Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems

In this paper, concepts of knowledge granulation, knowledge entropy and knowledge uncertainty measure are given in ordered information systems, and some important properties of them are investigated. From these properties, it can be shown that these measures provides important approaches to measuring the discernibility ability of different knowledge in ordered information systems. And relationship between knowledge granulation, knowledge entropy and knowledge uncertainty measure are considered. As an application of knowledge granulation, we introduce definition of rough entropy of rough sets in ordered information systems. By an example, it is shown that the rough entropy of rough sets is more accurate than classical rough degree to measure the roughness of rough sets in ordered information systems. 2009 Elsevier B.V. All rights reserved. * Corresponding author. E-mail addresses: datongxuweihua@126.com (X. Wei-hua), zxy19790915@163.com (Z. Xiao-yan), wxzhang@mail.xjtu.edu.cn (Z. Wen-xiu).

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

[2]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[3]  Roman Słowiński,et al.  A New Rough Set Approach to Evaluation of Bankruptcy Risk , 1998 .

[4]  Ming-Wen Shao,et al.  Knowledge Reduction Based on Evidence Reasoning Theory in Ordered Information Systems , 2006, KSEM.

[5]  K. Thangavel,et al.  Dimensionality reduction based on rough set theory: A review , 2009, Appl. Soft Comput..

[6]  Roman Słowiński,et al.  Generation of reducts and rules in multi-attribute and multi-criteria classification , 2000 .

[7]  Wen-Xiu Zhang,et al.  Measuring roughness of generalized rough sets induced by a covering , 2007, Fuzzy Sets Syst..

[8]  Y. Yao.  Granular Computing : basic issues and possible solutions , 2000 .

[9]  Salvatore Greco,et al.  Rough approximation of a preference relation by dominance relations , 1999, Eur. J. Oper. Res..

[10]  Salvatore Greco,et al.  Rough sets methodology for sorting problems in presence of multiple attributes and criteria , 2002, Eur. J. Oper. Res..

[11]  Wei-Zhi Wu,et al.  Knowledge reduction in random information systems via Dempster-Shafer theory of evidence , 2005, Inf. Sci..

[12]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[13]  Salvatore Greco,et al.  Dominance-Based Rough Set Approach as a Proper Way of Handling Graduality in Rough Set Theory , 2007, Trans. Rough Sets.

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

[15]  Robert Susmaga,et al.  Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach , 2003, RSKD.

[16]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

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

[18]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[19]  Yee Leung,et al.  Connections between rough set theory and Dempster-Shafer theory of evidence , 2002, Int. J. Gen. Syst..

[20]  C. Zopounidis.  Operational tools in the management of financial risks , 1997 .

[21]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

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

[23]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[24]  Qinghua Hu,et al.  Uncertainty measures for fuzzy relations and their applications , 2007, Appl. Soft Comput..

[25]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[26]  Jiye Liang,et al.  Measures for evaluating the decision performance of a decision table in rough set theory , 2008, Inf. Sci..

[27]  George J. Klir,et al.  Basic issues of computing with granular probabilities , 1998 .

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

[29]  Salvatore Greco,et al.  A New Rough Set Approach to Multicriteria and Multiattribute Classification , 1998, Rough Sets and Current Trends in Computing.

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

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

[32]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

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

[34]  Robert Susmaga,et al.  Dominance-based Rough Set Classifier without Induction of Decision Rules , 2003, RSKD.