An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attr...An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.展开更多
This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept ...This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.展开更多
基金国家高技术研究发展计划(863)(the National High- Tech Research and Development Plan of China under Grant No.2006AA01Z148)教育部科学技术研究重点项目(the Scientific Key Project of Ministry of Education of China under Grant No.207148)
文摘An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.
文摘This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.
