analyzed to verify the validity and rationality of cooperation group decision making model and application of the fuzzy integral method.