A MATHEMATICAL EXTENSION OF ROUGH SET-BASED ISSUES TOWARD UNCERTAIN INFORMATION ANALYSIS

Rough set theory was originally proposed for analyzing data gathered in data tables, often referred to as information systems. The lower and upper approximations introduced within this theory are known as the very useful concepts. The theory as a whole now becomes a recognized foundation for granular computing. This paper investigates the rough set-based issues for analyzing table data with uncertainty. In reality, tables with non-deterministic information are focused on instead of tables with deterministic information, and several mathematical properties are examined. Especially, decision rule generation from tables with non-deterministic information is highlighted. This investigation is also applied to tables with uncertain numerical data. As a result, a new mathematical framework for analyzing tables with uncertain information is formalized.

[1]  Hiroshi Sakai,et al.  Rough Sets Based Rule Generation from Data with Categorical and Numerical Values , 2008, J. Adv. Comput. Intell. Intell. Informatics.

[2]  Witold Lipski,et al.  On semantic issues connected with incomplete information databases , 1979, ACM Trans. Database Syst..

[3]  Vladik Kreinovich,et al.  Handbook of Granular Computing , 2008 .

[4]  Jerzy W. Grzymala-Busse,et al.  Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction , 2004, Trans. Rough Sets.

[5]  Hiroshi Sakai,et al.  An Application of Discernibility Functions to Generating Minimal Rules in Non-Deterministic Information Systems , 2006, J. Adv. Comput. Intell. Intell. Informatics.

[6]  J. Ross Quinlan,et al.  Improved Use of Continuous Attributes in C4.5 , 1996, J. Artif. Intell. Res..

[7]  Jerzy W. Grzymala-Busse,et al.  On the Best Search Method in the LEM1 and LEM2 Algorithms , 1998 .

[8]  Jing-Yu Yang,et al.  Dominance-based rough set approach to incomplete interval-valued information system , 2009, Data Knowl. Eng..

[9]  Piotr Synak,et al.  Brighthouse: an analytic data warehouse for ad-hoc queries , 2008, Proc. VLDB Endow..

[10]  Hiroshi Sakai,et al.  Possible Equivalence Relations and Their Application to Hypothesis Generation in Non-deterministic Information Systems , 2004, Trans. Rough Sets.

[11]  Ramakrishnan Srikant,et al.  Fast algorithms for mining association rules , 1998, VLDB 1998.

[12]  Hiroshi Sakai,et al.  Basic Algorithms and Tools for Rough Non-deterministic Information Analysis , 2004, Trans. Rough Sets.

[13]  Piotr Synak,et al.  Descriptors and Templates in Relational Information Systems , 2007, RSKT.

[14]  Dominik Slezak,et al.  Rough Sets and Functional Dependencies in Data: Foundations of Association Reducts , 2009, Trans. Comput. Sci..

[15]  Akira Nakamura,et al.  A rough logic based on incomplete information and its application , 1996, Int. J. Approx. Reason..

[16]  J. Grzymala-Busse,et al.  Three discretization methods for rule induction , 2001 .

[17]  Zdzisław Pawlak,et al.  Rough set theory and its applications , 2002, Journal of Telecommunications and Information Technology.

[18]  Ewa Orlowska,et al.  Introduction: What You Always Wanted to Know about Rough Sets , 1998 .

[19]  Jerzy W. Grzymala-Busse,et al.  A New Version of the Rule Induction System LERS , 1997, Fundam. Informaticae.

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

[21]  Chris Cornelis,et al.  Attribute selection with fuzzy decision reducts , 2010, Inf. Sci..

[22]  Hiroshi Sakai.  Effective Procedures for Handling Possible Equivalence Relations in Non-deterministic Information Systems , 2001, Fundam. Informaticae.

[23]  Yiyu Yao,et al.  Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions , 2003, ISMIS.

[24]  Hiroshi Sakai,et al.  Lower and Upper Approximations in Data Tables Containing Possibilistic Information , 2007, Trans. Rough Sets.

[25]  Jan G. Bazan,et al.  Rough set algorithms in classification problem , 2000 .

[26]  Manfred M. Fischer,et al.  A Rough Set Approach for the Discovery of Classification Rules in Interval-Valued Information Systems , 2008, Int. J. Approx. Reason..

[27]  Dominik Slezak,et al.  Data warehouse technology by infobright , 2009, SIGMOD Conference.

[28]  Ewa Orlowska,et al.  Representation of Nondeterministic Information , 1984, Theor. Comput. Sci..

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

[30]  Salvatore Greco,et al.  Multi-criteria classification - A new scheme for application of dominance-based decision rules , 2007, Eur. J. Oper. Res..

[31]  Witold Lipski,et al.  On Databases with Incomplete Information , 1981, JACM.

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

[33]  Dominik Slezak,et al.  Automatic Extraction of Decision Rules from Non-deterministic Data Systems: Theoretical Foundations and SQL-Based Implementation , 2009, FGIT-DTA.

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

[35]  Heikki Mannila,et al.  Fast Discovery of Association Rules , 1996, Advances in Knowledge Discovery and Data Mining.

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

[37]  Jerzy W. Grzymala-Busse,et al.  Global discretization of continuous attributes as preprocessing for machine learning , 1996, Int. J. Approx. Reason..

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

[39]  Shusaku Tsumoto,et al.  Knowledge discovery in clinical databases and evaluation of discovered knowledge in outpatient clinic , 2000, Inf. Sci..

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

[41]  Hiroshi Sakai,et al.  Rules and Apriori Algorithm in Non-deterministic Information Systems , 2006, Trans. Rough Sets.

[42]  John F. Roddick,et al.  Association mining , 2006, CSUR.

[43]  Zdzislaw Pawlak,et al.  Some Issues on Rough Sets , 2004, Trans. Rough Sets.

[44]  Masahiro Inuiguchi,et al.  Variable-precision dominance-based rough set approach and attribute reduction , 2009, Int. J. Approx. Reason..