Table Representations of Granulations Revisited

This paper examines the knowledge representation theory of granulations. The key strengths of rough set theory are its capabilities in representing and processing knowledge in table format. For general granulation such capabilities are unknown. For single level granulation, two initial theories have been proposed previously by one of the authors. In this paper, the theories are re-visited, a new and deeper analysis is presented: Granular information table is an incomplete representation, so computing with words is the main method of knowledge processing. However for symmetrical granulation, the pre-topological information table is a complete representation, so the knowledge processing can be formal.

[1]  Lior Rokach,et al.  Data Mining And Knowledge Discovery Handbook , 2005 .

[2]  Jiawei Han,et al.  Attribute-Oriented Induction in Relational Databases , 1991, Knowledge Discovery in Databases.

[3]  T. Y. Lin,et al.  Neighborhood systems and relational databases , 1988, CSC '88.

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

[5]  Kenneth P. Bogart,et al.  Introductory Combinatorics , 1977 .

[6]  Barr and Feigenbaum Edward A. Avron,et al.  The Handbook of Artificial Intelligence , 1981 .

[7]  Keith Price,et al.  Review of "The Handbook of Artificial Intelligence Vol. 1 by Avron Barr & Edward A. Feigenbaum", William Kaufmann, Inc. 1981 , 1982, SGAR.

[8]  Tsau Young Lin,et al.  Granular Computing: Fuzzy Logic and Rough Sets , 1999 .

[9]  Tsau Young Lin,et al.  Chinese Wall Security Policy Models: Information Flows and Confining Trojan Horses , 2003, DBSec.

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

[11]  T. T. Lee.  An algebraic theory of relational databases , 1983, The Bell System Technical Journal.

[12]  Janusz Kacprzyk,et al.  Computing with Words in Information/Intelligent Systems 1 , 1999 .

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

[14]  William Frawley,et al.  Knowledge Discovery in Databases , 1991 .

[15]  Tsau Young Lin,et al.  Data Mining and Machine Oriented Modeling: A Granular Computing Approach , 2000, Applied Intelligence.

[16]  Paul R. Cohen,et al.  Handbook of AI , 1986 .

[17]  Tsau Young Lin.  Generating Concept Hierarchies/Networks: Mining Additional Semantics in Relational Data , 2001, PAKDD.

[18]  Tsau Young Lin,et al.  Granular Computing on Binary Relations , 2002, Rough Sets and Current Trends in Computing.

[19]  E. Louie,et al.  Modeling the real world for data mining: granular computing approach , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[20]  G. Birkhoff,et al.  A survey of modern algebra , 1942 .

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

[22]  Garrett Birkhoff,et al.  A survey of modern algebra , 1942 .