In the past twenty years, the auction theory has grown into one of the most prominent applied economics theories. Auction is an effective way to optimize the allocation of market through competitive bidding in order to produce the market equilibrium price. The early auction theory often studies the single-attribute auction, in which price is the only factor considered. Many researchers suggest that multi-attribute auction should be adopted because of its feasibility in the purchasing economics theory. How to design proper mechanisms and select the winner are two critical problems in the multi-attribute auction.rnMergers and acquisitions ( M&A) of state-owned enterprises in China are mostly done by the government through negotiation and consultation, which may not only increase the rent-seeking behavior, resulting in the loss of state assets, but also lead to inefficiency of resource allocation. It has demonstrated that auction in the M&A of state-owned enterprises can effectively enhance the effectiveness of asset allocation and reduce the loss of state-owned assets. From the perspective of the social overall effectiveness, the method of multi-attribute auctions is more effective than single-attribute auctions. Based on the analysis of the outstanding questions in M&A of state-owned enterprises, this article develops the multi-attribute auction and a set of decision-making attributes for state-owned enterprises. In this attribute set, some quantitative and qualitative factors have to be considered. As the extension of traditional fuzzy set, vague sets are characterized by a truth-membership function and a false-membership function, which makes it more flexible and practical than traditional fuzzy sets. As for this reason, vague sets method is used to describe the fuzzy information for state-owned enterprises.rnWe define a new distance measure of vague sets, which integrate the merits of Hamming distance and Hausdorff distance, and prove that the measure meets the basic requirements of distance measure of vague sets. According to practical situations, a general multi-attribute auction model for M&A decisions of state-owned enterprises under incomplete preference information is proposed. Positive and negative ideal solutions are determined by using score function of vague values. The distances between all solutions, as well as positive and negative ideal solutions are calculated simultaneously based on the newly-defined distance measures of vague sets. A comprehensive evaluation index, which can be derived from distance calculated and weight information, is used to rank all alternatives. In order to deal with incomplete information, a nonlinear programming model including unknown weights of some attributes is presented, and a cross-iterated algorithm is adopted for solving this model and obtaining the optimal weights. The proposed method is finally verified with respect to its effectiveness and feasibility via a case study.%拍卖是国有企业并购的一种有效市场配置方式.从社会整体效用的视角出发,国有企业并购多属性拍卖比以价格为目标的单属性拍卖的效用更高.在分析国有企业并购中凸显问题的基础上,构建了国有企业并购多属性拍卖决策的属性集.采用了Vague集的方法描述国有企业并购多属性拍卖中的模糊信息.根据实际的情况,建立了不完全偏好信息下的国有企业并购多属性拍卖的模糊决策模型.该决策模型中利用Vague值的得分函数确定理想解和负理想解,并依据新定义的Vague集的一种距离测度方式计算各方案与理想解和负理想解的距离.提出了一种交叉迭代法用于求解包含未知权重信息的非线性规划模型,得到属性集的最优权重.最后的应用算例分析表明了该方法的有效性和可行性,为国有企业并购的多属性拍卖决策提供了一种新的思路.
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