基于马田系统的2可加Choquet积分多属性决策方法  

Multi-Attribute Decision Making Method Based on Mahalanobis-Taguchi System and 2-additive Choquet integral

作　　者：常志朋[1,2] 程龙生[1] 刘家树[2] 

机构地区：[1]南京理工大学经济管理学院,江苏南京210094 [2]安徽工业大学经济学院,安徽马鞍山243002

出　　处：《管理工程学报》2016年第1期133-139,共7页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金资助项目(71271114);教育部人文社会科学规划基金资助项目(10YJA630020);国家社会科学基金资助项目(12CGL013)

摘　　要：在实际决策问题中,决策属性间往往存在一定的交互作用,而传统决策方法并不能有效处理。针对这种情况,提出了一种基于马田系统和2可加Choquet积分集成算子的多属性决策方法。2可加Choquet积分集成算子是在2可加模糊测度和Choquet积分算子的基础上推导而得,由单个属性的Shapley值和两两属性间的交互指标构成。为了计算Shapley值,首先提出了一种基于马田系统的属性集重要程度测度方法,并给出了合理性分析,然后根据属性集中的所有属性在决策过程中应表现出积极的合作关系来优化单个属性的全局重要程度,最后将单个属性的相对重要程度和全局重要程度进行融合,得到单个属性的Shapley值;对于交互指标的计算,根据无偏好决策方案集在相同约束条件下应平等竞争的原理,构建了基于多目标的交互指标优化模型。最后基于所得到的Shapley值和交互指标对各候选方案的评价信息进行集成。实例验证结果表明该方法是可行的,能够处理属性间存在交互作用的大规模决策问题。The interaction between attributes often exists in real decision-making problems. However, the traditional multiple attributive decision making method （MADM） assumes that all attributes are mutually independent. Therefore, traditional MADM cannot effectively deal with the interaction between attributes. To solve the problem, a new MADM based on 2-additive Choquet integral aggregation operator and Mahalanobis-Taguchi system （MTS） is proposed. In the new MADM, 2-additive Choquet integral aggregation operator is composed of Shapley value and interaction index. The operator is derived from 2-additive fuzzy measure and Cboquet integral. The 2-additive fuzzy measure can be more flexible to represent the interaction between attributes. Choquet integral is a nonlinear function and it can be taken as an integrated operator to deal with MADM. Choquet integral integrated operator doesn＇t need to meet with the assumption that attributes are mutually independent. Therefore, it can effectively deal with the interaction between attributes. MTS is a pattern recognition technology based on quality engineering and it is proposed by the famous Japanese quality engineer Dr. Taguchi. MTS has three key tools, including Orthogonal Arrays, Mahalanobis Distance and Signal to Noise Ratio. MTS can not only distinguish the category of a given sample, but also measure the importance of attributes that describe the sample. In MTS, the function of measuring the importance of attribute is based on the orthogonal experiment principle. In the new MADM, to calculate the Shapley value the Mahalanobis-Taguchi system is firstly used to measure the important degree of attribute set and the rationality of the measure method. The global important degree of a single attribute is optimized on the basis of the principle that all attributes should have positive cooperation in the decision-making process. Finally, the Shapley value is calculated with the degree of globalization and the relative degree of a single attribute. The multi-objective op

关 键 词：马田系统 2可加Choquet积分 2可加模糊测度 

分 类 号：C934[经济管理—管理学]