Characteristic Relations for Incomplete Data: A Generalization of the Indiscernibility Relation

This paper shows that attribute-value pair blocks, used for many years in rule induction, may be used as well for computing indiscernibility relations for completely specified decision tables. Much more importantly, for incompletely specified decision tables, i.e., for data with missing attribute values, the same idea of attribute-value pair blocks is a convenient tool to compute characteristic sets, a generalization of equivalence classes of the indiscernibility relation, and also characteristic relations, a generalization of the indiscernibility relation. For incompletely specified decision tables there are three different ways lower and upper approximations may be defined: singleton, subset and concept. Finally, it is shown that, for a given incomplete data set, the set of all characteristic relations for the set of all congruent decision tables is a lattice.

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

[2]  Jerzy W. Grzymala-Busse,et al.  On the Unknown Attribute Values in Learning from Examples , 1991, ISMIS.

[3]  Zbigniew W. Ras,et al.  Methodologies for Intelligent Systems , 1991, Lecture Notes in Computer Science.

[4]  Jerzy W. Grzymala-Busse,et al.  LERS-A System for Learning from Examples Based on Rough Sets , 1992, Intelligent Decision Support.

[5]  Roman Słowiński,et al.  Intelligent Decision Support , 1992, Theory and Decision Library.

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

[7]  Yiyu Yao,et al.  Two views of the theory of rough sets in finite universes , 1996, Int. J. Approx. Reason..

[8]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

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

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

[11]  Andrzej Skowron,et al.  New Directions in Rough Sets, Data Mining, and Granular-Soft Computing , 1999, Lecture Notes in Computer Science.

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

[13]  Alexis Tsoukiàs,et al.  On the Extension of Rough Sets under Incomplete Information , 1999, RSFDGrC.

[14]  Georgios I. Doukidis,et al.  Decision making : recent developments and worldwide applications , 2000 .

[15]  Daniel Vanderpooten,et al.  A Generalized Definition of Rough Approximations Based on Similarity , 2000, IEEE Trans. Knowl. Data Eng..

[16]  Roman Słowiński,et al.  Dealing with Missing Data in Rough Set Analysis of Multi-Attribute and Multi-Criteria Decision Problems , 2000 .

[17]  Jerzy W. Grzymala-Busse,et al.  A Comparison of Several Approaches to Missing Attribute Values in Data Mining , 2000, Rough Sets and Current Trends in Computing.

[18]  Alexis Tsoukiàs,et al.  Incomplete Information Tables and Rough Classification , 2001, Comput. Intell..

[19]  Yiyu Yao,et al.  On Generalizing Rough Set Theory , 2003, RSFDGrC.

[20]  Jerzy W. Grzymala-Busse,et al.  Rough Set Strategies to Data with Missing Attribute Values , 2006, Foundations and Novel Approaches in Data Mining.