Abstract: In order to make up for the deficiency of absolute degree of incidence ,synthetic degree of incidence and relative degree of incidence, the paper attempts to establish a new model. First of all, we set up a control factor and introduce the concept of metric space, in order to adjust the range of the value. We prove that this model satisfies the grey incidence axioms. We also study its some properties. Furthermore, we put forward a new model of quasi optimal value to meet a few principles, and combined with sensitivity analysis, the algorithm steps of the quasi optimal value are given. Finally, the effectiveness and practicability of this model is verified through practical examples. Therefore, the rest of the paper is organized as follows. In section 1, some basic concepts of absolute degree of incidence, synthetic degree of incidence and relative degree of grey incidence are reviewed. In this section, some limitations of them are proved. In section 2, we set up a control factor and introduce the concept of metric space to adjust the value them, and propose the quasi-“very close”-absolute degree of incidence, the quasi-“very close”-relative degree of incidence and the quasi-“very close”-synthetic degree of grey incidence, and so on. This section also studies some specific properties for them. Section 3 summarizes the specific algorithm steps. In section 4, we compare each kind of value of them by an example, and also obtain some useful results.

Key words: metric space, sensitivity analysis, grey incidence analysis, modeling

摘要： 本文针对绝对关联度、综合关联度以及相对关联度的取值范围存在的不足,首先,设置了控制因子λ以及空间中的距离d,以此来调节关联度值的范围,建立了新模型。其次,研究了它的一些性质,并在理论上证明了新模型满足灰色关联公理。另外,提出了新模型的准优值所满足的几个原则,并结合灵敏性分析原理给出了准优值的算法步骤。最后,通过实例研究,验证了新模型所得结果不但能够使关联度的值扩充到(0,1]这一更大的范围,而且提高了区分度和分辨效果。

关键词: 空间距离, 灵敏性分析, 灰色关联分析, 模型