A note on rough set and non-measurable set 被引量：1

A note on rough set and non-measurable set

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摘要 It is proved that rough set is equivalent to non-measurable set in measure theory. Hence, rough set is not a new concept in some sense. At the same time, we defined the measurable degree of a set by inner measure and outer measure. Its special case is the accuracy measure of rough set. It is proved that rough set is equivalent to non-measurable set in measure theory. Hence, rough set is not a new concept in some sense. At the same time, we defined the measurable degree of a set by inner measure and outer measure. Its special case is the accuracy measure of rough set.

作者 Jian Yu Qiansheng Cheng

机构地区 Peking Univ

出处《Chinese Science Bulletin》 SCIE EI CAS 2000年第16期1456-1458,共3页

关键词 ROUGH SET non-measurable SET INNER MEASURE outer measure. rough set non-measurable set inner measure outer measure

分类号 O159 [理学—基础数学]

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参考文献7

1Zdzis?aw Pawlak.Rough sets[J].International Journal of Computer & Information Sciences.1982(5)
2Pawlak Z.Rough sets[].International Journal of Computer and Information Sciences.1982
3Pawlak,Z.,Slowinski,K.,Slowinski,R.Rough classification of patients after highly selective vagotomy for duodenal ulcer[].International Journal of Man Machine Studies.1986
4TY Lin,N Cercone.Rough sets and data mining[]..1997
5Cohn D L.Measure Theory[]..1980
6Mrzek,A.Use ot Rough Sets and Decision Tables for Implementing Rule-based Control of Industrial Processes,Bull.Polish Acad[].Science and Technology.1986
7Pawlak,Z.Rough Sets[]..1991

同被引文献6

1PAWLAK Z.Rough sets[J].International J of Computer and Information Sciences,1982,11(5):341-356.
2PAWLAK Z.Rough sets,algebraic and topological approach[J].ICS PAS Reports,1982.
3IWINSKI T B.Algebraic approach to rough sets[J].Bulletin of the Polish Academy of Science Mathematic,1987,35(4):673-683
4HANNU S,HANNU N.A note on rough sets and common knowledge events[J].European J of Operation Research,1999,112:692-695.
5VAN-NAM H.YOSHITERU N.A roughness measure for fuzzy sets[J].Information Science,2005,173:255-275.
6YAO Y Y,LINGRAS P.Interpretations of belief functions in the theory of rough sets[J].Information Science,1998,104:81-106.

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1Hang YU.Controllability of the Heat Equation with a Control Acting on a Measurable Set[J].Chinese Annals of Mathematics,Series B,2012,33(1):149-160.
2钱涛.THE PRESERVATION OF THE LIPSCHITZ SPACES UNDER SEVERAL MAXIMAL OPERATORS[J].Chinese Science Bulletin,1984,29(4):443-447.
3Jitao Wang.Modern thermodynamics-New concepts based on the second law of thermodynamics[J].Progress in Natural Science:Materials International,2009,19(1):125-135. 被引量：2
4Yun-zhang LI,Chun-hua HAN.Supports of Fourier Transforms of Refinable Frame Functions and Their Applications to FMRA[J].Acta Mathematicae Applicatae Sinica,2012,28(4):757-768.
5Jin-cheng XIONG,Feng TAN,Jie Lü.Dependent sets of a family of relations of full measure on a probability space[J].Science China Mathematics,2007,50(4):475-484. 被引量：1
6熊金城,陈二才.Chaos caused by a strong-mixing measure-preserving transformation[J].Science China Mathematics,1997,40(3):253-260. 被引量：1
7欧阳华江.CRITERIA FOR FINITE ELEMENT ALGORITHM OF GENERALIZED HEAT CONDUCTION EQUATION[J].Applied Mathematics and Mechanics(English Edition),1992,13(6):587-596.
8刘蓉滨,李西和.Conditional Expectation Depending on a Parameter And Strong Holomorphic Conditional Probability[J].Chinese Quarterly Journal of Mathematics,1993,8(1):50-54.
9褚仁华,张文武.从勒贝革积分理论的建立和发展看函数黎曼可积条件的推广[J].内燃机与动力装置,2009,26(B06):70-72.
10鹿晓阳,许焕然,刘玉文.ON THE TWO NEW CONCEPTS OF WILSON NONCONFORMING ELEMENT[J].Chinese Science Bulletin,1988,33(22):1894-1895.

Chinese Science Bulletin

2000年第16期

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A note on rough set and non-measurable set 被引量：1

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