Knowledge reduction in random information systems via Dempster-Shafer theory of evidence

Knowledge reduction is one of the main problems in the study of rough set theory. This paper deals with knowledge reduction in (random) information systems based on Dempster-Shafer theory of evidence. The concepts of belief and plausibility reducts in (random) information systems are first introduced. It is proved that both of belief reduct and plausibility reduct are equivalent to classical reduct in (random) information systems. The relative belief and plausibility reducts in consistent and inconsistent (random) decision systems are then proposed and compared to the relative reduct and relationships between the new reducts and some existing ones are examined.

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

[2]  Zdzislaw Pawlak,et al.  Rough Set Theory and its Applications to Data Analysis , 1998, Cybern. Syst..

[3]  Tsau Young Lin,et al.  Rough Set Methods and Applications , 2000 .

[4]  Jan G. Bazan.  Chapter 17 a Comparison of Dynamic and Non{dynamic Rough Set Methods for Extracting Laws from Decision Tables , 1998 .

[5]  R. Słowiński.  Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory , 1992 .

[6]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

[7]  Malcolm J. Beynon,et al.  Reducts within the variable precision rough sets model: A further investigation , 2001, Eur. J. Oper. Res..

[8]  Mohamed Quafafou,et al.  alpha-RST: a generalization of rough set theory , 2000, Inf. Sci..

[9]  Jerzy Stefanowski,et al.  On rough set based approaches to induction of decision rules , 1998 .

[11]  Dominik Slezak,et al.  Approximate Reducts and Association Rules - Correspondence and Complexity Results , 1999, RSFDGrC.

[12]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[13]  S. Tsumoto,et al.  Rough set methods and applications: new developments in knowledge discovery in information systems , 2000 .

[14]  Marzena Kryszkiewicz.  Comparative study of alternative types of knowledge reduction in inconsistent systems , 2001, Int. J. Intell. Syst..

[15]  Jerzy W. Grzymala-Busse,et al.  Classification Strategies Using Certain and Possible Rules , 1998, Rough Sets and Current Trends in Computing.

[16]  Yiyu Yao,et al.  Interpretation of Belief Functions in The Theory of Rough Sets , 1998, Inf. Sci..

[17]  Andrzej Skowron,et al.  Rough-Fuzzy Hybridization: A New Trend in Decision Making , 1999 .

[18]  T. Y. Lin,et al.  Rough Sets and Data Mining , 1997, Springer US.

[19]  Wojciech Ziarko,et al.  Variable Precision Rough Set Model , 1993, J. Comput. Syst. Sci..

[20]  Wojciech Ziarko,et al.  Variable Precision Rough Sets with Asymmetric Bounds , 1993, RSKD.

[21]  C. J. V. Rijsbergen,et al.  Rough Sets, Fuzzy Sets and Knowledge Discovery , 1994, Workshops in Computing.

[22]  Andrzej Skowron,et al.  Rough Sets: A Tutorial , 1998 .

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

[24]  Wei-Zhi Wu,et al.  Approaches to knowledge reduction based on variable precision rough set model , 2004, Inf. Sci..

[25]  Lech Polkowski,et al.  Rough Sets in Knowledge Discovery 2 , 1998 .

[26]  Wei-Zhi Wu,et al.  Approaches to knowledge reductions in inconsistent systems , 2003, Int. J. Intell. Syst..

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

[28]  Dominik Slezak,et al.  Approximate Reducts in Decision Tables , 1996 .

[29]  Andrzej Skowron,et al.  The Discernibility Matrices and Functions in Information Systems , 1992, Intelligent Decision Support.