基于Shapley值的优势关系粗糙集客观权重分配方法及应用

摘要

Weight determination is a key problem in studying the decision,the existing weight determina-tion method based on rough set overcomes the shortcomings of relying too heavily on prior knowledge,but it neglects the interaction among attributes.In consideration of the limitations of equivalence relation,this paper focuses on attribute weight determination in the information system based on dominance relation, the importance of attribute determined by information quantity of the attribute set is firstly put forward. And the attribute reductions are acquired based on information quantity,which ensures the distinguish quality at the same time,and simplifies the calculation;Secondly the Shapley value method is initially cho-sen for the loss of information allocation,and then the attribute weights are determined.The method,tak-ing strict km as basis,fully considers the interaction among attributes and guarantees the fair and reasona-ble allocation of attribute weights.The example demonstrates the specific operation steps of the Shapley value method used to determine the attribute weights.The method is easily popularized in intuitiveness and operability,provides reference for attribute weights determination in all kinds of information system,and is also a successful cross application of the game theory.%权重的确定是决策研究中的关键性问题，已有的基于粗糙集的权重确定方法克服了过于依赖先验知识的缺陷，但其未充分考虑属性间的相互作用，此外考虑到等价关系的局限性，着重研究优势关系信息系统的属性权重确定问题，首先提出由属性集包含信息量的多少来确定属性的重要性，并基于信息量对属性集进行约简，在保证对元素间优劣关系区分能力不变的同时简化了计算；其次开创性选用 Shapley值方法对“损失信息量”进行分配，进而确定属性权重，该方法以严格的公理为基础，充分考虑了属性间的相互作用，保证了属性权重分配的公正、合理；最后通过实例演示了利用Shapley值确定属性权重的具体操作步骤。该方法直观性和可操作性强易于推广，为各类信息系统属性权重确定提供了参考，亦是对策论方法交叉应用的成功探索。