计算OWA算子权重的最小最大不一致方法及讨论

权重向量的确定是有序加权平均（ordered weighted aweraging,OWA）算子理论中的一个关键问题，目前已有不少获取权重向量的模型。2010年EMROUZNEJAD 和AMIN两位专家在计算OWA算子权重向量时提出了改进最小最大不一致模型：对于给定的orness测度建立一个最小最大目标规划问题，求解该模型可以得到最优权重向量。但由该方法得到的最优解并不唯一，且存在无穷多解，因此，该模型存在不可靠性。本文通过引理给出定理，证明了其最优解的不唯一性，并用简单有效的数值例子予以说明。

Minimax disparity model for obtaining OWA operator weights: Issues of multiple solutions

The determination of weights vector is one of the key issues in the theory of ordered weighted averaging(OWA) operators. Therefore, many weight generating models have been proposed in the literature.The main purpose of this paper is to point out the problems in the improved minimax disparity model for calculating OWA weight vector, which is suggested by EMROUZNEJAD and AMIN (2010). In this model, a minimax objective programming problem for a given orness measure is proposed, and the optimal weight can be obtained by solving the model, but the optimal solution obtained by this method is not unique,which has infinite solutions even with the same model, different decision makers may get different decision results. From this point of view, there is a certain risk in using this method in decision-making. As a consequence, this model is not reliable. The non-uniqueness of the optimal solution is proved by applying lemma and giving theorem. Some numerical examples is provided to illustrate this reason at the end of the article in a simple and effective way.