灰模糊积分关联度决策模型

Grey Fuzzy Integral Correlation Degree Decision Model

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.