An Improved Axiomatic Definition of Information Granulation

To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. In this paper, we try to improve these axiomatic definitions and give a universal construction of information granulation by relating information granulations with a class of functions of multiple variables. We show that the improved axiomatic definition has some concrete information granulations in the literature as instances.

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

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

[3]  Yiyu,et al.  Notes on Rough Set Approximations and Associated Measures , 2010 .

[4]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[5]  Hung Son Nguyen,et al.  Approximate Boolean Reasoning: Foundations and Applications in Data Mining , 2006, Trans. Rough Sets.

[6]  Gianpiero Cattaneo,et al.  Information Entropy and Granulation Co-Entropy of Partitions and Coverings: A Summary , 2009, Trans. Rough Sets.

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

[8]  Ivo Düntsch,et al.  Uncertainty Measures of Rough Set Prediction , 1998, Artif. Intell..

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

[10]  Jerzy Stefanowski,et al.  Rough classification in incomplete information systems , 1989 .

[11]  Dominik Lzak.  Degrees of conditional (in)dependence: A framework for approximate Bayesian networks and examples related to the rough set-based feature selection , 2009 .

[12]  Jiye Liang,et al.  The Algorithm on Knowledge Reduction in Incomplete Information Systems , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[14]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[15]  Marzena Kryszkiewicz,et al.  Rough Set Approach to Incomplete Information Systems , 1998, Inf. Sci..

[16]  Sankar K. Pal,et al.  Granular computing, rough entropy and object extraction , 2005, Pattern Recognit. Lett..

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

[18]  Witold Lipski,et al.  On semantic issues connected with incomplete information databases , 1979, ACM Trans. Database Syst..

[19]  Dominik Slezak,et al.  Approximate Entropy Reducts , 2002, Fundam. Informaticae.

[20]  Andrzej Skowron,et al.  From the Rough Set Theory to the Evidence Theory , 1991 .

[21]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[22]  Zdzislaw Pawlak,et al.  Information systems theoretical foundations , 1981, Inf. Syst..

[23]  A. Kusiak.  Information Entropy , 2006 .

[24]  Qinghua Hu,et al.  Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation , 2007, Pattern Recognit..

[25]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[26]  Jiye Liang,et al.  Combination Entropy and Combination Granulation in Incomplete Information System , 2006, RSKT.

[27]  Huan Liu,et al.  Consistency-based search in feature selection , 2003, Artif. Intell..

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

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

[30]  Yiyu Yao,et al.  The Art of Granular Computing , 2007, RSEISP.

[31]  Qiaoyan Wen,et al.  Entropy and co-entropy of a covering approximation space , 2012, Int. J. Approx. Reason..

[32]  Dominik Slezak,et al.  Stable rule extraction and decision making in rough non-deterministic information analysis , 2011, Int. J. Hybrid Intell. Syst..

[33]  Hiroshi Sakai.  Effective Procedures for Handling Possible Equivalence Relations in Non-deterministic Information Systems , 2001, Fundam. Informaticae.

[34]  Yiyu Yao,et al.  User-centric query refinement and processing using granularity-based strategies , 2010, Knowledge and Information Systems.

[35]  Constantin Zopounidis,et al.  Prediction of company acquisition in Greece by means of the rough set approach , 1997, Eur. J. Oper. Res..

[36]  Lluís A. Belanche Muñoz,et al.  Feature selection algorithms: a survey and experimental evaluation , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[37]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[38]  Jiye Liang,et al.  Information granules and entropy theory in information systems , 2008, Science in China Series F: Information Sciences.

[39]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[40]  Jiye Liang,et al.  A New Method for Measuring the Uncertainty in Incomplete Information Systems , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..