串行概率粗糙集近似
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摘要
经典的概率粗糙集模型是基于等价关系和条件概率提出的。但在实际应用中,知识库存在多种不确定性因素,使得对象间的关系未必满足等价关系。因此在保证条件概率有意义的情况下,将等价关系推广到串行二元关系,讨论了串行关系下的概率粗糙集近似;研究了当目标概念发生变化时,串行概率粗糙下、上近似的性质;进一步,通过调整两个阈值,给出了对应的串行概率粗糙下、上近似的变化趋势。
The classical probabilistic rough set model was proposed based on an equivalence relation and a conditional probability.However,uncertainty in knowledge base makes it difficult to satisfy the equivalence relation between any two objects.This paper considered the serial binary relation instead of an equivalence relation,making the conditional probability meaningful.Then the serial probabilistic rough set approximations were introduced based on a serial relation.Properties of the serial probabilistic rough lower and upper approximations were discussed when the target concepts are variable.Furthermore,by adjusting the two thresholds,the corresponding serial probabilistic rough lower and upper approximations were also investigated.
The classical probabilistic rough set model was proposed based on an equivalence relation and a conditional probability.However,uncertainty in knowledge base makes it difficult to satisfy the equivalence relation between any two objects.This paper considered the serial binary relation instead of an equivalence relation,making the conditional probability meaningful.Then the serial probabilistic rough set approximations were introduced based on a serial relation.Properties of the serial probabilistic rough lower and upper approximations were discussed when the target concepts are variable.Furthermore,by adjusting the two thresholds,the corresponding serial probabilistic rough lower and upper approximations were also investigated.
引文
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[3]Chan C C.A rough set approach to attribute generalization in data mining[J].Information Sciences,1998,107(1-4):169-176.
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[8]YAO Y Y.Relational Interpretations of Neighborhood Operators and Rough Set Approximation Operators[J].Information Sciences,1998,111(1-4):239-259.
[9]GRECO S,MATARAZZO B,SLOWINSKI R.Rough Approximation of a Preference Relation by Dominance Relations[J].European Journal of Operational Research,1999,117(1):63-83.
[10]ZHU W.Generalized Rough Sets based on Relations[J].Information Sciences,2007,177(22):4997-5011.
[11]PEI Z,PEI D W,ZHENG L.Topology vs Generalized Rough Sets[J].International Journal of Approximate Reasoning,2011,52(2):231-239.
[12]PAWLAK Z,WONG S K M,ZIARKO W.Rough Sets:Probabilistic Versus Deterministic Approach[J].International Journal of Man-Machine Studies,1988,29(1):81-95.
[13]YAO Y Y,WONG S K M.A Decision Theoretic Framework for Approximating Concepts[J].International Journal of Man-Machine Studies,1992,37(6):793-809.
[14]ZIARKO W.Variable Precision Rough Set Model[J].Journal of Computer and System Science,1993,46(1):39-59.
[15]YAO Y Y.Probabilistic Rough Set Approximations[J].International Journal of Approximate Reasoning,2008,49(2):255-271.
[16]张文修,吴伟志,梁吉业,等.粗糙集理论与方法[M].北京:科学出版社,2001.
[17]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.
[18]于洪.三支决策:复杂问题求解方法与实践[M].北京:科学出版社,2015.
[19]YAO Y Y,LIN T Y.Generalization of rough sets using modal logic[J].Intelligent Automation and Soft Computing,1996,2(2):103-120.
[20]朱成熹.近世实分析基础[M].天津:南开大学出版社,1993.
[21]匡继昌.实分析与泛函分析[M].北京:高等教育出版社,2002.
[22]薛昌兴.实变函数与泛函分析[M].北京:高等教育出版社,1997.
[23]GONG Z T,SUN B Z,SHAO Y B,et al.The Variable Precision Rough Set Model based on the General Relationship[J].Journal of Lanzhou University,2005,4(6):110-114.(in Chinese)巩曾泰,孙秉珍,邵亚斌,等.一般关系下的变精度粗糙集模型[J].兰州大学学报(自科版),2005,4(6):110-114.
[2]PAWLAK Z.Rough Sets:Theoretical Aspects of Reasoning About Data[M].Boston:Kluwer Academic Publishers,1991.
[3]Chan C C.A rough set approach to attribute generalization in data mining[J].Information Sciences,1998,107(1-4):169-176.
[4]HU X.Knowledge discovery in database:an attribute-oriented rough set approach[D].Canada:University of Regina,1995.
[5]SKOWRON A,STEPANIUK J.Tolerance Approximation Spaces[J].Fundamenta Information,1996,27(2/3):245-253.
[6]YAO Y Y.Two Views of the Theory of Rough Sets in Finite Universes[J].International Journal of Approximate Reasoning,1996,15(4):291-318.
[7]YAO Y Y.Constructive and Algebraic Methods of the Theory of Rough Set[J].Information Sciences,1998,109(1-4):21-47.
[8]YAO Y Y.Relational Interpretations of Neighborhood Operators and Rough Set Approximation Operators[J].Information Sciences,1998,111(1-4):239-259.
[9]GRECO S,MATARAZZO B,SLOWINSKI R.Rough Approximation of a Preference Relation by Dominance Relations[J].European Journal of Operational Research,1999,117(1):63-83.
[10]ZHU W.Generalized Rough Sets based on Relations[J].Information Sciences,2007,177(22):4997-5011.
[11]PEI Z,PEI D W,ZHENG L.Topology vs Generalized Rough Sets[J].International Journal of Approximate Reasoning,2011,52(2):231-239.
[12]PAWLAK Z,WONG S K M,ZIARKO W.Rough Sets:Probabilistic Versus Deterministic Approach[J].International Journal of Man-Machine Studies,1988,29(1):81-95.
[13]YAO Y Y,WONG S K M.A Decision Theoretic Framework for Approximating Concepts[J].International Journal of Man-Machine Studies,1992,37(6):793-809.
[14]ZIARKO W.Variable Precision Rough Set Model[J].Journal of Computer and System Science,1993,46(1):39-59.
[15]YAO Y Y.Probabilistic Rough Set Approximations[J].International Journal of Approximate Reasoning,2008,49(2):255-271.
[16]张文修,吴伟志,梁吉业,等.粗糙集理论与方法[M].北京:科学出版社,2001.
[17]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.
[18]于洪.三支决策:复杂问题求解方法与实践[M].北京:科学出版社,2015.
[19]YAO Y Y,LIN T Y.Generalization of rough sets using modal logic[J].Intelligent Automation and Soft Computing,1996,2(2):103-120.
[20]朱成熹.近世实分析基础[M].天津:南开大学出版社,1993.
[21]匡继昌.实分析与泛函分析[M].北京:高等教育出版社,2002.
[22]薛昌兴.实变函数与泛函分析[M].北京:高等教育出版社,1997.
[23]GONG Z T,SUN B Z,SHAO Y B,et al.The Variable Precision Rough Set Model based on the General Relationship[J].Journal of Lanzhou University,2005,4(6):110-114.(in Chinese)巩曾泰,孙秉珍,邵亚斌,等.一般关系下的变精度粗糙集模型[J].兰州大学学报(自科版),2005,4(6):110-114.