第14卷第6期 智能系统学报 Vol.14 No.6 2019年11月 CAAI Transactions on Intelligent Systems Nov.2019 D0:10.11992/tis.201905048 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20190909.1712.008.html 面向混合数据的多伴随三支决策 赵天娜，苗夺谦2，米据生3，张远健2 (1.同济大学电子与信息工程学院，上海201804：2.同济大学嵌入式系统与服务计算教有部重点实验室，上海 201804;3.河北师范大学数学与信息科学学院，河北石家庄050024) 摘要：针对混合数据的知识表示和分类的问题，在思考混合数据的有效表示时，提出代价敏感多伴随模糊粗 糙集模型，在解决混合数据的分类问题上，引入三支决策思想，同时在多伴随模型基础上做了两点改进：)提 出贴近代价敏感多伴随模糊粗糙集模型特点的概率定义；2)借助双量化延迟代价目标函数的思想，构造面向混 合数据的新型三支决策模型。该模型具有如下特点：1)引入多个伴随对，模拟了数值型属性和符号型属性之间 异构互补的关系；2)定义多伴随算子，充分表达了不同类型属性之间的偏好：3)结合模糊粗糙集，克服了分类 问题的不确定性：4)考虑获取不同类型属性的代价，提高了应用到实际生活的可能性。最后用实例验证了此模 型的有效性。 关键词：混合数据：模糊粗糙集；三支决策：多伴随：代价敏感：知识表示：分类 中图分类号：TP391文献标志码：A文章编号：1673-4785(2019)06-1092-08 中文引用格式：赵天娜，苗夺谦，米据生，等.面向混合数据的多伴随三支决策智能系统学报，2019,14(6)：1092-1099 英文引用格式：ZHAO Tianna,MIAO Duoqian,,MI Jusheng,etal.Multi--adjoint three--way decisions on heterogeneous data[J. CAAI transactions on intelligent systems,2019,14(6):1092-1099 Multi-adjoint three-way decisions on heterogeneous data ZHAO Tianna,MIAO Duoqian"2,MI Jusheng',ZHANG Yuanjian2 (1.College of Computer Science and Technology,Tongji University,Shanghai 201804,China;2.Key Laboratory of Embedded Sys- tem and Service Computing of Ministry of Education,Tongji University,Shanghai 201804,China;3.College of Mathematics and In- formation Science,Hebei Normal University,Shijiazhuang 050024,China) Abstract:Considering the problem of knowledge representation and classification relating to heterogeneous data,a cost- sensitive multi-adjoint fuzzy rough set model is proposed for the effective representation of heterogeneous data and in order to solve the classification problem of heterogeneous data,the idea of three-way decisions is introduced.Moreover, two improvements are made on the basis of the multi-adjoint model:1)A revised probability definition is presented to approximately characterize the cost-sensitive fuzzy rough set model.2)Based on the idea of the dual quantization delay cost objective function,a novel three-way decisions model is constructed for heterogeneous data.This model has the fol- lowing characteristics:1)Multiple adjoint pairs are introduced to simulate the relationship of heterogeneous comple- mentarity between numerical attribute and categorical attribute.2)The multi-adjoint operator is defined to fully express the preference among different attributes.3)A fuzzy rough set is combined to overcome the uncertainty of the classifica- tion problem.4)The cost of acquiring both numerical and categorical attributes is considered to improve the possibility of application to real life.The effectiveness of the model is verified in the heterogeneous dataset. Keywords:heterogeneous data;fuzzy rough set;three-way decisions;multi-adjoint;cost-sensitive;knowledge repres- entation;classification 收稿日期：2019-05-24.网络出版日期：2019-09-10. 混合数据是非结构化的、互补的、超高维 基金项目：国家重点研发项目(213)：国家自然科学基金项目 (61673301,61573127,61763031):河北省自然科学基金 的，包含大量冗余信息，研究如何有效表示，特征 项目(A2018210120):公安部重大专项项目(20170004). 通信作者：赵天娜.E-mail:1810375@tongji.edu.cn 选择和融合混合数据有重要的实际意义。尤其是DOI: 10.11992/tis.201905048 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20190909.1712.008.html 面向混合数据的多伴随三支决策 赵天娜1,2，苗夺谦1,2，米据生3 ，张远健1,2 （1. 同济大学 电子与信息工程学院，上海 201804; 2. 同济大学 嵌入式系统与服务计算教育部重点实验室，上海 201804; 3. 河北师范大学 数学与信息科学学院，河北 石家庄 050024） 摘 要：针对混合数据的知识表示和分类的问题，在思考混合数据的有效表示时，提出代价敏感多伴随模糊粗 糙集模型，在解决混合数据的分类问题上，引入三支决策思想，同时在多伴随模型基础上做了两点改进：1) 提 出贴近代价敏感多伴随模糊粗糙集模型特点的概率定义；2) 借助双量化延迟代价目标函数的思想，构造面向混 合数据的新型三支决策模型。该模型具有如下特点：1) 引入多个伴随对，模拟了数值型属性和符号型属性之间 异构互补的关系；2) 定义多伴随算子，充分表达了不同类型属性之间的偏好；3) 结合模糊粗糙集，克服了分类 问题的不确定性；4) 考虑获取不同类型属性的代价，提高了应用到实际生活的可能性。最后用实例验证了此模 型的有效性。 关键词：混合数据；模糊粗糙集；三支决策；多伴随；代价敏感；知识表示；分类 中图分类号：TP391 文献标志码：A 文章编号：1673−4785(2019)06−1092−08 中文引用格式：赵天娜, 苗夺谦, 米据生, 等. 面向混合数据的多伴随三支决策 [J]. 智能系统学报, 2019, 14(6): 1092–1099. 英文引用格式：ZHAO Tianna, MIAO Duoqian, MI Jusheng, et al. Multi-adjoint three-way decisions on heterogeneous data[J]. CAAI transactions on intelligent systems, 2019, 14(6): 1092–1099. Multi-adjoint three-way decisions on heterogeneous data ZHAO Tianna1,2 ，MIAO Duoqian1,2 ，MI Jusheng3 ，ZHANG Yuanjian1,2 (1. College of Computer Science and Technology, Tongji University, Shanghai 201804, China; 2. Key Laboratory of Embedded Sys￾tem and Service Computing of Ministry of Education, Tongji University, Shanghai 201804, China; 3. College of Mathematics and In￾formation Science, Hebei Normal University, Shijiazhuang 050024, China) Abstract: Considering the problem of knowledge representation and classification relating to heterogeneous data, a cost￾sensitive multi-adjoint fuzzy rough set model is proposed for the effective representation of heterogeneous data and in order to solve the classification problem of heterogeneous data, the idea of three-way decisions is introduced. Moreover, two improvements are made on the basis of the multi-adjoint model: 1) A revised probability definition is presented to approximately characterize the cost-sensitive fuzzy rough set model. 2) Based on the idea of the dual quantization delay cost objective function, a novel three-way decisions model is constructed for heterogeneous data. This model has the fol￾lowing characteristics: 1) Multiple adjoint pairs are introduced to simulate the relationship of heterogeneous comple￾mentarity between numerical attribute and categorical attribute. 2) The multi-adjoint operator is defined to fully express the preference among different attributes. 3) A fuzzy rough set is combined to overcome the uncertainty of the classifica￾tion problem. 4) The cost of acquiring both numerical and categorical attributes is considered to improve the possibility of application to real life. The effectiveness of the model is verified in the heterogeneous dataset. Keywords: heterogeneous data; fuzzy rough set; three-way decisions; multi-adjoint; cost-sensitive; knowledge repres￾entation; classification 混合数据[1] 是非结构化的、互补的、超高维 的，包含大量冗余信息，研究如何有效表示，特征 选择和融合混合数据有重要的实际意义。尤其是 收稿日期：2019−05−24. 网络出版日期：2019−09−10. 基金项目：国家重点研发项目（213）；国家自然科学基金项目 (61673301,61573127,61763031)；河北省自然科学基金 项目 (A2018210120)；公安部重大专项项目 (20170004). 通信作者：赵天娜. E-mail: 1810375@tongji.edu.cn.. 第 14 卷第 6 期 智 能 系 统 学 报 Vol.14 No.6 2019 年 11 月 CAAI Transactions on Intelligent Systems Nov. 2019