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CN 34-1054/N

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Quasi-consistency of interval complementary judgment matrix and its weights

  • School of Management, Hefei University of Technology, Hefei 230009, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.03.015
  • Received Date: 19 March 2013
  • Accepted Date: 10 July 2013
  • Rev Recd Date: 10 July 2013
  • Publish Date: 30 March 2014
    Abstract

  • Abstract

    Based on the idea of the relative superiority degree found in the additive consistency and the multiplicative consistency of fuzzy complementary judgment matrix (FCJM), the quasi-additive consistency and the quasi-multiplicative consistency of interval complementary judgment matrix (ICJM) were given. And they were merged into the quasi-consistency of ICJM by the complementary property of possibility degree. The problem of how to determine ICJM weights was analyzed under two conditions. In the condition of the IRJM with quasi-consistency, by the method of possibility degree an FCJM was derived from the comparison among its interval weights, and its precise value ranking vector was also achieved using the middle translation method. Then, under the condition of general ICJM, its interval weights were obtained by a deviation model which is established by the deviation between ICJM and its interval weights in the respect of possibility degree. And an FCJM was derived from the comparison among its interval weights, and its precise value ranking vector was also achieved using the middle translation method. And it was pointed out that the solution process of the former condition is in fact the specific one of the latter condition. A necessary and sufficient condition of the quasi-consistency of ICJM was achieved. Finally, the validity and the practicability of the proposed method were illustrated with an example.

    Abstract

    Based on the idea of the relative superiority degree found in the additive consistency and the multiplicative consistency of fuzzy complementary judgment matrix (FCJM), the quasi-additive consistency and the quasi-multiplicative consistency of interval complementary judgment matrix (ICJM) were given. And they were merged into the quasi-consistency of ICJM by the complementary property of possibility degree. The problem of how to determine ICJM weights was analyzed under two conditions. In the condition of the IRJM with quasi-consistency, by the method of possibility degree an FCJM was derived from the comparison among its interval weights, and its precise value ranking vector was also achieved using the middle translation method. Then, under the condition of general ICJM, its interval weights were obtained by a deviation model which is established by the deviation between ICJM and its interval weights in the respect of possibility degree. And an FCJM was derived from the comparison among its interval weights, and its precise value ranking vector was also achieved using the middle translation method. And it was pointed out that the solution process of the former condition is in fact the specific one of the latter condition. A necessary and sufficient condition of the quasi-consistency of ICJM was achieved. Finally, the validity and the practicability of the proposed method were illustrated with an example.
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    • References(22)
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    Xu Z S. Consistency of interval fuzzy preference relations in group decision making[J]. Applied Soft Computing, 2011,11:3 898-3 909.
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    Tanino T. Fuzzy preference orderings in group decision making[J]. Fuzzy Sets and Systems, 1984,12:117-131.
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    徐泽水. 不确定多属性决策方法及应用[M]. 北京:清华大学出版社,2004.
    [20]
    Gong Z W, Li L S, Forrest J, et al. The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity[J]. Expert Systems with Applications,2011,38(4):4 394-4 402.
    [21]
    Sugihara K, Ishii H, Tanaka H. Interval priorities in AHP by interval regression analysis[J]. European Journal of Operation Research, 2004,158:745-754.
    [22]
    Gong Z W, Li L S, Yao T X. Group decision making based on incomplete intuitionistic fuzzy preference relations[J].Operations Research and Management Science, 2010,19(6):45-51.
    巩在武,李廉水,姚天祥.基于残缺信息的直觉模糊判断矩阵群决策方法[J].运筹与管理,2010,19(6):45-51.
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    [1]
    徐泽水.直觉模糊信息集成理论及应用[M].北京：科学出版社,2008.
    [2]
    Xu Z S. A practical method for priority of interval number complementary judgment matrix[J]. Operations Research and Management Science,2001, 10(1):16-19.
    徐泽水. 区间数互补判断矩阵排序的一种实用方法[J]. 运筹与管理,2001, 10(1):16-19.
    [3]
    Xu Z S. Priority method based on possibility and error analysis for interval number complementary judgment matrix [J]. Journal of PLA University of Science and Technology, 2003,4(2):96-98.
    徐泽水. 基于可能度和误差分析的区间互补矩阵排序法[J]. 解放军理工大学学报,2003,4(2):96-98.
    [4]
    Gong Z W, Liu S F. Research on consistency and priority of interval number complementary judgment matrix[J]. Chinese Journal of Management Science, 2006,14(4):64-69.
    巩在武,刘思峰. 区间数互补判断矩阵的一致性及其排序研究[J]. 中国管理科学,2006,14(4):64-69.
    [5]
    Liu F, Shi L H. An approach for interval number priority weight based on convex-combination and possibility degree[J]. Fuzzy Systems and Mathematics, 2008,22(4):112-119.
    刘芳,兰继斌,史丽华.基于凸组合和可能度的区间数优先权重法[J].模糊系统与数学,2008,22(4):112-119.
    [6]
    Xu Y J, Zhang Y Z, Wei C P. Acceptable consistency analysis of interval complement comparison matrices[J]. Control and Decision, 2011,26(3):327-331.
    徐迎军,张玉忠,魏翠萍. 区间互补判断矩阵可接受一致性[J]. 控制与决策,2011,26(3):327-331.
    [7]
    Yue Q, Fan Z P, Shi L H. New approach to determine the priorities from interval fuzzy preference relations[J]. Journal of Systems Engineering and Electronics, 2011,22(2):267-273.
    [8]
    Liu F, Zhang W G, Fu J H. A new method of obtaining the priority weights from an interval fuzzy preference relation[J]. Information Sciences,2012,185:32-42.
    [9]
    Xu Z S, Chen J. Some models for deriving the priority weights from interval fuzzy preference relations[J]. European Journal of Operational Research,2008,184:266-280.
    [10]
    Wang J, Lan J B, Ren P Y, et al. Some programming models to derive priority weights from additive interval fuzzy preference relation[J]. Knowledge-Based Systems, 2012,27:69-77.
    [11]
    Lan J B, Hu M M, Ye X M, et al. Deriving interval weights from an interval multiplicative consistent fuzzy preference relation[J]. Knowledge-Based Systems, 2012,26:128-134.
    [12]
    Wang Z J, Li K. Goal programming approaches to deriving interval weights based on interval fuzzy preference relations[J]. Information Sciences,2012,193:180-198.
    [13]
    Xu Z S. Approaches to multiple attribute decision making with intuitionistic fuzzy preference information[J]. Systems Engineering: Theory & Practice, 2007, 27(11):62-71.
    徐泽水. 直觉模糊偏好信息下的多属性决策途径[J]. 系统工程理论与实践,2007, 27(11):62-71.
    [14]
    Gong Z W, Li L S, Zhou F X, et al. Goal programming approaches to obtain the priority Vectors from the intuitionistic fuzzy preference relations[J]. Computers ＆ Industrial Engineering, 2009,57:1 187-1 193.
    [15]
    Genc S, Boran F E, Akay D, et al. Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations[J]. Informations Sciences,2010,180:4 877-4 891.
    [16]
    Xu Z S. Consistency of interval fuzzy preference relations in group decision making[J]. Applied Soft Computing, 2011,11:3 898-3 909.
    [17]
    Tanino T. Fuzzy preference orderings in group decision making[J]. Fuzzy Sets and Systems, 1984,12:117-131.
    [18]
    李荣钧. 模糊多准则决策理论与应用[M]. 北京:科学出版社,2000.
    [19]
    徐泽水. 不确定多属性决策方法及应用[M]. 北京:清华大学出版社,2004.
    [20]
    Gong Z W, Li L S, Forrest J, et al. The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity[J]. Expert Systems with Applications,2011,38(4):4 394-4 402.
    [21]
    Sugihara K, Ishii H, Tanaka H. Interval priorities in AHP by interval regression analysis[J]. European Journal of Operation Research, 2004,158:745-754.
    [22]
    Gong Z W, Li L S, Yao T X. Group decision making based on incomplete intuitionistic fuzzy preference relations[J].Operations Research and Management Science, 2010,19(6):45-51.
    巩在武,李廉水,姚天祥.基于残缺信息的直觉模糊判断矩阵群决策方法[J].运筹与管理,2010,19(6):45-51.
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