粗糙集的论域扩展理论及在专家系统中的应用
|
摘要
粗糙集建立在分类机制基础上,利用已知的知识库近似刻画不精确或不确定的研究对象。粗糙集已成功地应用到了社会生活中的很多方面,随着其应用广度和深度的不断拓展,粗糙集的扩展研究引起了学者们的重视。目前,粗糙集的扩展理论主要指粗糙集在等价关系、近似空间和论域三个方向的扩展。其中,粗糙集在关系扩展和近似空间扩展理论已经成功应用于多属性决策、故障诊断等领域。但是,粗糙集的论域扩展理论研究刚刚起步、定义还不统一、性质还不够完善；另一方面,现实问题大都涉及到两个论域的情况,比如：个性化营销中商品属性集与顾客特征集、企业经营诊断中企业出现的问题集和解决方案集、疾病诊断中疾病的症状集和药物集、机械故障诊断中故障集和解决方案集等都可以看作两个不同的论域,利用粗糙集的论域扩展理论对上述问题进行推理、分析和获取相关规则,可以为我们做决策提供帮助。因此,粗糙集的论域扩展研究在理论和应用两个方面均有重要的意义。
已有的粗糙集的论域扩展理论是建立在相容关系基础上的,在一定程度上限制了其应用。本文通过比较分析已有粗糙集论域扩展理论的相关定义,将两个论域之间的相容关系扩展为无限制的二元关系：一般关系,构建基于一般关系的论域扩展粗糙集近似算子：双论域粗糙集近似算子,基于双论域粗糙集近似算子的粗糙集称为双论域粗糙集。具体来说,本文的主要工作如下：
(1)丰富和发展粗糙集的论域扩展理论。在双论域粗糙集近似算子的基础上,定义了双论域粗糙集的属性重要度、属性约简、相对属性约简、信息熵和信息粒度等概念,研究双论域粗糙集的基本性质和不确定性度量。
(2)在模糊信息系统中研究双论域粗糙集。利用模糊关系和水平截集构造模糊双论域粗糙集近似算子,定义基于模糊双论域粗糙集近似算子的粗糙集为模糊双论域粗糙集。从粗糙集和模糊关系两个角度研究模糊双论域粗糙集的性质和定义,研究模糊双论域粗糙集的属性重要度、属性约简、相对属性约简等基本概念和性质,并给出实例予以说明。
(3)在概率近似空间中研究双论域粗糙集。利用包含度和阈值构造了变精度双论域粗糙集近似算子,定义基于变精度双论域粗糙集近似算子的粗糙集为变精度双论域粗糙集。从粗糙集和包含度两个角度研究变精度双论域粗糙集的性质,研究不同阂值下变精度双论域粗糙集的包含关系；定义并研究变精度双论域粗糙集的属性重要度、属性约简、相对属性约简等基本概念和性质,并给出实例予以说明。类似地,定义并研究双参数变精度双论域粗糙集近似算子的基本概念和性质。
(4)设计基于双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集的专家系统。设计双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集上、下近似算子的求解算法；同时,提出研究对象的双论域、模糊双论域和变精度双论域正域、负域、可能域和边界域的计算方法。针对研究对象与专家系统中规则不完全匹配的问题,利用双论域、模糊双论域和变精度双论域正域、负域、可能域和边界域提取与研究对象匹配的确定性规则和可能性规则。
本文利用构造性方法研究粗糙集的论域扩展理论及应用,通过比较分析已有的粗糙集的论域扩展定义,构造双论域粗糙集,深入研究双论域粗糙集的重要概念和性质；针对多决策问题中常见的不确定性信息,在模糊近似空间和概率近似空间中研究模糊双论域粗糙集和变精度双论域粗糙集；另外,将双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集引入到专家系统中,促进了双论域粗糙集的理论和应用的发展。
Rough set theory as a new mathematical tool is fit for data mining. Rough set theory has received a lot of attention on areas in both of real-life applications and the theory itself. Meanwhile, the real-life applications promote rough set theory research by means of extending structures of rough set. Pawlak rough set is discussed in approximation space, which is constituted by universe, equivalence relation, and approximation space. The promoted research of rough set is extension of universe, equivalence relation and approximation space. At the aspect of approximation space, many research communities have done much in rough set theory and application research on extension of equivalence relation and approximation space. However, the study on rough set on universe extension has just started internally. Definitions about rough set on universe extension are lack of unity. Properties of rough set on universe extension are not perfect. Applications from rough set on universe extension are few. On the other hand, practical problems are mostly related to two universes. For example, characteristics of customer and attributes of product in marketing, problems and solutions in the diagnosis of enterprise business, symptoms of disease and diagnosis in fault diagnosis and so on are problems with two different universes. Rough set on universe extension is especially applicable to solve these issues, which can help us make decisions. Thus, rough set on universe extension is significant in theory and applications.
In this paper, rough set on universe extension is discussed by relax tolerance relation to general relation, which is named Rough Set over Dual-universe (RSDU for short). Approximation operators, basic concepts and uncertainty measures of RSDU are discussed. RSDU in fuzzy information system and probability space are also studied in this dissertation. Applications based on RSDU, FRSDU and VPRSDU are illustrated in expert system. Specifically, the main contributions can be formulated as follows:
(1) This paper has made positive contributions to the enrichment and development of RSDU theory. In accordance with the limitation of research on traditional rough set on universe extension, we proposed RSDU by general relation in place of tolerance relation. Attribute significance, attribute reduction, information entropy and information granular of RSDU are presented. The relations between Pawlak rough set and RSDU are studied and uncertainty measures of RSDU are discussed.
(2) For vague description of problems often comes up in our real life. RSDU are researched in fuzzy information system, which is named Fuzzy Rough Set over Dual-universes(FRSDU for short). FRSDU is introduced by discussing fuzzy relation and cut set. Approximation operators are derived. Attribute significance and attribute reduction of FRSDU are presented. Properties of FRSDU are discussed from the angles of rough set and fuzzy set and examples are advanced to illustrate FRSDU.
(3) For dependency degree formula is accurately described in RSDU and noise data exerts a considerable influence when we deal with problems. Variable Precision Rough Set over Dual-universes (VPRSDU) is introduced by discussing inclusion degree. Approximation operators of VPRSDU are derived by using general relation and inclusion degree. Properties of VPRSDU are discussed from the angles of inclusion degree and threshold. Attribute significance, attribute reduction and relative attribute reduction of VPRSDU are presented. Then, two parametric variable precision rough set over Dual-universes is presented and examples are advanced to illustrate VPRSDU.
(4) For research objects and expert system may be not perfectly matched, RSDU, FRSDU and VPRSDU are utilized to construct expert system. Algorithms for lower and upper approximation of RSDU, FRSDU and VPRSDU are advanced. Positive region, negative region, boundary region and possibility region are obtained. Expert knowledge and research objects draw certainty rules and possible rules.
In this paper, constructive method is utilized to research rough set on universe extension:RSDU. New concepts of RSDU are presented by comparing with traditional concepts. RSDU in fuzzy and probability information system are researched for uncertainty in real life. Applications of rough set on universe extension are discussed in expert system.
已有的粗糙集的论域扩展理论是建立在相容关系基础上的,在一定程度上限制了其应用。本文通过比较分析已有粗糙集论域扩展理论的相关定义,将两个论域之间的相容关系扩展为无限制的二元关系：一般关系,构建基于一般关系的论域扩展粗糙集近似算子：双论域粗糙集近似算子,基于双论域粗糙集近似算子的粗糙集称为双论域粗糙集。具体来说,本文的主要工作如下：
(1)丰富和发展粗糙集的论域扩展理论。在双论域粗糙集近似算子的基础上,定义了双论域粗糙集的属性重要度、属性约简、相对属性约简、信息熵和信息粒度等概念,研究双论域粗糙集的基本性质和不确定性度量。
(2)在模糊信息系统中研究双论域粗糙集。利用模糊关系和水平截集构造模糊双论域粗糙集近似算子,定义基于模糊双论域粗糙集近似算子的粗糙集为模糊双论域粗糙集。从粗糙集和模糊关系两个角度研究模糊双论域粗糙集的性质和定义,研究模糊双论域粗糙集的属性重要度、属性约简、相对属性约简等基本概念和性质,并给出实例予以说明。
(3)在概率近似空间中研究双论域粗糙集。利用包含度和阈值构造了变精度双论域粗糙集近似算子,定义基于变精度双论域粗糙集近似算子的粗糙集为变精度双论域粗糙集。从粗糙集和包含度两个角度研究变精度双论域粗糙集的性质,研究不同阂值下变精度双论域粗糙集的包含关系；定义并研究变精度双论域粗糙集的属性重要度、属性约简、相对属性约简等基本概念和性质,并给出实例予以说明。类似地,定义并研究双参数变精度双论域粗糙集近似算子的基本概念和性质。
(4)设计基于双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集的专家系统。设计双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集上、下近似算子的求解算法；同时,提出研究对象的双论域、模糊双论域和变精度双论域正域、负域、可能域和边界域的计算方法。针对研究对象与专家系统中规则不完全匹配的问题,利用双论域、模糊双论域和变精度双论域正域、负域、可能域和边界域提取与研究对象匹配的确定性规则和可能性规则。
本文利用构造性方法研究粗糙集的论域扩展理论及应用,通过比较分析已有的粗糙集的论域扩展定义,构造双论域粗糙集,深入研究双论域粗糙集的重要概念和性质；针对多决策问题中常见的不确定性信息,在模糊近似空间和概率近似空间中研究模糊双论域粗糙集和变精度双论域粗糙集；另外,将双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集引入到专家系统中,促进了双论域粗糙集的理论和应用的发展。
Rough set theory as a new mathematical tool is fit for data mining. Rough set theory has received a lot of attention on areas in both of real-life applications and the theory itself. Meanwhile, the real-life applications promote rough set theory research by means of extending structures of rough set. Pawlak rough set is discussed in approximation space, which is constituted by universe, equivalence relation, and approximation space. The promoted research of rough set is extension of universe, equivalence relation and approximation space. At the aspect of approximation space, many research communities have done much in rough set theory and application research on extension of equivalence relation and approximation space. However, the study on rough set on universe extension has just started internally. Definitions about rough set on universe extension are lack of unity. Properties of rough set on universe extension are not perfect. Applications from rough set on universe extension are few. On the other hand, practical problems are mostly related to two universes. For example, characteristics of customer and attributes of product in marketing, problems and solutions in the diagnosis of enterprise business, symptoms of disease and diagnosis in fault diagnosis and so on are problems with two different universes. Rough set on universe extension is especially applicable to solve these issues, which can help us make decisions. Thus, rough set on universe extension is significant in theory and applications.
In this paper, rough set on universe extension is discussed by relax tolerance relation to general relation, which is named Rough Set over Dual-universe (RSDU for short). Approximation operators, basic concepts and uncertainty measures of RSDU are discussed. RSDU in fuzzy information system and probability space are also studied in this dissertation. Applications based on RSDU, FRSDU and VPRSDU are illustrated in expert system. Specifically, the main contributions can be formulated as follows:
(1) This paper has made positive contributions to the enrichment and development of RSDU theory. In accordance with the limitation of research on traditional rough set on universe extension, we proposed RSDU by general relation in place of tolerance relation. Attribute significance, attribute reduction, information entropy and information granular of RSDU are presented. The relations between Pawlak rough set and RSDU are studied and uncertainty measures of RSDU are discussed.
(2) For vague description of problems often comes up in our real life. RSDU are researched in fuzzy information system, which is named Fuzzy Rough Set over Dual-universes(FRSDU for short). FRSDU is introduced by discussing fuzzy relation and cut set. Approximation operators are derived. Attribute significance and attribute reduction of FRSDU are presented. Properties of FRSDU are discussed from the angles of rough set and fuzzy set and examples are advanced to illustrate FRSDU.
(3) For dependency degree formula is accurately described in RSDU and noise data exerts a considerable influence when we deal with problems. Variable Precision Rough Set over Dual-universes (VPRSDU) is introduced by discussing inclusion degree. Approximation operators of VPRSDU are derived by using general relation and inclusion degree. Properties of VPRSDU are discussed from the angles of inclusion degree and threshold. Attribute significance, attribute reduction and relative attribute reduction of VPRSDU are presented. Then, two parametric variable precision rough set over Dual-universes is presented and examples are advanced to illustrate VPRSDU.
(4) For research objects and expert system may be not perfectly matched, RSDU, FRSDU and VPRSDU are utilized to construct expert system. Algorithms for lower and upper approximation of RSDU, FRSDU and VPRSDU are advanced. Positive region, negative region, boundary region and possibility region are obtained. Expert knowledge and research objects draw certainty rules and possible rules.
In this paper, constructive method is utilized to research rough set on universe extension:RSDU. New concepts of RSDU are presented by comparing with traditional concepts. RSDU in fuzzy and probability information system are researched for uncertainty in real life. Applications of rough set on universe extension are discussed in expert system.
引文
[1]PAWLAK Z. Rough Sets[J]. International Journal of Computer and Information Sciences,1982,11(5):341-56.
[2]PAWLAK Z. Rough sets:Theoretical aspects of reasoning about data [M]. Springer, 1991.
[3]张文修.粗糙集理论与方法[M].科学出版社,2001.
[4]THANGAVEL K, PETHALAKSHMI A. Dimensionality reduction based on rough set theory:A review [J]. Applied Soft Computing,2009,9(1):1-12.
[5]JENSEN R, SHEN Q. Rough set based feature selection: A review[J]. Rough Computing:Theories, Technologies and Applications,2007,2:1-50.
[6]PAWLAK Z. Reasoning about data—A rough set perspective [J]. Rough Sets and Current Trends in Computing,2009,1424:25-34.
[7]ILCZUK G, WAKULICZ-DEJA A. Visualization of Rough Set Decision Rules for Medical Diagnosis Systems[J]. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing,2007,4482:371-378.
[8]ZHANG Z, SHI Y, GAO G. A rough set-based multiple criteria linear programming approach for the medical diagnosis and prognosis[J]. Expert Systems with Applications,2009,36(5):8932-8937.
[9]PATTARAINTAKORN P, CERCONE N. Integrating rough set theory and medical applications[J]. Applied Mathematics Letters,2008,21(4):400-403.
[10]DONG Y, XIANG B, WANG T, et al. Rough set-based SAR analysis:An inductive method[J]. Expert Systems with Applications,2010,37(7):5032-5039.
[11]LIU H, QU L B, GAO H B, et al. Study on the quantitative structure-activity relationship of C-10 substituted artemisinin(QHS)'s derivatives using rough set theory[J]. Science in China Series B:Chemistry,2008,51(10):937-945.
[12]ZOU Z, TSENG T L B, SONG G, et al. A rough set based approach to distributor selection in supply chain management [J]. Expert Systems with Applications,2010, 24(4):297-304.
[13]TEOH H J, CHENG C H, CHU H H, et al. Fuzzy time series model based on probabilistic approach and rough set rule induction for empirical research in stock markets[J]. Data & Knowledge Engineering,2008,67(1):103-117.
[14]YAO Y Y. Two views of the theory of rough sets in finite universes[J]. International journal of approximate reasoning,1996,15(4):291-317.
[15]辛清泉,林斌,杨德明.中国资本投资回报率的估算和影响因素分析——1999—2004年上市公司的经验[J].经济学,2007,6(004)：1143-1164.
[16]孔欣欣,罗晖.我国高技术产业利润率偏低对产业结构调整的影响及对策研究[J].中国软科学,2007,(08)：46-55.
[17]李存芳,周德群.基于模糊数学的企业综合竞争力评价和实证[J].控制与决策,2007,3：337-340,348.
[18]GRECO S, MATARAZZO B. S lowinski, R.:A new rough set approach to multicriteria and multiattribute classification[J], European Journal of Operational Research,1998,15 (1):96-106.
[19]LIOU J J H, TZENG G H. A dominance-based rough set approach to customer behavior in the airline market[J]. Information Sciences,2010,180(11):2230-2238.
[20]GRECO S, MATARAZZO B, S OWINSKI R. The use of rough sets and fuzzy sets in MCDM[M]. Kluwer Academic Publisher,1999.
[21]GRECO S, MATARAZZO B, SLOWINSKI R. Rough sets theory for multicriteria decision analysis[J]. European Journal of Operational Research,2001,129(1):1-47.
[22]GRECO S, MATARAZZO B, S OWINSKI R. Fuzzy set extensions of the dominance-based rough set approach[J]. Fuzzy Sets and Their Extensions: Representation, Aggregation and Models,2008,239-261.
[23]FAN T F, LIAU C J, LIU D R. Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables[J]. International journal of approximate reasoning,2011,4:33-42.
[24]ZARAS K. Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems[J]. European Journal of Operational Research,2004,159(1):196-206.
[25]HU Q, YU D, GUO M. Fuzzy preference based rough sets[J]. Information Sciences, 2010,180(10):2003-2022.
[26]ZHAI L Y, KHOO L P, ZHONG Z W. A dominance-based rough set approach to Kansei Engineering in product development[J]. Expert Systems with Applications, 2009,36(1):393-402.
[27]INUIGUCHI M, YOSHIOKA Y, KUSUNOKIY. Variable-precision dominance-based rough set approach and attribute reduction[J]. International journal of approximate reasoning,2009,50(8):1199-1214.
[28]YANG X, YANG J, WU C, et al. Dominance-based rough set approach and knowledge reductions in incomplete ordered information system[J]. Information Sciences,2008,178(4):1219-1234.
[29]YANG X, YU D, YANG J, et al. Dominance-based rough set approach to incomplete interval-valued information system[J]. Data & Knowledge Engineering,2009,68(11): 1331-1347.
[30]黄兵,胡作进,周献中.优势模糊粗糙模型及其在审计风险评估中的应用[J].控制与决策,2009,24(6)：899-902.
[31]菅利荣,唐学文,刘思峰等.基于优势粗糙集的建设项目过程评价[J].系统管理学报,2009,18(05)：577-582.
[32]SLOWINSKI R, VANDERPOOTEN D. Similarity relation as a basis for rough approximations[M]. Citeseer,1995.
[33]SLOWINSKI R, VANDERPOOTEN D. A generalized definition of rough approximations based on similarity[J]. Knowledge and Data Engineering,2000,12(2): 331-336.
[34]GRECO S, MATARAZZO B, SLOWINSKI R. Fuzzy similarity relation as a basis for rough approximations[J], Information Sciences,2009,18(1):230-238.
[35]JIANG Y, CHEN J, RUAN X. Fuzzy similarity-based rough set method for case-based reasoning and its application in tool selection[J]. International Journal of Machine Tools and Manufacture,2006,46(2):107-113.
[36]YIN X. A Threshold-based Similarity Relation Under Incomplete Information[J]. Computer And Computinjg Technologies In Agriculture,2008,1:103-110.
[37]张东波,王耀南.基于粗糙集相容关系的图像聚类分割[J].计算机工程与应用,2006,42(011)：24-26.
[38]高阳,钟波.基于(α,τ)限制相似关系的变精度粗糙集模型[J].系统工程与电子技术,2009,31(07)：1639-1641.
[39]GRZYMALA-BUSSE J. On the unknown attribute values in learning from examples[J]. Methodologies for intelligent systems,1991,542:368-377.
[40]KRYSIKIEWICZ M. Rough set approach to incomplete information system[J]. Information Sciences,1998,112(1-4):39-49.
[41]KRYSZKIEWICZ M. Rules in incomplete information systems[J]. Information Sciences,1999,113(3-4):271-292.
[42]STEFANOWSKI J, TSOUKIAS A. Incomplete information tables and rough classification[J]. Computational Intelligence,2002,17(3):545-566.
[43]MENG Z, SHI Z. A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets[J]. Information Sciences,2009, 179(16):2774-2793.
[44]QIAN Y, LIANG J, PEDRYCZ W, et al. An efficient accelerator for attribute reduction from incomplete data in rough set framework[J]. Pattern Recognition,2011, 44(8):1658-1670.
[45]朱颢东,钟勇.相容关系的改进及其属性约简[J].北京理工大学学报,2010,30(01)：55-59.
[46]YANG X, ZHANG M, DOU H, et al. Neighborhood systems-based rough sets in incomplete information system[J]. Knowledge-Based Systems,2011,24(6):858-867.
[47]OUYANG Y, WANG Z, ZHANG H. On fuzzy rough sets based on tolerance relations[J]. Information Sciences,2010,180(4):532-542.
[48]曾雪兰,梅良才,陈胜等.IIS中基于限制容差关系的变精度粗糙集模型[J].广西大学学报：自然科学版,2009,34(006)：819-822.
[49]XU Y, LI L S. Variable Precision Rough Set Model Based on (α,λ) Connection Degree Tolerance Relation[J]. Acta Automatica Sinica,2011,37(3):303-308.
[50]ZHU W. Topological approaches to covering rough sets[J]. Information Sciences, 2007,177(6):1499-1508.
[51]苗夺谦,李道国.粗糙集理论,算法与应用[M].清华大学出版社,2008.
[52]TSANG E C C, DEGANG C, YEUNG D S. Approximations and reducts with covering generalized rough sets[J]. Computers & Mathematics with Applications, 2008,56(1):279-289.
[53]GONG K H, QIU T R, XIONG S J, et al. Hierarchical clustering algorithm based on cover rough set model[J]. Computer Engineering and Design,2009,30(22): 5185-5188.
[54]DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of general systems,1990,17(2):191-209.
[55]BAZAN J, SKOWRON A, SWINIARSKI R. Rough sets and vague concept approximation:From sample approximation to adaptive learning[J]. Transactions on Rough Sets V,2006,4100:39-62.
[56]BONIKOWSKI Z, WYBRANIEC-SKARDOWSKA U. Rough sets and vague sets[J]. Rough Sets and Intelligent Systems Paradigms,2007,4585:122-132.
[57]PAWLAK Z. Sets, fuzzy sets and rough sets[M], Springer,2004.
[58]路艳丽,雷英杰,周炜.基于包含度的直觉模糊粗糙集模型[J].计算机应用,2008,28(008)：1997-1999.
[59]LIU M, CHEN D, WU C, et al. Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems[J]. Computers & Mathematics with Applications,2006,51(9-10):1507-1518.
[60]GRECO S, INUIGUCHI M, SLOWINSKI R. Fuzzy rough sets and multiple-premise gradual decision rules[J]. International journal of approximate reasoning,2006,41(2): 179-211.
[61]XU F F, MIAO D Q, WEI L. Fuzzy-rough attribute reduction via mutual information with an application to cancer classification[J]. Computers & Mathematics with Applications,2009,57(6):1010-1017.
[62]ZHANG D, WANG Y, HUANG H. Rough neural network modeling based on fuzzy rough model and its application to texture classification[J]. Neurocomputing,2009, 72(10-12):2433-2443.
[63]ZIARKO W. Variable precision rough set model[J]. Journal of computer and system sciences,1993,46(1):39-59.
[64]AN A, SHAN N, CHAN C, et al. Discovering rules for water demand prediction:an enhanced rough-set approach[J]. Engineering Applications of Artificial Intelligence, 1996,9(6):645-654.
[65]KATZBERG J D, ZIARKO W. Variable precision extension of rough sets[J]. Fundamenta Informaticae,1996,27(2):155-168.
[66]LE ZAK D, ZIARKO W. The investigation of the Bayesian rough set model[J]. International journal of approximate reasoning,2005,40(1-2):81-91.
[67]HONG T P, WANG T T, WANG S L. Mining fuzzy [beta]-certain and [beta]-possible rules from quantitative data based on the variable precision rough-set model[J]. Expert Systems with Applications,2007,32(1):223-232.
[68]XIE G, ZHANG J, LAI K K, et al. Variable precision rough set for group decision-making:an application[J]. International journal of approximate reasoning, 2008,49(2):331-343.
[69]NINGLER M, STOCKMANNS G, SCHNEIDER G, et al. Adapted variable precision rough set approach for EEG analysis[J]. Artificial intelligence in medicine,2009, 47(3):239-261.
[70]PAN X, ZHANG S, ZHANG H, et al. A variable precision rough set approach to the remote sensing land use/cover classification[J]. Computers & Geosciences,2010, 36(12):1466-1473.
[71]DEMPSTER A P. New approaches for reasoning toeards posterior distributions based on sample data[J]. Annals of Mathematical Statistics,1966,37:335-374.
[72]SHAFER G. A mathematical theory of evidence[M]. Princeton university press Princeton, NJ,1976.
[73]PAWLAK Z. Rough probability[J]. Bulletin of the Polish Academy of Sciences Mathematics,1984,32(9-10):607-612.
[74]WONG S K M, WANG L S, YAO Y Y On modeling uncertainty with interval structures[J]. Computational Intelligence,1995,11(2):406-426.
[75]YAO P J. Interpretations of belief functions in the theory of rough sets[J]. Information Sciences,1998,104(1-2):81-106.
[76]YAO Y Y. Generalized rough set models[J]. Rough Sets in Knowledge Discovery, 1998,1:286-318.
[77]KONDO M. On the structure of generalized rough sets[J]. Information Sciences, 2006,176(5):589-600.
[78]YAO Y Y. On generalizing rough set theory[C]. RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing,2003:44-51.
[79]WU W Z, MI J S, ZHANG W X. Generalized fuzzy rough sets[J]. Information Sciences,2003,151:263-282.
[80]WU W Z, ZHANG W X. Constructive and axiomatic approaches of fuzzy approximation operators[J]. Information Sciences,2004,159(3-4):233-254.
[81]WU W Z, LEUNG Y, MI J S. On characterizations of-fuzzy rough approximation operators[J]. Fuzzy Sets and Systems,2005,154(1):76-102.
[82]LI T J. Rough approximation operators on two universes of discourse and their fuzzy extensions[J]. Fuzzy Sets and Systems,2008,159(22):3033-3050.
[83]LI T J, ZHANG W X. Rough fuzzy approximations on two universes of discourse[J]. Information Sciences,2008,178(3):892-906.
[84]ZHANG H Y, ZHANG W X, WU W Z. On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse[J]. International journal of approximate reasoning,2009,51(1):56-70.
[85]LIU G. Rough set theory based on two universal sets and its applications[J]. Knowledge-Based Systems,2010,23(2):110-115.
[86]YANG H L. Short communication:A note on Rough set theory based on two universal sets and its applications Knowledge-Based Systems 23 (2010) 110-115[J]. Knowledge-Based Systems,24(3):465-466.
[87]SUN B, MA W. Fuzzy rough set model on two different universes and its application[J]. Applied Mathematical Modeling,2010,35(4):1789-1809.
[88]YAN R, ZHENG J, LIU J. Rough set over dual-universes and its applications in: Expert systems k[J]. ICIC Express Letters,2010,4(3):833-838.
[89]YAN R, ZHENG J, LIU J, et al. Research on the model of rough set over dual-universes[J]. Knowledge-Based Systems,2010,23(8):817-822.
[90]DASH M, LIU H. Consistency-based search in feature selection [J]. Artificial intelligence,2003,151(1-2):155-176.
[91]GUYON I, ELISSEEFF A. An introduction to variable and feature selection [J]. The Journal of Machine Learning Research,2003,3:1157-1182.
[92]PEDRYCZ W, VUKOVICH G. Feature analysis through information granulation and fuzzy sets [J]. Pattern Recognition,2002,35(4):825-834.
[93]QIAN Y, LIANG J, LI D, et al. Measures for evaluating the decision performance of a decision table in rough set theory [J]. Information Sciences,2008,178(1):181-202.
[94]HU Q, XIE Z, YU D. Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation [J]. Pattern Recognition,2007,40(12):3509-3521.
[95]PAVLENKO T. On feature selection, curse-of-dimensionality and error probability in discriminant analysis [J]. Journal of Statistical Planning and Inference,2003,115(2): 565-584.
[96]SWINIARSKI R W, SKOWRON A. Rough set methods in feature selection and recognition [J]. Pattern recognition letters,2003,24(6):833-849.
[97]KOHAVI R, JOHN G H. Wrappers for feature subset selection [J]. Artificial intelligence,1997,97(1-2):273-324.
[98]LEE C, LEE G G. Information gain and divergence-based feature selection for machine learning-based text categorization [J]. Information processing & management,2006,42(1):155-165.
[99]QIAN Y, LIANG J, DANG C. Converse approximation and rule extraction from decision tables in rough set theory [J]. Computers & Mathematics with Applications, 2008,55(8):1754-1765.
[100]SHEN Q, JENSEN R. Selecting informative features with fuzzy-rough sets and its application for complex systems monitoring [J]. Pattern Recognition,2004,37(7): 1351-1363.
[101]BHATT R B, GOPAL M. On fuzzy-rough sets approach to feature selection [J]. Pattern Recognition Letters,2005,26(7):965-975.
[102]BHATT R B, GOPAL M. On the compact computational domain of fuzzy-rough sets [J]. Pattern Recognition Letters,2005,26(11):1632-1640.
[103]HU Q, YU D, XIE Z, et al. Fuzzy probabilistic approximation spaces and their information measures [J]. Fuzzy Systems, IEEE Transactions on,2006,14(2): 191-201.
[104]HU Q, YU D, XIE Z. Information-preserving hybrid data reduction based on fuzzy-rough techniques [J]. Pattern Recognition Letters,2006,27(5):414-423.
[105]CHMIELEWSKI M R, GRZYMALA-BUSSE J W. Global discretization of continuous attributes as preprocessing for machine learning [J]. International journal of approximate reasoning,1996,15(4):319-331.
[106]LIU H, SETIONO R. Feature selection via discretization [J]. Knowledge and Data Engineering, IEEE Transactions on,1997,9(4):642-645.
[107]ZIARKO W. Variable precision rough set model [J]. Journal of computer and system sciences,1993,46(1):39-59.
[108]WU W Z, ZHANG M, LI H Z, et al. Knowledge reduction in random information systems via Dempster-shafer theory of evidence [J]. Information Sciences,2005, 174(3):143-164.
[109]KRYSZKIEWICZ M. Comparative study of alternative types of knowledge reduction in inconsistent systems [J]. International Journal of Intelligent Systems,2001,16(1): 105-120.
[110]LEUNG Y E E. On knowledge reduction in inconsistent decision information systems [J]. World,2004,12(5):651-672.
[111]SKOWRON A. Extracting laws from decision tables:a rough set approach [J]. Computational Intelligence,1995,11(2):371-388.
[112]SHAO M W, ZHANG W X. Dominance relation and rules in an incomplete ordered information system [J]. International Journal of Intelligent Systems,2005,20(1): 13-27.
[113]KRYSZKIEWICZ M, LASEK P. FUN:fast discovery of minimal sets of attributes functionally determining a decision attribute [J]. Transactions on Rough Sets IX, 2008,76-95.
[114]HU X, CERCONE N. Learning in relational databases:a rough set approach [J]. Computational Intelligence,1995,11(2):323-338.
[115]LIANG J, CHIN K S, DANG C, et al. A new method for measuring uncertainty and fuzziness in rough set theory [J]. International Journal of general systems,2002,31(4): 331-342.
[116]LIANG J, XU Z B. The algorithm on knowledge reduction in incomplete information systems [J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2002,10(1):95-103.
[117]SLEZAK D. Approximate entropy reducts [J]. Fundamenta Informaticae,2002, 53(3-4):365-390.
[118]GUO-YIN W, HONG Y, DA-CHUN Y. Decision table reduction based on conditional information entropy [J]. Chinese Journal of computers,2002,25(7):759-766.
[119]WANG X, YANG J, JENSEN R, et al. Rough set feature selection and rule induction. for prediction of malignancy degree in brain glioma [J]. Computer methods and programs in biomedicine,2006,83(2):147-156.
[120]TSUMOTO S. Extraction of experts'decision rules from clinical databases using rough set model [J]. Intelligent Data Analysis,1998,2(1):215-227.
[121]TSUMOTO S. Automated extraction of hierarchical decision rules from clinical databases using rough set model [J]. Expert Systems with Applications,2003,24(2): 189-197.
[122]GRZYMALA-BUSSE J W. LERS-a system for learning from examples based on rough sets [J]. Intelligent Decision Support Handbook of Applications and Advances of the Rough Sets Theory,1992,3-18.
[123]GRZYMALA-BUSSE P, GRZYMALA-BUSSE J W, HIPPE Z S. Melanoma prediction using data mining system LERS [C]. Computer Software and Applications Conference,2001:615-620.
[124]STEFANOWSKI J. On rough set based approaches to induction of decision rules [J]. Rough Sets in Knowledge Discovery,1998,1(1):500-529.
[125]LAW R, AU N. Relationship modeling in tourism shopping: a decision rules induction approach [J]. Tourism Management,2000,21(3):241-249.
[126]SHEN Q, CHOUCHOULAS A. A modular approach to generating fuzzy rules with reduced attributes for the monitoring of complex systems [J]. Engineering Applications of Artificial Intelligence,2000,13(3):263-278.
[2]PAWLAK Z. Rough sets:Theoretical aspects of reasoning about data [M]. Springer, 1991.
[3]张文修.粗糙集理论与方法[M].科学出版社,2001.
[4]THANGAVEL K, PETHALAKSHMI A. Dimensionality reduction based on rough set theory:A review [J]. Applied Soft Computing,2009,9(1):1-12.
[5]JENSEN R, SHEN Q. Rough set based feature selection: A review[J]. Rough Computing:Theories, Technologies and Applications,2007,2:1-50.
[6]PAWLAK Z. Reasoning about data—A rough set perspective [J]. Rough Sets and Current Trends in Computing,2009,1424:25-34.
[7]ILCZUK G, WAKULICZ-DEJA A. Visualization of Rough Set Decision Rules for Medical Diagnosis Systems[J]. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing,2007,4482:371-378.
[8]ZHANG Z, SHI Y, GAO G. A rough set-based multiple criteria linear programming approach for the medical diagnosis and prognosis[J]. Expert Systems with Applications,2009,36(5):8932-8937.
[9]PATTARAINTAKORN P, CERCONE N. Integrating rough set theory and medical applications[J]. Applied Mathematics Letters,2008,21(4):400-403.
[10]DONG Y, XIANG B, WANG T, et al. Rough set-based SAR analysis:An inductive method[J]. Expert Systems with Applications,2010,37(7):5032-5039.
[11]LIU H, QU L B, GAO H B, et al. Study on the quantitative structure-activity relationship of C-10 substituted artemisinin(QHS)'s derivatives using rough set theory[J]. Science in China Series B:Chemistry,2008,51(10):937-945.
[12]ZOU Z, TSENG T L B, SONG G, et al. A rough set based approach to distributor selection in supply chain management [J]. Expert Systems with Applications,2010, 24(4):297-304.
[13]TEOH H J, CHENG C H, CHU H H, et al. Fuzzy time series model based on probabilistic approach and rough set rule induction for empirical research in stock markets[J]. Data & Knowledge Engineering,2008,67(1):103-117.
[14]YAO Y Y. Two views of the theory of rough sets in finite universes[J]. International journal of approximate reasoning,1996,15(4):291-317.
[15]辛清泉,林斌,杨德明.中国资本投资回报率的估算和影响因素分析——1999—2004年上市公司的经验[J].经济学,2007,6(004)：1143-1164.
[16]孔欣欣,罗晖.我国高技术产业利润率偏低对产业结构调整的影响及对策研究[J].中国软科学,2007,(08)：46-55.
[17]李存芳,周德群.基于模糊数学的企业综合竞争力评价和实证[J].控制与决策,2007,3：337-340,348.
[18]GRECO S, MATARAZZO B. S lowinski, R.:A new rough set approach to multicriteria and multiattribute classification[J], European Journal of Operational Research,1998,15 (1):96-106.
[19]LIOU J J H, TZENG G H. A dominance-based rough set approach to customer behavior in the airline market[J]. Information Sciences,2010,180(11):2230-2238.
[20]GRECO S, MATARAZZO B, S OWINSKI R. The use of rough sets and fuzzy sets in MCDM[M]. Kluwer Academic Publisher,1999.
[21]GRECO S, MATARAZZO B, SLOWINSKI R. Rough sets theory for multicriteria decision analysis[J]. European Journal of Operational Research,2001,129(1):1-47.
[22]GRECO S, MATARAZZO B, S OWINSKI R. Fuzzy set extensions of the dominance-based rough set approach[J]. Fuzzy Sets and Their Extensions: Representation, Aggregation and Models,2008,239-261.
[23]FAN T F, LIAU C J, LIU D R. Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables[J]. International journal of approximate reasoning,2011,4:33-42.
[24]ZARAS K. Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems[J]. European Journal of Operational Research,2004,159(1):196-206.
[25]HU Q, YU D, GUO M. Fuzzy preference based rough sets[J]. Information Sciences, 2010,180(10):2003-2022.
[26]ZHAI L Y, KHOO L P, ZHONG Z W. A dominance-based rough set approach to Kansei Engineering in product development[J]. Expert Systems with Applications, 2009,36(1):393-402.
[27]INUIGUCHI M, YOSHIOKA Y, KUSUNOKIY. Variable-precision dominance-based rough set approach and attribute reduction[J]. International journal of approximate reasoning,2009,50(8):1199-1214.
[28]YANG X, YANG J, WU C, et al. Dominance-based rough set approach and knowledge reductions in incomplete ordered information system[J]. Information Sciences,2008,178(4):1219-1234.
[29]YANG X, YU D, YANG J, et al. Dominance-based rough set approach to incomplete interval-valued information system[J]. Data & Knowledge Engineering,2009,68(11): 1331-1347.
[30]黄兵,胡作进,周献中.优势模糊粗糙模型及其在审计风险评估中的应用[J].控制与决策,2009,24(6)：899-902.
[31]菅利荣,唐学文,刘思峰等.基于优势粗糙集的建设项目过程评价[J].系统管理学报,2009,18(05)：577-582.
[32]SLOWINSKI R, VANDERPOOTEN D. Similarity relation as a basis for rough approximations[M]. Citeseer,1995.
[33]SLOWINSKI R, VANDERPOOTEN D. A generalized definition of rough approximations based on similarity[J]. Knowledge and Data Engineering,2000,12(2): 331-336.
[34]GRECO S, MATARAZZO B, SLOWINSKI R. Fuzzy similarity relation as a basis for rough approximations[J], Information Sciences,2009,18(1):230-238.
[35]JIANG Y, CHEN J, RUAN X. Fuzzy similarity-based rough set method for case-based reasoning and its application in tool selection[J]. International Journal of Machine Tools and Manufacture,2006,46(2):107-113.
[36]YIN X. A Threshold-based Similarity Relation Under Incomplete Information[J]. Computer And Computinjg Technologies In Agriculture,2008,1:103-110.
[37]张东波,王耀南.基于粗糙集相容关系的图像聚类分割[J].计算机工程与应用,2006,42(011)：24-26.
[38]高阳,钟波.基于(α,τ)限制相似关系的变精度粗糙集模型[J].系统工程与电子技术,2009,31(07)：1639-1641.
[39]GRZYMALA-BUSSE J. On the unknown attribute values in learning from examples[J]. Methodologies for intelligent systems,1991,542:368-377.
[40]KRYSIKIEWICZ M. Rough set approach to incomplete information system[J]. Information Sciences,1998,112(1-4):39-49.
[41]KRYSZKIEWICZ M. Rules in incomplete information systems[J]. Information Sciences,1999,113(3-4):271-292.
[42]STEFANOWSKI J, TSOUKIAS A. Incomplete information tables and rough classification[J]. Computational Intelligence,2002,17(3):545-566.
[43]MENG Z, SHI Z. A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets[J]. Information Sciences,2009, 179(16):2774-2793.
[44]QIAN Y, LIANG J, PEDRYCZ W, et al. An efficient accelerator for attribute reduction from incomplete data in rough set framework[J]. Pattern Recognition,2011, 44(8):1658-1670.
[45]朱颢东,钟勇.相容关系的改进及其属性约简[J].北京理工大学学报,2010,30(01)：55-59.
[46]YANG X, ZHANG M, DOU H, et al. Neighborhood systems-based rough sets in incomplete information system[J]. Knowledge-Based Systems,2011,24(6):858-867.
[47]OUYANG Y, WANG Z, ZHANG H. On fuzzy rough sets based on tolerance relations[J]. Information Sciences,2010,180(4):532-542.
[48]曾雪兰,梅良才,陈胜等.IIS中基于限制容差关系的变精度粗糙集模型[J].广西大学学报：自然科学版,2009,34(006)：819-822.
[49]XU Y, LI L S. Variable Precision Rough Set Model Based on (α,λ) Connection Degree Tolerance Relation[J]. Acta Automatica Sinica,2011,37(3):303-308.
[50]ZHU W. Topological approaches to covering rough sets[J]. Information Sciences, 2007,177(6):1499-1508.
[51]苗夺谦,李道国.粗糙集理论,算法与应用[M].清华大学出版社,2008.
[52]TSANG E C C, DEGANG C, YEUNG D S. Approximations and reducts with covering generalized rough sets[J]. Computers & Mathematics with Applications, 2008,56(1):279-289.
[53]GONG K H, QIU T R, XIONG S J, et al. Hierarchical clustering algorithm based on cover rough set model[J]. Computer Engineering and Design,2009,30(22): 5185-5188.
[54]DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of general systems,1990,17(2):191-209.
[55]BAZAN J, SKOWRON A, SWINIARSKI R. Rough sets and vague concept approximation:From sample approximation to adaptive learning[J]. Transactions on Rough Sets V,2006,4100:39-62.
[56]BONIKOWSKI Z, WYBRANIEC-SKARDOWSKA U. Rough sets and vague sets[J]. Rough Sets and Intelligent Systems Paradigms,2007,4585:122-132.
[57]PAWLAK Z. Sets, fuzzy sets and rough sets[M], Springer,2004.
[58]路艳丽,雷英杰,周炜.基于包含度的直觉模糊粗糙集模型[J].计算机应用,2008,28(008)：1997-1999.
[59]LIU M, CHEN D, WU C, et al. Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems[J]. Computers & Mathematics with Applications,2006,51(9-10):1507-1518.
[60]GRECO S, INUIGUCHI M, SLOWINSKI R. Fuzzy rough sets and multiple-premise gradual decision rules[J]. International journal of approximate reasoning,2006,41(2): 179-211.
[61]XU F F, MIAO D Q, WEI L. Fuzzy-rough attribute reduction via mutual information with an application to cancer classification[J]. Computers & Mathematics with Applications,2009,57(6):1010-1017.
[62]ZHANG D, WANG Y, HUANG H. Rough neural network modeling based on fuzzy rough model and its application to texture classification[J]. Neurocomputing,2009, 72(10-12):2433-2443.
[63]ZIARKO W. Variable precision rough set model[J]. Journal of computer and system sciences,1993,46(1):39-59.
[64]AN A, SHAN N, CHAN C, et al. Discovering rules for water demand prediction:an enhanced rough-set approach[J]. Engineering Applications of Artificial Intelligence, 1996,9(6):645-654.
[65]KATZBERG J D, ZIARKO W. Variable precision extension of rough sets[J]. Fundamenta Informaticae,1996,27(2):155-168.
[66]LE ZAK D, ZIARKO W. The investigation of the Bayesian rough set model[J]. International journal of approximate reasoning,2005,40(1-2):81-91.
[67]HONG T P, WANG T T, WANG S L. Mining fuzzy [beta]-certain and [beta]-possible rules from quantitative data based on the variable precision rough-set model[J]. Expert Systems with Applications,2007,32(1):223-232.
[68]XIE G, ZHANG J, LAI K K, et al. Variable precision rough set for group decision-making:an application[J]. International journal of approximate reasoning, 2008,49(2):331-343.
[69]NINGLER M, STOCKMANNS G, SCHNEIDER G, et al. Adapted variable precision rough set approach for EEG analysis[J]. Artificial intelligence in medicine,2009, 47(3):239-261.
[70]PAN X, ZHANG S, ZHANG H, et al. A variable precision rough set approach to the remote sensing land use/cover classification[J]. Computers & Geosciences,2010, 36(12):1466-1473.
[71]DEMPSTER A P. New approaches for reasoning toeards posterior distributions based on sample data[J]. Annals of Mathematical Statistics,1966,37:335-374.
[72]SHAFER G. A mathematical theory of evidence[M]. Princeton university press Princeton, NJ,1976.
[73]PAWLAK Z. Rough probability[J]. Bulletin of the Polish Academy of Sciences Mathematics,1984,32(9-10):607-612.
[74]WONG S K M, WANG L S, YAO Y Y On modeling uncertainty with interval structures[J]. Computational Intelligence,1995,11(2):406-426.
[75]YAO P J. Interpretations of belief functions in the theory of rough sets[J]. Information Sciences,1998,104(1-2):81-106.
[76]YAO Y Y. Generalized rough set models[J]. Rough Sets in Knowledge Discovery, 1998,1:286-318.
[77]KONDO M. On the structure of generalized rough sets[J]. Information Sciences, 2006,176(5):589-600.
[78]YAO Y Y. On generalizing rough set theory[C]. RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing,2003:44-51.
[79]WU W Z, MI J S, ZHANG W X. Generalized fuzzy rough sets[J]. Information Sciences,2003,151:263-282.
[80]WU W Z, ZHANG W X. Constructive and axiomatic approaches of fuzzy approximation operators[J]. Information Sciences,2004,159(3-4):233-254.
[81]WU W Z, LEUNG Y, MI J S. On characterizations of-fuzzy rough approximation operators[J]. Fuzzy Sets and Systems,2005,154(1):76-102.
[82]LI T J. Rough approximation operators on two universes of discourse and their fuzzy extensions[J]. Fuzzy Sets and Systems,2008,159(22):3033-3050.
[83]LI T J, ZHANG W X. Rough fuzzy approximations on two universes of discourse[J]. Information Sciences,2008,178(3):892-906.
[84]ZHANG H Y, ZHANG W X, WU W Z. On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse[J]. International journal of approximate reasoning,2009,51(1):56-70.
[85]LIU G. Rough set theory based on two universal sets and its applications[J]. Knowledge-Based Systems,2010,23(2):110-115.
[86]YANG H L. Short communication:A note on Rough set theory based on two universal sets and its applications Knowledge-Based Systems 23 (2010) 110-115[J]. Knowledge-Based Systems,24(3):465-466.
[87]SUN B, MA W. Fuzzy rough set model on two different universes and its application[J]. Applied Mathematical Modeling,2010,35(4):1789-1809.
[88]YAN R, ZHENG J, LIU J. Rough set over dual-universes and its applications in: Expert systems k[J]. ICIC Express Letters,2010,4(3):833-838.
[89]YAN R, ZHENG J, LIU J, et al. Research on the model of rough set over dual-universes[J]. Knowledge-Based Systems,2010,23(8):817-822.
[90]DASH M, LIU H. Consistency-based search in feature selection [J]. Artificial intelligence,2003,151(1-2):155-176.
[91]GUYON I, ELISSEEFF A. An introduction to variable and feature selection [J]. The Journal of Machine Learning Research,2003,3:1157-1182.
[92]PEDRYCZ W, VUKOVICH G. Feature analysis through information granulation and fuzzy sets [J]. Pattern Recognition,2002,35(4):825-834.
[93]QIAN Y, LIANG J, LI D, et al. Measures for evaluating the decision performance of a decision table in rough set theory [J]. Information Sciences,2008,178(1):181-202.
[94]HU Q, XIE Z, YU D. Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation [J]. Pattern Recognition,2007,40(12):3509-3521.
[95]PAVLENKO T. On feature selection, curse-of-dimensionality and error probability in discriminant analysis [J]. Journal of Statistical Planning and Inference,2003,115(2): 565-584.
[96]SWINIARSKI R W, SKOWRON A. Rough set methods in feature selection and recognition [J]. Pattern recognition letters,2003,24(6):833-849.
[97]KOHAVI R, JOHN G H. Wrappers for feature subset selection [J]. Artificial intelligence,1997,97(1-2):273-324.
[98]LEE C, LEE G G. Information gain and divergence-based feature selection for machine learning-based text categorization [J]. Information processing & management,2006,42(1):155-165.
[99]QIAN Y, LIANG J, DANG C. Converse approximation and rule extraction from decision tables in rough set theory [J]. Computers & Mathematics with Applications, 2008,55(8):1754-1765.
[100]SHEN Q, JENSEN R. Selecting informative features with fuzzy-rough sets and its application for complex systems monitoring [J]. Pattern Recognition,2004,37(7): 1351-1363.
[101]BHATT R B, GOPAL M. On fuzzy-rough sets approach to feature selection [J]. Pattern Recognition Letters,2005,26(7):965-975.
[102]BHATT R B, GOPAL M. On the compact computational domain of fuzzy-rough sets [J]. Pattern Recognition Letters,2005,26(11):1632-1640.
[103]HU Q, YU D, XIE Z, et al. Fuzzy probabilistic approximation spaces and their information measures [J]. Fuzzy Systems, IEEE Transactions on,2006,14(2): 191-201.
[104]HU Q, YU D, XIE Z. Information-preserving hybrid data reduction based on fuzzy-rough techniques [J]. Pattern Recognition Letters,2006,27(5):414-423.
[105]CHMIELEWSKI M R, GRZYMALA-BUSSE J W. Global discretization of continuous attributes as preprocessing for machine learning [J]. International journal of approximate reasoning,1996,15(4):319-331.
[106]LIU H, SETIONO R. Feature selection via discretization [J]. Knowledge and Data Engineering, IEEE Transactions on,1997,9(4):642-645.
[107]ZIARKO W. Variable precision rough set model [J]. Journal of computer and system sciences,1993,46(1):39-59.
[108]WU W Z, ZHANG M, LI H Z, et al. Knowledge reduction in random information systems via Dempster-shafer theory of evidence [J]. Information Sciences,2005, 174(3):143-164.
[109]KRYSZKIEWICZ M. Comparative study of alternative types of knowledge reduction in inconsistent systems [J]. International Journal of Intelligent Systems,2001,16(1): 105-120.
[110]LEUNG Y E E. On knowledge reduction in inconsistent decision information systems [J]. World,2004,12(5):651-672.
[111]SKOWRON A. Extracting laws from decision tables:a rough set approach [J]. Computational Intelligence,1995,11(2):371-388.
[112]SHAO M W, ZHANG W X. Dominance relation and rules in an incomplete ordered information system [J]. International Journal of Intelligent Systems,2005,20(1): 13-27.
[113]KRYSZKIEWICZ M, LASEK P. FUN:fast discovery of minimal sets of attributes functionally determining a decision attribute [J]. Transactions on Rough Sets IX, 2008,76-95.
[114]HU X, CERCONE N. Learning in relational databases:a rough set approach [J]. Computational Intelligence,1995,11(2):323-338.
[115]LIANG J, CHIN K S, DANG C, et al. A new method for measuring uncertainty and fuzziness in rough set theory [J]. International Journal of general systems,2002,31(4): 331-342.
[116]LIANG J, XU Z B. The algorithm on knowledge reduction in incomplete information systems [J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2002,10(1):95-103.
[117]SLEZAK D. Approximate entropy reducts [J]. Fundamenta Informaticae,2002, 53(3-4):365-390.
[118]GUO-YIN W, HONG Y, DA-CHUN Y. Decision table reduction based on conditional information entropy [J]. Chinese Journal of computers,2002,25(7):759-766.
[119]WANG X, YANG J, JENSEN R, et al. Rough set feature selection and rule induction. for prediction of malignancy degree in brain glioma [J]. Computer methods and programs in biomedicine,2006,83(2):147-156.
[120]TSUMOTO S. Extraction of experts'decision rules from clinical databases using rough set model [J]. Intelligent Data Analysis,1998,2(1):215-227.
[121]TSUMOTO S. Automated extraction of hierarchical decision rules from clinical databases using rough set model [J]. Expert Systems with Applications,2003,24(2): 189-197.
[122]GRZYMALA-BUSSE J W. LERS-a system for learning from examples based on rough sets [J]. Intelligent Decision Support Handbook of Applications and Advances of the Rough Sets Theory,1992,3-18.
[123]GRZYMALA-BUSSE P, GRZYMALA-BUSSE J W, HIPPE Z S. Melanoma prediction using data mining system LERS [C]. Computer Software and Applications Conference,2001:615-620.
[124]STEFANOWSKI J. On rough set based approaches to induction of decision rules [J]. Rough Sets in Knowledge Discovery,1998,1(1):500-529.
[125]LAW R, AU N. Relationship modeling in tourism shopping: a decision rules induction approach [J]. Tourism Management,2000,21(3):241-249.
[126]SHEN Q, CHOUCHOULAS A. A modular approach to generating fuzzy rules with reduced attributes for the monitoring of complex systems [J]. Engineering Applications of Artificial Intelligence,2000,13(3):263-278.