改进的多目标灰靶决策方法

考虑到各指标间的相关性、不同量纲和重要性差异对决策效果的影响，利用加权马氏距离对传统的灰靶决策方法进行改进，并研究了改进后灰靶的性质。结果表明，改进后的灰靶满足：靶心距对效果样本作非奇异线性变换的不变性；当观测指标间不存在相关性时，加权马氏距离就是加权欧氏距离。避免了决策指标间的相关性、不同量纲和重要性差异对决策效果的影响以及灰靶变换的不相容问题。最后以实例验证了该模型的有效性与实用性。

Improvements on decision method of grey target

Taking into account the correlation among different indexes as well as the influences of both different dimensions and differences of importance on effect of decisions, this paper deals with improving tradi-tional grey target decision methods with the approach of weighted Mahalanobis distance and discusses the property of the improved grey target method. The results indicate that the improved grey target could meet the invariance of effect samples after nonsingular linear transformation caused by clout distance; the weighted Ma-halanobis distance is just the weighted Euclidean distance when there is no correlation among observed indexes, which avoids correlation of decision indexes, influences of different dimension and differences of importance on effect of decisions, and the incompatibility of grey target transformation. Finally, the effectiveness and availa-bility of the model are proved by a real case in point.