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A method of knowledge acquisition for the decision information system whose attribute value of alternatives is three-parameter interval grey number is proposed in this paper. First, in classic rough set, the decision table must be given in advance, but we can only establish information system from the collected data. So, we establish the decision table from information system with the grey relational clustering decision method. Then, we construct the grey dominance relation based on the dominance extent between two three-parameter interval grey numbers, and put forward a method of extracting decision rules and attribute reduction. The last case about the comprehensive evaluation of icebreaking car is given to illustrate the effectiveness of the proposed method.

By the Mountain Pass Theorem, we study existence and multiplicity of positive solutions of p-laplacian equation of the form − Δ p u = λ f ( x , u ) , the nonlinearity f(x, u) grows as uσ at infinity with a singular coefficient, where σ ∈ ( p − 1 , p * − 1 ) . To manage the asymptotic behavior of its positive solutions with respect to λ, we establish a new Liouville-type theorem for the p-Laplacian operator.

The paper establishes a comprehensive evaluation index system of the college educational management system, and then based on neural network theory, constructs a comprehensive evaluation model of college educational management system based on BP neural network. The empirical analysis shows that the results of the evaluation model are reasonable, and the model is simple and has good application value.

The problem of grey multi-attribute risk group decision-making is studied, when the attributive values are interval grey numbers and the attribute weights are unknown. Using grey incidence method of the grey system theory, Relative deviation degree based on the optimum alternative group and the worst alternative group, a new method is proposed. It establishes the integrated optimization model dealing the weights of index based on that the deviation of group members is minimum and the deviation between two groups is maximum. By using the model, the attribute weights can be gotten. Then, based on subjective preferences of decision-maker group, synthetically deviations of each alternative to the optimum alternative group and the worst alternative group are calculated to determine the ranking order of alternatives. Finally, an example is given to show the feasibility and availability of this method.

The problem of grey multi-attribute risk group decision-making is studied, when the attributive values are interval grey numbers and the attribute weights are unknown. Using grey incidence method of the grey system theory, relative deviation degree based on the optimum alternative group and the worst alternative group, a new method is proposed. It establishes an integrated optimization model dealing the weights of index based on that the deviation of group members is minimum and the deviation between two groups is maximum. By using the model, the attribute weights can be gotten. Then, based on subjective preferences of decision-maker group, synthetically deviations of each alternative to the optimum alternative group and the worst alternative group are calculated to determine the ranking order of alternatives. Finally, an example is given to show the feasibility and availability of this method.

The authors researches on the problem of the multiple criteria decision making under risk that attribute weight is completely unknown and criteria values are interval grey numbers. The method of grey multiple criteria decision making under risk based on priority index is proposed. By using the possibility, the priority index matrix and analytical technique of comparing interval grey numbers, the former problem is converted to no risky multiple criteria problems, in which criteria values are real numbers. By using information entropy to determine the attribute weight, the authors states two corresponding algorithms to attain the ranking of alternatives and choosing the best. In the final, one example is given to illustrate the validity and efficiency of two algorithms.

The authors researches the grey multi-attribute problem, in which the attribute weights and the attribute values are interval numbers, and states the decision-making method based on two-phase optimization. Firstly, a linear objective programming model is established by considering in local, and ideal attribute weight of each alternative is obtained by solving the model. Secondly, a quadratic programming model is established by considering in whole, and the solving formula of the attribute weights is given. Therefore, the complex attribute value of each alternative is obtained. Based on these values, the prioritizing or optimization for alternatives is made. Finally, a practical example is given to show the feasibility and availability of the method.

The problem of grey multi-attribute group decision making under risk, in which the attributes are interval grey number and the attribute weights are unknown is studied. Based on the ideal matrix, relative subordinate degree method is presented. Combining thoughts and method of grey system theory with classical risk decision-making method, the attribute of each alternative is obtained by grey relation degree. Then the relative subordinate degree in which an alternative corresponds to the ideal matrix is obtained by means of the synthetically weighted distance among the alternative and positive and the negative matrix. An example illustrates the validity and efficiency of this method.

This paper studies multi-attribute decision making problem, which include alternative scheme preference information and the attribute values are internal grey numbers. We construct grey deviated function through subjective conditional probability and objective conditional probability. Based on grey deviated function, an approach to get subjective conditional probability optimized model is proposed. By using the model, the attribute weights can be got. The decision alternatives are ranked by using the priority formula of interval grey number. Finally, an example is given to show the feasibility and availability of this method.