基于施密特正交马田系统和φs转换的灰模糊积分关联度决策模型

针对传统灰关联度不能有效处理属性间存在的交互作用问题,定义了灰模糊积分关联度的概念,并给出了利用Фs函数将属性权重与属性间的交互度转换为λ模糊测度的方法;对于属性权重的计算,提出一种利用施密特正交马田系统计算属性权重的方法,该方法不但考虑了决策者的主观偏好,而且可以消除属性间的重叠信息,从而使权重的计算更加合理;构建了灰模糊积分关联度决策模型,并给出了详细的决策步骤.最后,通过实例验证了所提出的决策模型的可行性,并分析了不同交互度对决策结果的敏感性.

Grey fuzzy integral correlation degree decision model based on Mahalanobis-Taguchi Gram-Schmidt and φs transformation

To solve the problem that the traditional grey correlation degree can not effectively deal with the interaction between attributes, the grey fuzzy integral correlation degree is defined. At the same time, a calculation method of fuzzy measures is given. In the method, weights of attributes and the interaction degree between attributes are transformed into lambda fuzzy measure with φ_s  transformation function. A calculation method of weights based on Mahalanobis-Taguchi Gram- Schmidt is proposed, which can not only consider the subjective preference of decision makers, also can eliminate the overlap information between attributes, so that the weights of attributes the method calculated is more reasonable. A decision making model based on grey fuzzy integral correlation degree is presented, and an application example is analyzed. Finally, the example verifies the feasibility of the decision making model, and the sensitivity of the decision result is analyzed based on different interaction degree.