区间互反判断矩阵权重确定的一种新方法
A Method of Obtaining a Priority Vector from Interval Multiplicative Reciprocal Matrices
DOI: 10.12677/AAM.2017.67098, PDF, HTML, XML, 下载: 1,675  浏览: 2,129  国家自然科学基金支持
作者: 刘祖林, 刘芳, 吴宇豪：广西大学数学与信息科学学院，广西 南宁
关键词: 区间互反判断矩阵；权重；余弦最大方法；近似一致性；Interval Multiplicative Reciprocal Matrix； Priority Vector； Cosine Maximization Method； Approximation-Consistency
摘要: 本文研究了一种从区间互反判断矩阵中获得权重的新方法，考虑决策者在两两比较方案的判断中存在的随机性，把余弦最大化方法推广到研究近似一致性区间互反判断矩阵，给出了一种求解区间互反判断矩阵决策问题的新算法，数值结果阐明了新方法的应用。
Abstract: A new method of obtaining a priority vector from interval multiplicative reciprocal matrices is proposed in the present paper. By considering the randomness experienced by decision makers in pairwise comparisons, the cosine maximization method is extended to interval multiplicative re-ciprocal matrices with approximation-consistency. A new algorithm is proposed to solve the deci-sion making problem with the interval-valued judgements. Numerical results are reported to show the application of the proposed method.
文章引用：刘祖林, 刘芳, 吴宇豪. 区间互反判断矩阵权重确定的一种新方法[J]. 应用数学进展, 2017, 6(7): 808-815. https://doi.org/10.12677/AAM.2017.67098

参考文献

[1] Saaty, T.L. and Vargas, L.G. (1987) Uncertainty and Rank Order in the Analytic Hierarchy Process. European Journal of Operational Research, 32, 107-117.
[2] Wang, Y.M., Yang, J.B. and Xu, D.L. (2005) A Two-Stage Logarithmic Goal Programming Method for Generating Weights from Interval Comparison Matrices. Fuzzy Sets and Systems, 152, 475-498.
[3] Liu, F. (2009) Acceptable Consistency Analysis of Interval Reciprocal Comparison Matrices. Fuzzy Sets and Systems, 160, 2686-2700.
[4] Xia, M.M. and Chen, J. (2015) Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making. Group Decision and Negotiation, 24, 115-144.
https://doi.org/10.1007/s10726-014-9383-9
[5] Saaty, T.L. (1980) The Analytic Hierarchy Process. McGraw-Hill, New York.
[6] Xu, Z.S. and Wei, C.P. (1999) A Consistency Improving Method in the Analytic Hierarchy Process. European Journal of Operational Research, 116, 443-449.
[7] Liu, F., Pedrycz, W. and Zhang, W.G. (2017) Limited Ra-tionality and Its Quantification through the Interval Number Judgments with Permutations. IEEE Transactions on Cybernetics. (In Press)
[8] Meng, F, Chen, X., Zhu, M. and Lin, J. (2015) Two New Methods for Deriving the Priority Vector from Interval Mul-tiplicative Preference Relations. Information Fusion, 26, 122-135.
[9] Kou, G. and Lin, C. (2014) A Cosine Maximization Method for the Priority Vector Derivation in AHP. European Journal of Operational Research, 235, 225-232.

为你推荐