灰关联度决策模型是在假设属性之间彼此相互独立的基础上构建的,但是在很多实际问题中属性之间往往存在一定的交互作用,从而导致灰关联度决策模型失效。针对这一问题,引入模糊积分理论,构建了灰模糊积分关联度决策模型。为求解该模型,定义了基于属性权重和属性间交互度的默比乌斯变换系数,来计算2可加模糊测度,其中属性权重通过序关系分析法和施密特正交马田系统共同确定,属性间的交互关系和交互度由专家确定。以廉租房保障家庭经济状况评估为例,对灰模糊积分关联度决策模型和灰关联度决策模型进行比较验证,验证结果表明灰模糊积分关联度决策模型的决策结果更加科学合理,有较好的应用价值。
In grey correlation degree decision model (GRCM), it is assumed that all the attributes are mutually independent. However, in real decision making problems, the interaction often exists between attributes which leads GRCM to lose effectiveness. For this problem, the fuzzy integral theory is introduced and grey fuzzy integral correlation degree decision model (GRFICM) is established. To solve the model, the Mobius transformation coefficients based on weights and interaction degrees are defined to calculate 2-order additive fuzzy measures. In Mobius transformation coefficients, the weights are determined by the rank correlation analysis method and Mahalanobis-Taguchi Gram-Schmidt jointly, and the interaction relations and interaction degrees are judged by experts. An evaluation of the financial situation of low-rent housing safeguard family is provided as a practical case in order to validate GRCM and GRFICM by comparing. The validation results show that GRFICM makes the decision results more scientific and reasonable, and is more worth of spreading.
[1] 邓聚龙.灰色系统的基本方法[M].武汉:华中理工大学出版社, 1987.
[2] 刘思峰,党耀国,方志耕,等.灰色系统理论及其应用[M].北京:科学出版社, 2010.
[3] 金佳佳,米传民,徐伟宣,等.考虑专家判断信息的灰色关联极大熵权重模型[J].中国管理科学. 2012, 20(2):135-143.
[4] 卫海英,张蕾,梁彦明,等.多维互动对服务品牌资产的影响——基于灰关联分析的研究[J].管理科学学报. 2011, 14(10):43-53.
[5] 施红星,刘思峰,方志耕,等.灰色周期关联度模型及其应用研究[J].中国管理科学. 2008, 16(3):131-136.
[6] 马保国,成国庆.一种相似性关联度公式[J].系统工程理论与实践. 2000, (7):69-71.
[7] 施红星,刘思峰,方志耕,等.灰色振幅关联度模型[J].系统工程理论与实践. 2010, 30(10):1828-1833.
[8] 吴利丰,王义闹,刘思峰.灰色凸关联及其性质[J].系统工程理论与实践. 2012, 32(7):1501-1505.
[9] Ishii K, Sugeno M. A model of human evaluation process using fuzzy measure[J]. International Journal of Man-Machine Studies. 1985, (22):19-38.
[10] Grabisch M. Fuzzy integral in multicriteria decision making[J]. Fuzzy Sets and Systems. 1995, 69(3):279-298.
[11] Sugeno M. Theory of fuzzy integral and its applications[D]. Tokyo:Tokyo Institute of Technology, 1974.
[12] Grabisch M. K-order additive discrete fuzzy measures and their representation[J]. Fuzzy Sets and Systems. 1997, 92(2):167-189.
[13] Grabisch M, Labreuche C, Vansnick J C. On the extension of Pseudo-Boolean functions for the aggregation of interacting criteria[J]. European Journal of operational Research. 2003, 148(1):28-47.
[14] Chateauneuf A, Jaffray J Y. Some characterizations of lower probabilities and other monotone capacities through the use of mobius inversion[J]. Mathematical Social Sciences. 1989, 17(3):263-283.
[15] 郭亚军.综合评价理论、方法及应用[M].北京:科学出版社, 2006.
[16] 邱菀华.管理决策熵学及其应用[M].北京:中国电力出版社, 2011.
[17] 徐泽水,孙在东.一类不确定型多属性决策问题的排序方法[J].管理科学学报. 2002, 5(3):35-39.
[18] Taguchi G, Chowdhury S, Wu Y. The Mahalanobis-Taguchi system[M]. New York:McGraw-Hill, 2001.
[19] Taguchi G, Jugulum R. The Mahalanobis-Taguchi strategy:A pattern technology system[M]. Hoboken, New Jersge:John Wiley & Sons, 2002.
