Abstract: A method is proposed to solve screening alternatives problems based on soft set theory, in which the criteria sets given by multiple participants are different. In the method, the evaluation criteria subsets of each participant are first constructed based on the acceptance of which each alternative satisfies the requirements of evaluation criteria given by each participant. Then, according to the results that each alternative satisfies the requirements of evaluation criteria, the soft sets for the evaluation criteria subsets of each participant are constructed. Furthermore, the soft set that all alternatives satisfy the requirements of all evaluation criteria of multiple participants are built, and based on the operations of product and operators between the soft sets of evaluation criteria subsets and the soft set all alternatives satisfy the requirements of all evaluation criteria of multiple participants, the alternatives sets of each evaluation criteria subsets accepted by each participant can be obtained. And, according to the union and intersection operation between the alternatives sets in which the each alternatives set is accepted by each participant, the ultimate alternatives set passing screening can be obtained. Finally, a numerical example is given to illustrate the feasibility and validity of the proposed method.

Key words: management science, method for screening alternatives, soft set theory, evaluation criteria, product, operators

摘要： 针对多方给出评价指标集存在差异情形的方案筛选问题,提出了一种基于软集理论的方案筛选方法。在该方法中,首先依据各方给出关于备选方案符合评价指标要求的可接受水平,构建各方相应的评价指标子集,进而针对各备选方案符合评价指标要求的结果构建针对各方评价指标子集的软集;然后构建所有方案均符合全部指标要求的软集,进而通过各评价指标子集的软集与所有方案均符合全部指标要求的软集的积运算和算子运算,得到对应评价指标子集的每方可接受的备选方案集;进一步地,通过各方可接受的备选方案集间的并集运算及交集运算,可得到最终的方案筛选结果。最后,通过一个算例说明了本文给出方法的可行性和有效性。

关键词: 管理科学, 方案筛选方法, 软集理论, 评价指标, 积运算, 算子