基于决策表的多粒度粗糙集属性约简研究
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摘要
针对决策表,从三支决策理论的角度给出基于多粒度粗糙集(MGRS)的正域、负域、边界域的定义,并将其分别与Pawlak粗糙集的正域、负域、边界域进行比较;提出基于多粒度的保持正域不变、保持负域不变及保持边界域不变的约简的定义,并研究其性质。
On the basis of a decision table, MG-positive region, MG-negative region, MG-boundary region are defined from the perspective of three-way decisions, and compares them with positive region, negative region, boundary region of Pawlak rough set respectively. Then, three attribute reductions, which can preserve the MG-positive region, MG-negative region and MG-boundary region respectively are defined, and the properties of the attribute reductions have also been studied.
On the basis of a decision table, MG-positive region, MG-negative region, MG-boundary region are defined from the perspective of three-way decisions, and compares them with positive region, negative region, boundary region of Pawlak rough set respectively. Then, three attribute reductions, which can preserve the MG-positive region, MG-negative region and MG-boundary region respectively are defined, and the properties of the attribute reductions have also been studied.
引文
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[9] 魏玲.粗糙集与概念格约简理论与方法[D].西安:西安交通大学,2005.
[10] 钱进,吕萍,岳晓冬.决策粗糙集属性约简算法与属性核研究[J].计算机科学与探索,2014,8(3):345-351.
[11] 魏玲,祁建军,张文修.决策形式背景的概念格属性约简[J].中国科学E辑:信息科学,2008,38(2):195-208.
[12] 苗夺谦.Rough set理论及其在机器学习中的应用研究[D].北京:中国科学院自动化研究所,1997.
[13] YAO Y Y.An outline of a theory of three-way decisions[C]//Proceedings of RSCTC.Heidelberg:Springer,2012:1-17.
[14] YAO Y Y.Three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180:341-353.
[15] WANG G Y,ZHAO J,AN J J,et al.A comparative study of algebra viewpoint and information viewpoint in attribute reduction[J].Fundamenta Informaticae,2005,68(3):289-301.
[16] 赵思雨,魏玲.决策表的多种属性约简之间的关系研究[J].西北大学学报(自然科学版),2017,47(1):18-22.
[2] PAWLAK Z.Theoretical aspects of reasoning about data[M].Boston:Kluwer Academic Publishers,1991.
[3] PAWLAK Z,SKOWRON A.Rudiments of rough sets[J].Information Science,2007,177:3-27.
[4] ZADEH L A.Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic[J].Fuzzy Sets and Systems,1997,90:111-127.
[5] MA J M,ZHANG W X,LEUNG Y,et al.Granular computing and dual Galois connection[J].Information Sciences,2007,177:5365-5377.
[6] QIAN Y H,LIANG J Y,DANG C Y.Knowledge structure,knowledge granulation and knowledge distance in a knowledge base[J].International Journal of Approximate Reasoning,2009,50 (1):174-188.
[7] YAO Y Y.Granular computing basis issues and possible solutions[C]//Proceedings of the Fifth International Conference on Computing and Information.Washington D C:IEEE Computer Society,2000:186-189.
[8] QIAN Y H,LIANG J Y,YAO Y Y,et al.MGRS:a multigranulation rough set[J].Information Sciences,2010,180:949-970.
[9] 魏玲.粗糙集与概念格约简理论与方法[D].西安:西安交通大学,2005.
[10] 钱进,吕萍,岳晓冬.决策粗糙集属性约简算法与属性核研究[J].计算机科学与探索,2014,8(3):345-351.
[11] 魏玲,祁建军,张文修.决策形式背景的概念格属性约简[J].中国科学E辑:信息科学,2008,38(2):195-208.
[12] 苗夺谦.Rough set理论及其在机器学习中的应用研究[D].北京:中国科学院自动化研究所,1997.
[13] YAO Y Y.An outline of a theory of three-way decisions[C]//Proceedings of RSCTC.Heidelberg:Springer,2012:1-17.
[14] YAO Y Y.Three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180:341-353.
[15] WANG G Y,ZHAO J,AN J J,et al.A comparative study of algebra viewpoint and information viewpoint in attribute reduction[J].Fundamenta Informaticae,2005,68(3):289-301.
[16] 赵思雨,魏玲.决策表的多种属性约简之间的关系研究[J].西北大学学报(自然科学版),2017,47(1):18-22.