序信息系统知识约简的优势关系粗糙集方法
|
摘要
经典粗糙集理论建立在等价关系对论域的分类的基础上,适用于离散型的完备信息系统的知识约简。国内外学者在这一方面做出了大量的研究,并取得了丰硕的成果。但在序信息系统中,属性值表达对象之间的优势关系,此时,经典粗糙集模型不再适用。为此,Greco等提出了优势关系粗糙集模型,用以处理序信息系统的知识约简问题。
本文基于优势关系粗糙集理论,研究了几类序决策信息系统的属性约简与决策规则获取问题,研究内容主要分为以下几章:
第二章主要介绍了优势关系粗糙集理论的基本知识,如序信息系统、优势关系、上、下近似、序决策规则和知识约简等,为后面的研究做好准备。
第三章研究了优势关系下序信息系统的协调约简问题。首先,给出协调约简的定义,并证明协调约简与L-约简和Q-约简是等价的。最后,给出一种计算协调约简的区分函数方法。
第四章研究了不协调序决策信息系统的下近似约简问题。我们改进袁修久等作者提出的关于下近似约简的计算方法,并给出一种新的计算下近似约简的区分函数方法,同时验证了约简结果的正确性。
第五章研究了模糊目标序信息系统的属性约简与优化序决策规则的获取问题。首先在序决策信息系统中定义模糊上(下)近似,由此定义由对象生成的三类序决策规则,并讨论它们的确定度。然后定义对象的三种类型的约简:下近似约简、上近似约简和区间近似约简,并给出相应的判定定理,且构造区分函数用于计算对象的三类近似约简。基于对象的三类约简,我们可以得到三种类型的优化序决策规则。最后,讨论系统的相对约简,并给出具体的计算方法。
第六章总结上面几章的主要内容,并对后续工作做出展望。
Classical rough set theory is based on the classification of universe determined by equivalent relation and successfully used in knowledge reduction of complete symbolic information systems. However, in ordered information systems, attribute values of the objects represent the dominance relation between the objects. Therefore, classical rough set theory, which is established based on the indiscernibility, is inapplicable in dealing with knowledge reduction problem of the ordered information systems. So Greco et al. proposed the dominance-based rough set approach to draw decision rules and compute reducts of the ordered information systems.
In this paper, dominance-based rough set approach and its extended models are used to discuss attribute reduction and decision rule acquisition in ordered information systems. The paper is organized as follows:
In Chapter 2, primary knowledge of ordered information systems and dominance-based rough set approach such as dominance relation, upper (lower) appproximation, ordered decision rules and knowledge reduction are introduced. In Chapter 3, the consistent reducts of ordered decision information systems are studied. Firstly, the definition of consistent reduct is proposed. Then, it is proved that the consistent reduct is actually a L - reduct as well as a Q - reduct. Finally, the discernibility function of the consistent reduct is constructed, and used to compute the consistent reduct by using Boolean reasoning techniques. By discussing the consistent reduct, we get a new computing method which employs discernibility function for Q - reduct.
In Chapter 4, lower approximation reducts in inconsistent ordered decision information systems based on dominance relation are studied. We improve the computing method of lower approximation reducts proposed by other authors and construct a new discernibility function to compute the lower approximation reducts.
In Chapter 5, attribute reduction and optimal decision rules acquisition problems in fuzzy objective ordered information systems are studied. Firstly, fuzzy lower approximation and fuzzy upper approximation are defined, three new types of decision rules generated by an object are proposed, and the degrees of certainty of the decision rules are given. Then, reduct of the object is defined, the judgment theorems are given, and discernibility function with respect to three types of reducts are constructed, by which reducts of the object can be derived. Based on these reducts, three new types of optimal ordered decision can be induced. At last, three kinds of reducts of the systems and their computing methods are given.
In Chapter 6, conclusions of the work in this paper are given, and the future work is pointed out.
本文基于优势关系粗糙集理论,研究了几类序决策信息系统的属性约简与决策规则获取问题,研究内容主要分为以下几章:
第二章主要介绍了优势关系粗糙集理论的基本知识,如序信息系统、优势关系、上、下近似、序决策规则和知识约简等,为后面的研究做好准备。
第三章研究了优势关系下序信息系统的协调约简问题。首先,给出协调约简的定义,并证明协调约简与L-约简和Q-约简是等价的。最后,给出一种计算协调约简的区分函数方法。
第四章研究了不协调序决策信息系统的下近似约简问题。我们改进袁修久等作者提出的关于下近似约简的计算方法,并给出一种新的计算下近似约简的区分函数方法,同时验证了约简结果的正确性。
第五章研究了模糊目标序信息系统的属性约简与优化序决策规则的获取问题。首先在序决策信息系统中定义模糊上(下)近似,由此定义由对象生成的三类序决策规则,并讨论它们的确定度。然后定义对象的三种类型的约简:下近似约简、上近似约简和区间近似约简,并给出相应的判定定理,且构造区分函数用于计算对象的三类近似约简。基于对象的三类约简,我们可以得到三种类型的优化序决策规则。最后,讨论系统的相对约简,并给出具体的计算方法。
第六章总结上面几章的主要内容,并对后续工作做出展望。
Classical rough set theory is based on the classification of universe determined by equivalent relation and successfully used in knowledge reduction of complete symbolic information systems. However, in ordered information systems, attribute values of the objects represent the dominance relation between the objects. Therefore, classical rough set theory, which is established based on the indiscernibility, is inapplicable in dealing with knowledge reduction problem of the ordered information systems. So Greco et al. proposed the dominance-based rough set approach to draw decision rules and compute reducts of the ordered information systems.
In this paper, dominance-based rough set approach and its extended models are used to discuss attribute reduction and decision rule acquisition in ordered information systems. The paper is organized as follows:
In Chapter 2, primary knowledge of ordered information systems and dominance-based rough set approach such as dominance relation, upper (lower) appproximation, ordered decision rules and knowledge reduction are introduced. In Chapter 3, the consistent reducts of ordered decision information systems are studied. Firstly, the definition of consistent reduct is proposed. Then, it is proved that the consistent reduct is actually a L - reduct as well as a Q - reduct. Finally, the discernibility function of the consistent reduct is constructed, and used to compute the consistent reduct by using Boolean reasoning techniques. By discussing the consistent reduct, we get a new computing method which employs discernibility function for Q - reduct.
In Chapter 4, lower approximation reducts in inconsistent ordered decision information systems based on dominance relation are studied. We improve the computing method of lower approximation reducts proposed by other authors and construct a new discernibility function to compute the lower approximation reducts.
In Chapter 5, attribute reduction and optimal decision rules acquisition problems in fuzzy objective ordered information systems are studied. Firstly, fuzzy lower approximation and fuzzy upper approximation are defined, three new types of decision rules generated by an object are proposed, and the degrees of certainty of the decision rules are given. Then, reduct of the object is defined, the judgment theorems are given, and discernibility function with respect to three types of reducts are constructed, by which reducts of the object can be derived. Based on these reducts, three new types of optimal ordered decision can be induced. At last, three kinds of reducts of the systems and their computing methods are given.
In Chapter 6, conclusions of the work in this paper are given, and the future work is pointed out.
引文
[1]. Pawlak Z. Rough sets. International Journal of Computer and Information Science [J]. 1982, 11: 341-356.
[2]. Pawlak Z. Rough sets: Theoretical aspects of reasoning about data [M]. London: Kluwer Academic Publishers, 1991.
[3]. Pawlak Z, Skowron A. Rudiments of rough sets [J]. Information Sciences, 2007, 177: 3-27.
[4]. Skowron A, Rauszer A. The discernibility matrices and functions in information systems. In: Intelligent Decision Support: Handbook of applications and advances of rough sets theory[C]. Dordrecht: Kluwer Academic Publisher, 1992: 331-362.
[5]. Skowron A. Boolean reasoning for decision rules generation. In: Proceedings of the Seventh International Symposium ISMIS’93, Lecture Notes in Artificial Intelligence[C]. Berlin: Springer, 1993: 295-305.
[6]. Hu X H, Cercone N. Learning in relational databases: a rough set approach [J]. International Journal of Computational Intelligence, 1995, 11(2): 323-337.
[7].叶东毅,陈昭炯.一个新的差别矩阵及其核方法[J].电子学报,2002,30(7):1086-1088.
[8].王国胤.决策表的核属性算法[J].计算机学报,2003,26(5):611-615.
[9].闫德勤.不相容信息系统的规范格式与差别矩阵[J].计算机工程与应用,2004,36: 45-46.
[10]. Guan Y Y, Li J P, Wang Y. Improved discernibility matrices on decision tables [J]. Advances in Systems Science and Applications, 2006, 6(3): 439-445.
[11]. Kryszkiewicz M. Comparative study of alternative types of knowledge reduction in inconsistent systems [J]. International Journal of Intelligent Systems, 2001, 16: 105-120.
[12]. Zhang W X, Mi J S, Wu W Z. Approaches to knowledge reductions in inconsistent systems[J]. International Journal of Intelligent Systems, 2003, 18: 989-1000.
[13].张文修,仇国芳.粗糙集属性约简的一般理论[J].中国科学E辑,2005,35(12): 1304-1313.
[14].邓大勇,黄厚宽,李向军.不一致决策系统中约简之间的比较[J].电子学报,2007, 35(2):252-255.
[15].唐建国,谭明术.粗糙集理论中的求核与约简[J].控制与决策,2003,18(4):450-452.
[16]. Skowron A, Stepaniuk J. Tolerance approximation spaces [J]. Fundamenta Informaticae, 1996, 27/2-3:245-253.
[17]. Kryszkiewicz M. Rough set approach to incomplete information systems [J]. Information Sciences, 1998, 112: 39-49.
[18]. Kryszkiewicz M. Rules in incomplete information systems [J]. Information Sciences, 1999, 113: 271-292.
[19]. Leung Y, Li D Y. Maximal consistent block technique for rule acquisition in incomplete information system [J]. Information Sciences, 2003, 153: 85-106.
[20]. Leung Y, Wu W Z, Zhang W X. Knowledge acquisition in incomplete information systems: a rough set approach [J]. European Journal of Operational Research, 2006, 168: 164-180.
[21].王国胤. Rough集理论在不完备信息系统中的扩充[J].计算机研究与发展,2002, 39(10):1238-1243.
[22].管延勇,薛佩军,王洪凯.不完备信息系统的可信决策规则获取与E-相对约简[J].系统工程理论与实践,2005,25(12):76-82.
[23]. Guan Y Y, Wang H K. Set-valued information systems [J]. Information Sciences, 2006, 176 (17): 2507-2525.
[24].陈子春,秦克云.集值信息系统基于变精度相容关系的知识约简[J].计算机工程与应用,2008,44(9):27-29.
[25].王虹,张文修,李鸿儒.集值信息系统的知识发现与约简[J].计算机工程与应用, 2005,6:37-38.
[26]. Hong T P, Wang T T, Wang S L. Knowledge acquisition from quantitative data using the rough-set theory [J]. Intelligent Data Analysis, 2000, 4: 289 -304.
[27]. Roy A, Pal S K. Fuzzy discretization of feature space for a rough set classier [J]. Pattern Recognition Letters, 2003, 24(6): 895-902.
[28].李然.连续值域信息系统的规则提取与知识约简[J].模糊系统与数学,2003,17(4): 40-47.
[29].闫德勤,高艳,迟忠先.连续属性信息系统的规则约简新方法[J].计算机工程与应用, 2003,27:96-97.
[30]. Yang H, Ding Z S. Decision rule acquisition on information system with continuous attribute [J]. Journal of Xi’an University of Engineering Science and Technology, 2007, 21(5): 653-656.
[31].刘文军.连续值域决策表的一种属性权重确定方法[J].模糊系统与数学,2008,22(3): 160-166.
[32]. Guan Y Y, Wang H K, Wang Y et al. Attribute reduction and optimal decision rules acquisition for continuous valued information system [J]. Information Sciences, 2009, 179: 2974-2984.
[33]. Greco S, Matarazzo B, Slowinski R. A new rough set approach to evaluation of bankruptcy risk. In: C. Zopounidis (ed.), Operational tools in the management of financial risks [C].Dordrecht: Kluwer Academic Publishers, 1998, pp: 121-136.
[34]. Greco S, Matarazzo B, Slowinski R. Rough sets theory for multicriteria decision analysis [J]. European Journal of Operational Research, 2001, 129: 181-47.
[35]. Greco S, Matarazzo B, Slowinski R. Rough approximation by dominance relation [J]. International Journal of Intelligent Systems, 2002, 17: 153-171.
[36].张文修,吴伟志,梁吉业等.粗糙集理论与方法[M].北京:中国青年出版社,2000.
[37].张文修,梁怡,吴伟志.信息系统与知识发现[M].北京:科学出版社,2003.
[38].梁吉业,李德玉.信息系统中的不确定性与知识获取[M].北京:科学出版社,2005.
[39].张文修,仇国芳.基于粗糙集的不确定决策[M].北京:清华大学出版社,2005.
[40]. Susmaga R, Slowinski R, Greco S et al. Generation of reducts and rules in multi-attribute and multi-criteria classification [J]. Control and Cybernetics, 2000, 29(4): 969-988.
[41].徐伟华,张文修.基于优势关系下不协调目标信息系统的知识约简[J].计算机科学,2006,33(2):182-184.
[42].徐伟华,张文修.基于优势关系下不协调目标信息系统的分布约简[J].模糊系统与数学,2007,21(4):124-131.
[43].徐伟华,张晓燕,张文修.优势关系下不协调目标信息系统的下近似约简[J].计算机工程与应用,2009,45(16):66-68.
[44].徐伟华,张晓燕,张文修.优势关系下不协调目标信息系统的上近似约简[J].计算机工程,2009,35(18):191-193.
[45].袁修久,何华灿.优势关系下的相容约简和下近似约简[J].西北工业大学学报,2006, 24(5):604-608.
[46].袁修久,何华灿.优势关系下广义决策约简和上近似约简[J].计算机工程与应用, 2006,42(10):4-7.
[47].陈娟,王国胤,胡军.优势关系下不协调信息系统的正域约简[J].计算机科学,2008, 35(13):216-218.
[48]. Fortemps P, Greco S, S?owinski R. Multicriteria decision support using rules that represent rough-graded preference relations [J]. European Journal of Operational Research, 2008, 188: 206-223.
[49]. Yang X B, Yang J Y, Wu C et al. Dominance-based rough set approach and knowledge reduct in incomplete ordered information system [J]. Information Sciences, 2008, 178: 1219-1234.
[50]. Inuiguchi M, Yoshioka Y. Several reducts in dominance-based rough set approach. In: Huynh, V.-N., et al. (eds.): Interval/Probabilistic Uncertainty and Non-classical Logics [C], ASC46, 2008, pp. 163-175.
[51]. Kusunoki Y, Inuiguchi M. A comprehensive study on reducts in dominance-based rough setapproach. In: V. Torra and Y. Narukawa (Eds.): MDAI 2008, LNAI 5285 [C]. 2008, pp. 167-178.
[52]. Dembczynski K, Greco S, Kotlowski W et al. Quality of rough approximation in multi-criteria classification problems. In: Greco S et al (eds) RSCTC2006, LNCS (LNAI), vol 4259 [C]. Springer: Heidelberg, 2006, pp. 318-327.
[53]. Kusunoki K, Inuiguchi M. A unified approach to reducts in dominance-based rough set approach [J]. Soft Computing, 2010, 14 (5): 507-515.
[54]. Shao M W, Zhang W X. Dominance relation and rules in an incomplete ordered information system [J]. International Journal of Intelligent Systems, 2005, 20: 13-27.
[55].何亚群,胡寿松.不完全信息的多属性粗糙决策分析方法[J].系统工程学报,2004,19 (2):117-120.
[56].胡明礼,刘思峰.基于有限扩展优势关系的粗糙决策分析方法[J].系统工程,2006, 24(4):106-111.
[57].胡明礼,刘思峰.基于广义扩展优势关系的粗糙决策分析方法[J].控制与决策,2007, 22(12):1347-1351.
[58].骆公志,杨晓江,周德群.基于限制扩展优势关系的粗糙决策分析模型[J].系统管理学报,2009,18(4):391-396.
[59].谢军,宋余庆,陈健美等.不完备序值决策系统中的拓展粗集模型及集对分析[J].计算机科学,2008,35(12):154-157.
[60].杨习贝,杨静宇,吴小俊等.不完备系统中基于优势关系的最优可信规则获取[J].小型微型计算机系统,2009,30(3):518-523.
[61].管延勇,薛佩军,史开泉.基于描述子的信息系统属性约简及决策规则优化[J].控制与决策,2006,21(7):787-791.
[62].谢军,杨习贝,孙怀江等.序值决策系统中基于描述子的可信规则获取[J].系统工程理论与实践,2009,29(7):105-112.
[63].宋笑雪,解争龙,张文修.集值决策信息系统的知识约简与规则提取[J].计算机科学, 2007,34(4):182-191.
[64].宋笑雪,张文修.不协调集值决策信息系统的属性约简[J].计算机工程与应用,2009, 45(1):33-35.
[65]. Qian Y H, Dang C Y, Liang J Y et al. Set-valued ordered information systems [J]. Information Sciences, 2009, 179: 2809-2832.
[66].王珏,刘三阳,张杰.区间值属性决策表的数据挖掘[J].计算机科学,2003,30(8):121- 123.
[67]. Qian Y H , Liang J Y, Dang C Y. Interval ordered information systems [J]. Computers andMathematics with Applications, 2008, 56: 1994-2009.
[68]. Dembczynski K, Greco S, S?owinski R. Rough set approach to multiple criteria classification with imprecise evaluations and assignments [J]. European Journal of Operational Research, 2009, 198: 626-636.
[69]. Yang X B, Yu D J, Yang J T et al. Dominance-based rough set approach to incomplete interval-valued information system [J]. Data & Knowledge Engineering, 2009, 68(11): 1331-1347.
[70]. Hu Q H, Yu D R, Guo M Z. Fuzzy preference based rough sets [J]. Information Sciences, 2010, 180(10): 2003-2022.
[71]. Guan Y Y, Du L, Wang Y. Ordered-based decision rules acquisition in continuous-valued decision information systems. In: IEEE Proceedings of 2009 Sixth International Conference on Fuzzy System and Knowledge Discovery [C]. Tian Jin: 2009, pp.435-439.
[72]. Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets [J]. International Journal of General Systems, 1990, 17:191-208.
[73].袁修久,何华灿.优势关系下模糊目标信息系统约简的辨识矩阵[J].空军工程大学学报(自然科学版),2006,7(2):81-84.
[74].杜蕾,管延勇,杨芳.优势关系下模糊目标信息系统的决策规则优化[J].计算机工程与应用,2010,46(35):136-138.
[75].魏利华,唐振民,杨习贝等.不完备模糊系统的优势关系粗糙集与知识约简[J].计算机科学,2009,36(6):192-195.
[76].骆公志,杨习贝,杨晓江.基于限制优势关系的粗糙模糊集及知识约简[J].系统工程与电子技术,2010,32(8):1657-1661.
[77]. Greco S, Matarazzo B, Slowinski R et al. Variable consistency model of dominance-based rough set approach. In: W. Ziarko, Y. Yao (Eds.), Rough Sets and Current Trends in Computing, LNAI 2005 [C]. Berlin: Springer-Verlag, 2001, pp. 170-181.
[78]. B?aszczynski J, Greco S, S?owinski R et al. Monotonic variable consistency rough set approaches [J]. International Journal of Approximate Reasoning, 2009, 50: 979- 999.
[79]. Kot?owski W, Dembczynski K, Greco S et al. Stochastic dominance-based rough set model for ordinal classification [J]. Information Sciences, 2008, 178: 4019-4037.
[80]. Inuiguchi M, Yoshioka Y, Kusunoki Y. Variable-precision dominance-based rough set approach and attribute reduction [J]. International Journal of Approximate Reasoning, 2009, 50(8): 1199-1214.
[2]. Pawlak Z. Rough sets: Theoretical aspects of reasoning about data [M]. London: Kluwer Academic Publishers, 1991.
[3]. Pawlak Z, Skowron A. Rudiments of rough sets [J]. Information Sciences, 2007, 177: 3-27.
[4]. Skowron A, Rauszer A. The discernibility matrices and functions in information systems. In: Intelligent Decision Support: Handbook of applications and advances of rough sets theory[C]. Dordrecht: Kluwer Academic Publisher, 1992: 331-362.
[5]. Skowron A. Boolean reasoning for decision rules generation. In: Proceedings of the Seventh International Symposium ISMIS’93, Lecture Notes in Artificial Intelligence[C]. Berlin: Springer, 1993: 295-305.
[6]. Hu X H, Cercone N. Learning in relational databases: a rough set approach [J]. International Journal of Computational Intelligence, 1995, 11(2): 323-337.
[7].叶东毅,陈昭炯.一个新的差别矩阵及其核方法[J].电子学报,2002,30(7):1086-1088.
[8].王国胤.决策表的核属性算法[J].计算机学报,2003,26(5):611-615.
[9].闫德勤.不相容信息系统的规范格式与差别矩阵[J].计算机工程与应用,2004,36: 45-46.
[10]. Guan Y Y, Li J P, Wang Y. Improved discernibility matrices on decision tables [J]. Advances in Systems Science and Applications, 2006, 6(3): 439-445.
[11]. Kryszkiewicz M. Comparative study of alternative types of knowledge reduction in inconsistent systems [J]. International Journal of Intelligent Systems, 2001, 16: 105-120.
[12]. Zhang W X, Mi J S, Wu W Z. Approaches to knowledge reductions in inconsistent systems[J]. International Journal of Intelligent Systems, 2003, 18: 989-1000.
[13].张文修,仇国芳.粗糙集属性约简的一般理论[J].中国科学E辑,2005,35(12): 1304-1313.
[14].邓大勇,黄厚宽,李向军.不一致决策系统中约简之间的比较[J].电子学报,2007, 35(2):252-255.
[15].唐建国,谭明术.粗糙集理论中的求核与约简[J].控制与决策,2003,18(4):450-452.
[16]. Skowron A, Stepaniuk J. Tolerance approximation spaces [J]. Fundamenta Informaticae, 1996, 27/2-3:245-253.
[17]. Kryszkiewicz M. Rough set approach to incomplete information systems [J]. Information Sciences, 1998, 112: 39-49.
[18]. Kryszkiewicz M. Rules in incomplete information systems [J]. Information Sciences, 1999, 113: 271-292.
[19]. Leung Y, Li D Y. Maximal consistent block technique for rule acquisition in incomplete information system [J]. Information Sciences, 2003, 153: 85-106.
[20]. Leung Y, Wu W Z, Zhang W X. Knowledge acquisition in incomplete information systems: a rough set approach [J]. European Journal of Operational Research, 2006, 168: 164-180.
[21].王国胤. Rough集理论在不完备信息系统中的扩充[J].计算机研究与发展,2002, 39(10):1238-1243.
[22].管延勇,薛佩军,王洪凯.不完备信息系统的可信决策规则获取与E-相对约简[J].系统工程理论与实践,2005,25(12):76-82.
[23]. Guan Y Y, Wang H K. Set-valued information systems [J]. Information Sciences, 2006, 176 (17): 2507-2525.
[24].陈子春,秦克云.集值信息系统基于变精度相容关系的知识约简[J].计算机工程与应用,2008,44(9):27-29.
[25].王虹,张文修,李鸿儒.集值信息系统的知识发现与约简[J].计算机工程与应用, 2005,6:37-38.
[26]. Hong T P, Wang T T, Wang S L. Knowledge acquisition from quantitative data using the rough-set theory [J]. Intelligent Data Analysis, 2000, 4: 289 -304.
[27]. Roy A, Pal S K. Fuzzy discretization of feature space for a rough set classier [J]. Pattern Recognition Letters, 2003, 24(6): 895-902.
[28].李然.连续值域信息系统的规则提取与知识约简[J].模糊系统与数学,2003,17(4): 40-47.
[29].闫德勤,高艳,迟忠先.连续属性信息系统的规则约简新方法[J].计算机工程与应用, 2003,27:96-97.
[30]. Yang H, Ding Z S. Decision rule acquisition on information system with continuous attribute [J]. Journal of Xi’an University of Engineering Science and Technology, 2007, 21(5): 653-656.
[31].刘文军.连续值域决策表的一种属性权重确定方法[J].模糊系统与数学,2008,22(3): 160-166.
[32]. Guan Y Y, Wang H K, Wang Y et al. Attribute reduction and optimal decision rules acquisition for continuous valued information system [J]. Information Sciences, 2009, 179: 2974-2984.
[33]. Greco S, Matarazzo B, Slowinski R. A new rough set approach to evaluation of bankruptcy risk. In: C. Zopounidis (ed.), Operational tools in the management of financial risks [C].Dordrecht: Kluwer Academic Publishers, 1998, pp: 121-136.
[34]. Greco S, Matarazzo B, Slowinski R. Rough sets theory for multicriteria decision analysis [J]. European Journal of Operational Research, 2001, 129: 181-47.
[35]. Greco S, Matarazzo B, Slowinski R. Rough approximation by dominance relation [J]. International Journal of Intelligent Systems, 2002, 17: 153-171.
[36].张文修,吴伟志,梁吉业等.粗糙集理论与方法[M].北京:中国青年出版社,2000.
[37].张文修,梁怡,吴伟志.信息系统与知识发现[M].北京:科学出版社,2003.
[38].梁吉业,李德玉.信息系统中的不确定性与知识获取[M].北京:科学出版社,2005.
[39].张文修,仇国芳.基于粗糙集的不确定决策[M].北京:清华大学出版社,2005.
[40]. Susmaga R, Slowinski R, Greco S et al. Generation of reducts and rules in multi-attribute and multi-criteria classification [J]. Control and Cybernetics, 2000, 29(4): 969-988.
[41].徐伟华,张文修.基于优势关系下不协调目标信息系统的知识约简[J].计算机科学,2006,33(2):182-184.
[42].徐伟华,张文修.基于优势关系下不协调目标信息系统的分布约简[J].模糊系统与数学,2007,21(4):124-131.
[43].徐伟华,张晓燕,张文修.优势关系下不协调目标信息系统的下近似约简[J].计算机工程与应用,2009,45(16):66-68.
[44].徐伟华,张晓燕,张文修.优势关系下不协调目标信息系统的上近似约简[J].计算机工程,2009,35(18):191-193.
[45].袁修久,何华灿.优势关系下的相容约简和下近似约简[J].西北工业大学学报,2006, 24(5):604-608.
[46].袁修久,何华灿.优势关系下广义决策约简和上近似约简[J].计算机工程与应用, 2006,42(10):4-7.
[47].陈娟,王国胤,胡军.优势关系下不协调信息系统的正域约简[J].计算机科学,2008, 35(13):216-218.
[48]. Fortemps P, Greco S, S?owinski R. Multicriteria decision support using rules that represent rough-graded preference relations [J]. European Journal of Operational Research, 2008, 188: 206-223.
[49]. Yang X B, Yang J Y, Wu C et al. Dominance-based rough set approach and knowledge reduct in incomplete ordered information system [J]. Information Sciences, 2008, 178: 1219-1234.
[50]. Inuiguchi M, Yoshioka Y. Several reducts in dominance-based rough set approach. In: Huynh, V.-N., et al. (eds.): Interval/Probabilistic Uncertainty and Non-classical Logics [C], ASC46, 2008, pp. 163-175.
[51]. Kusunoki Y, Inuiguchi M. A comprehensive study on reducts in dominance-based rough setapproach. In: V. Torra and Y. Narukawa (Eds.): MDAI 2008, LNAI 5285 [C]. 2008, pp. 167-178.
[52]. Dembczynski K, Greco S, Kotlowski W et al. Quality of rough approximation in multi-criteria classification problems. In: Greco S et al (eds) RSCTC2006, LNCS (LNAI), vol 4259 [C]. Springer: Heidelberg, 2006, pp. 318-327.
[53]. Kusunoki K, Inuiguchi M. A unified approach to reducts in dominance-based rough set approach [J]. Soft Computing, 2010, 14 (5): 507-515.
[54]. Shao M W, Zhang W X. Dominance relation and rules in an incomplete ordered information system [J]. International Journal of Intelligent Systems, 2005, 20: 13-27.
[55].何亚群,胡寿松.不完全信息的多属性粗糙决策分析方法[J].系统工程学报,2004,19 (2):117-120.
[56].胡明礼,刘思峰.基于有限扩展优势关系的粗糙决策分析方法[J].系统工程,2006, 24(4):106-111.
[57].胡明礼,刘思峰.基于广义扩展优势关系的粗糙决策分析方法[J].控制与决策,2007, 22(12):1347-1351.
[58].骆公志,杨晓江,周德群.基于限制扩展优势关系的粗糙决策分析模型[J].系统管理学报,2009,18(4):391-396.
[59].谢军,宋余庆,陈健美等.不完备序值决策系统中的拓展粗集模型及集对分析[J].计算机科学,2008,35(12):154-157.
[60].杨习贝,杨静宇,吴小俊等.不完备系统中基于优势关系的最优可信规则获取[J].小型微型计算机系统,2009,30(3):518-523.
[61].管延勇,薛佩军,史开泉.基于描述子的信息系统属性约简及决策规则优化[J].控制与决策,2006,21(7):787-791.
[62].谢军,杨习贝,孙怀江等.序值决策系统中基于描述子的可信规则获取[J].系统工程理论与实践,2009,29(7):105-112.
[63].宋笑雪,解争龙,张文修.集值决策信息系统的知识约简与规则提取[J].计算机科学, 2007,34(4):182-191.
[64].宋笑雪,张文修.不协调集值决策信息系统的属性约简[J].计算机工程与应用,2009, 45(1):33-35.
[65]. Qian Y H, Dang C Y, Liang J Y et al. Set-valued ordered information systems [J]. Information Sciences, 2009, 179: 2809-2832.
[66].王珏,刘三阳,张杰.区间值属性决策表的数据挖掘[J].计算机科学,2003,30(8):121- 123.
[67]. Qian Y H , Liang J Y, Dang C Y. Interval ordered information systems [J]. Computers andMathematics with Applications, 2008, 56: 1994-2009.
[68]. Dembczynski K, Greco S, S?owinski R. Rough set approach to multiple criteria classification with imprecise evaluations and assignments [J]. European Journal of Operational Research, 2009, 198: 626-636.
[69]. Yang X B, Yu D J, Yang J T et al. Dominance-based rough set approach to incomplete interval-valued information system [J]. Data & Knowledge Engineering, 2009, 68(11): 1331-1347.
[70]. Hu Q H, Yu D R, Guo M Z. Fuzzy preference based rough sets [J]. Information Sciences, 2010, 180(10): 2003-2022.
[71]. Guan Y Y, Du L, Wang Y. Ordered-based decision rules acquisition in continuous-valued decision information systems. In: IEEE Proceedings of 2009 Sixth International Conference on Fuzzy System and Knowledge Discovery [C]. Tian Jin: 2009, pp.435-439.
[72]. Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets [J]. International Journal of General Systems, 1990, 17:191-208.
[73].袁修久,何华灿.优势关系下模糊目标信息系统约简的辨识矩阵[J].空军工程大学学报(自然科学版),2006,7(2):81-84.
[74].杜蕾,管延勇,杨芳.优势关系下模糊目标信息系统的决策规则优化[J].计算机工程与应用,2010,46(35):136-138.
[75].魏利华,唐振民,杨习贝等.不完备模糊系统的优势关系粗糙集与知识约简[J].计算机科学,2009,36(6):192-195.
[76].骆公志,杨习贝,杨晓江.基于限制优势关系的粗糙模糊集及知识约简[J].系统工程与电子技术,2010,32(8):1657-1661.
[77]. Greco S, Matarazzo B, Slowinski R et al. Variable consistency model of dominance-based rough set approach. In: W. Ziarko, Y. Yao (Eds.), Rough Sets and Current Trends in Computing, LNAI 2005 [C]. Berlin: Springer-Verlag, 2001, pp. 170-181.
[78]. B?aszczynski J, Greco S, S?owinski R et al. Monotonic variable consistency rough set approaches [J]. International Journal of Approximate Reasoning, 2009, 50: 979- 999.
[79]. Kot?owski W, Dembczynski K, Greco S et al. Stochastic dominance-based rough set model for ordinal classification [J]. Information Sciences, 2008, 178: 4019-4037.
[80]. Inuiguchi M, Yoshioka Y, Kusunoki Y. Variable-precision dominance-based rough set approach and attribute reduction [J]. International Journal of Approximate Reasoning, 2009, 50(8): 1199-1214.