On the evaluation of the decision performance of an incomplete decision table

As two classical measures, approximation accuracy and consistency degree can be extended for evaluating the decision performance of an incomplete decision table. However, when the values of these two measures are equal to zero, they cannot give elaborate depictions of the certainty and consistency of an incomplete decision table. To overcome this shortcoming, we first classify incomplete decision tables into three types according to their consistency and introduce four new measures for evaluating the decision performance of a decision-rule set extracted from an incomplete decision table. We then analyze how each of these four measures depends on the condition granulation and decision granulation of each of the three types of incomplete decision tables. Experimental analyses on three practical data sets show that the four new measures appear to be well suited for evaluating the decision performance of a decision-rule set extracted from an incomplete decision table and are much better than the two extended measures.

[1]  Witold Pedrycz,et al.  Presenting the special issue on Rough-neuro computing : Preface , 2001, Neurocomputing.

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

[3]  Rafal Latkowski,et al.  Data Decomposition and Decision Rule Joining for Classification of Data with Missing Values , 2004, Trans. Rough Sets.

[4]  Bart Baesens,et al.  A new approach for measuring rule set consistency , 2007, Data Knowl. Eng..

[5]  Liang,et al.  Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems , 2001 .

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

[7]  金田 重郎,et al.  C4.5: Programs for Machine Learning (書評) , 1995 .

[8]  Liang Jiye,et al.  Uncertainty measures of roughness of knowledge and rough sets in incomplete information systems , 2000, Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No.00EX393).

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

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

[11]  Jerzy W. Grzymala-Busse,et al.  Rough sets : New horizons in commercial and industrial AI , 1995 .

[12]  Jerzy W. Grzymala-Busse,et al.  An Experimental Comparison of Three Rough Set Approaches to Missing Attribute Values , 2007, Trans. Rough Sets.

[13]  DEYU LI,et al.  On Knowledge Reduction In Inconsistent Decision Information Systems , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[15]  Jerzy W. Grzymala-Busse,et al.  The Rule Induction System LERS-a version for personal computers in Foun-dations of Computing and Dec , 1993 .

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

[17]  James F. Peters,et al.  Rough Set Approach to Pattern Extraction from Classifiers , 2003, RSKD.

[18]  Yanyong Guan,et al.  Set-valued information systems , 2006, Inf. Sci..

[19]  Thomas G. Dietterich,et al.  Readings in Machine Learning , 1991 .

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

[21]  Rafal Latkowski.  On Decomposition for Incomplete Data , 2003, Fundam. Informaticae.

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

[23]  William W. Cohen.  Fast Effective Rule Induction , 1995, ICML.

[24]  Zdzislaw Pawlak,et al.  Probability, Truth and Flow Graph , 2003, RSKD.

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

[26]  Peter Clark,et al.  The CN2 Induction Algorithm , 1989, Machine Learning.

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

[28]  Yee Leung,et al.  Maximal consistent block technique for rule acquisition in incomplete information systems , 2003, Inf. Sci..

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

[30]  Zdzisław Pawlak,et al.  Can Bayesian confirmation measures be useful for rough set decision rules? , 2004, Eng. Appl. Artif. Intell..

[31]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

[32]  Rafal Latkowski,et al.  Flexible Indiscernibility Relations for Missing Attribute Values , 2005, Fundam. Informaticae.

[33]  Jiye Liang,et al.  Converse approximation and rule extraction from decision tables in rough set theory , 2008, Comput. Math. Appl..

[34]  Jerzy W. Grzymala-Busse,et al.  Characteristic Relations for Incomplete Data: A Generalization of the Indiscernibility Relation , 2005, Trans. Rough Sets.

[35]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

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

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

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

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

[40]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

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

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

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

[44]  Marzena Kryszkiewicz,et al.  Rules in Incomplete Information Systems , 1999, Inf. Sci..

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

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

[47]  Mi Ju,et al.  Comparative Studies of Knowledge Reductions in Inconsistent Systems , 2003 .

[48]  Zdzislaw Pawlak,et al.  Some remarks on conflict analysis , 2005, Eur. J. Oper. Res..

[49]  Ivan Bratko,et al.  Experiments in automatic learning of medical diagnostic rules , 1984 .

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

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

[52]  Roman Slowinski,et al.  Rough-Set Reasoning about Uncertain Data , 1996, Fundam. Informaticae.

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

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

[55]  Zheng Pei,et al.  Interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference , 2006, Inf. Sci..