It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria...It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria is incomplete certain. A new multiple criteria decision- making method with incomplete certain information based on ternary AHP is proposed. This improves on Takeda＇s method. In this method, the ternary comparison matrix of the alternatives under each pseudo-criteria is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained as to normalize priority vector of the alternatives, then the order of alternatives is obtained by solving two kinds of linear programming problems. Finally, an example is given to show the feasibility and effectiveness of the method.展开更多
The relationship between the importance of criterion and the criterion aggregation function is discussed, criterion＇s weight and combinational weights between some criteria are defined, and a multi-criteria classific...The relationship between the importance of criterion and the criterion aggregation function is discussed, criterion＇s weight and combinational weights between some criteria are defined, and a multi-criteria classification method with incomplete certain information and polynomial aggregation function is proposed. First, linear programming is constructed by classification to reference alternative set （assignment examples） and incomplete certain information on criterion＇s weights. Then the coefficient of the polynomial aggregation function and thresholds of categories are gained by solving the linear programming. And the consistency index of alternatives is obtained, the classification of the alternatives is achieved. The certain criteria＇s values of categories and uncertain criteria＇s values of categories are discussed in the method. Finally, an example shows the feasibility and availability of this method.展开更多
The problem of fusing multiagent preference orderings, with information on agent＇s importance being incomplete certain with respect to a set of possible courses of action, is described. The approach is developed for ...The problem of fusing multiagent preference orderings, with information on agent＇s importance being incomplete certain with respect to a set of possible courses of action, is described. The approach is developed for dealing with the fusion problem described in the following sections and requires that each agent provides a preference ordering over the different alternatives completely independent of the other agents, and the information on agent＇s importance is incomplete certain. In this approach, the ternary comparison matrix of the alternatives is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained so as to normalize priority vector of the alternatives. The interval number of the alternatives is then obtained by solving two sorts of linear programming problems. By comparing the interval numbers of the alternatives, the ranking of alternatives can be generated. Finally, some examples are given to show the feasibility and effectiveness of the method.展开更多
文摘It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria is incomplete certain. A new multiple criteria decision- making method with incomplete certain information based on ternary AHP is proposed. This improves on Takeda＇s method. In this method, the ternary comparison matrix of the alternatives under each pseudo-criteria is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained as to normalize priority vector of the alternatives, then the order of alternatives is obtained by solving two kinds of linear programming problems. Finally, an example is given to show the feasibility and effectiveness of the method.
基金This project was supported by the Social Science Foundation of Hunan(05YB74)
文摘The relationship between the importance of criterion and the criterion aggregation function is discussed, criterion＇s weight and combinational weights between some criteria are defined, and a multi-criteria classification method with incomplete certain information and polynomial aggregation function is proposed. First, linear programming is constructed by classification to reference alternative set （assignment examples） and incomplete certain information on criterion＇s weights. Then the coefficient of the polynomial aggregation function and thresholds of categories are gained by solving the linear programming. And the consistency index of alternatives is obtained, the classification of the alternatives is achieved. The certain criteria＇s values of categories and uncertain criteria＇s values of categories are discussed in the method. Finally, an example shows the feasibility and availability of this method.
基金This project was supported by the National Natural Science Foundation of China(70631004).
文摘The problem of fusing multiagent preference orderings, with information on agent＇s importance being incomplete certain with respect to a set of possible courses of action, is described. The approach is developed for dealing with the fusion problem described in the following sections and requires that each agent provides a preference ordering over the different alternatives completely independent of the other agents, and the information on agent＇s importance is incomplete certain. In this approach, the ternary comparison matrix of the alternatives is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained so as to normalize priority vector of the alternatives. The interval number of the alternatives is then obtained by solving two sorts of linear programming problems. By comparing the interval numbers of the alternatives, the ranking of alternatives can be generated. Finally, some examples are given to show the feasibility and effectiveness of the method.
