Notes on Rough Set Approximations and Associated Measures

We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.

[1]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[2]  Ping Zhu.  An Improved Axiomatic Definition of Information Granulation , 2012, Fundam. Informaticae.

[3]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[4]  Yee Leung,et al.  Knowledge acquisition in incomplete information systems: A rough set approach , 2006, Eur. J. Oper. Res..

[5]  Yiyu Yao,et al.  Three-way decisions with probabilistic rough sets , 2010, Inf. Sci..

[6]  Jiye Liang,et al.  Combination Entropy and Combination Granulation in Rough Set Theory , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  Fan Shi-dong.  The Calculation of Knowledge Granulation and Its Application , 2002 .

[8]  Theresa Beaubouef,et al.  Information-Theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases , 1998, Inf. Sci..

[9]  Zdzisław Pawlak,et al.  Algorithm for inductive learning , 1986 .

[10]  Van-Nam Huynh,et al.  A roughness measure for fuzzy sets , 2005, Inf. Sci..

[11]  Jiye Liang,et al.  Axiomatic Approach of Knowledge Granulation in Information System , 2006, Australian Conference on Artificial Intelligence.

[12]  Ping Zhu,et al.  An Axiomatic Approach to the Roughness Measure of Rough Sets , 2009, Fundam. Informaticae.

[13]  Qiang Yang,et al.  Axiomatic Definition of Knowledge Granularity and Its Constructive Method , 2008, RSKT.

[14]  J. Ross Quinlan,et al.  Learning Efficient Classification Procedures and Their Application to Chess End Games , 1983 .

[15]  Ivo Diintsch.  Uncertainty measures of rough set prediction , 2003 .

[16]  M. J. Wierman,et al.  MEASURING UNCERTAINTY IN ROUGH SET THEORY , 1999 .

[17]  E. Bryniarski.  A calculus of rough sets of the first order , 1989 .

[18]  Wen-Xiu Zhang,et al.  Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems , 2009, Appl. Soft Comput..

[19]  Tao Feng,et al.  Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets , 2007, RSFDGrC.

[20]  S. K. Michael Wong,et al.  Rough Sets: Probabilistic versus Deterministic Approach , 1988, Int. J. Man Mach. Stud..

[21]  Jie Zhou,et al.  A novel measure of knowledge granularity in rough sets , 2010, Int. J. Granul. Comput. Rough Sets Intell. Syst..

[22]  Ivo Düntsch,et al.  Rough approximation quality revisited , 2001, Artif. Intell..

[23]  Yiyu Yao,et al.  A Partition Model of Granular Computing , 2004, Trans. Rough Sets.

[24]  YaoYiyu.  Three-way decisions with probabilistic rough sets , 2010 .

[25]  Yuming Zhou,et al.  An improved accuracy measure for rough sets , 2005, J. Comput. Syst. Sci..

[26]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[27]  Jiye Liang,et al.  Information entropy, rough entropy and knowledge granulation in incomplete information systems , 2006, Int. J. Gen. Syst..

[28]  Jiye Liang,et al.  A new method for measuring uncertainty and fuzziness in rough set theory , 2002, Int. J. Gen. Syst..

[29]  Yiyu Yao,et al.  Probabilistic approaches to rough sets , 2003, Expert Syst. J. Knowl. Eng..

[30]  Jiye Liang,et al.  The Information Entropy, Rough Entropy And Knowledge Granulation In Rough Set Theory , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[31]  Y. Yao.  Information granulation and rough set approximation , 2001 .

[32]  Jerzy W. Grzymala-Busse,et al.  Knowledge acquisition under uncertainty — a rough set approach , 1988, J. Intell. Robotic Syst..

[33]  Jiye Liang,et al.  Knowledge structure, knowledge granulation and knowledge distance in a knowledge base , 2009, Int. J. Approx. Reason..

[34]  Jiye Liang,et al.  A new measure of uncertainty based on knowledge granulation for rough sets , 2009, Inf. Sci..