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Benefit and loss matrix of uncertain decision-making analysis reflects both the objective information structure of uncertain decision-making problem and the risk information of benefit chance and loss chance faced by decision-maker. The transform vector consisted of the natural state weights is quantitative expression of uncertain decision-making rule adopted by decision-maker. The essential for resolving uncertain decision-making problem is how to transform benefit and loss matrix into compressed real vector with one dimension, where the biggest weight of the vector corresponds to the best action scheme. Now the information of benefit and loss matrix has been not mined sufficiently using the common methods for uncertain decision-making problems. Therefore in this paper, the whole difference weights of the natural states can be determined using projection pursuit method, the local difference weights of the natural states can be determined directly using information entropy and accelerating genetic algorithm based fuzzy analytic hierarchy process, and the two kinds of weights can be combined into comprehensive weights according to the minimum relative information entropy principle, which can form a new uncertain decision-making analysis method based on information entropy principles, named UDM-IEP for short. The application result show that the information of benefit and loss matrix can be mined more sufficiently using UDM-IEP than the common methods, that the decision-making information can be more provided by UDM-IEP than the common methods, that decision-maker can actively or safely choose the best scheme based on the comparison between of benefit chance risk and loss chance risk contained in the benefit and loss matrix, that UDM-IEP is both simple and general, that its computation result is objective and stability, and that UDM-IEP can be widely applied in theory and practice of systems engineering.