Pawlak’s Many Valued Information System, Non-deterministic Information System, and a Proposal of New Topics on Information Incompleteness Toward the Actual Application

This chapter considers Pawlak’s Many Valued Information System (MVIS), Non-deterministic Information System (NIS), and related new topics on information incompleteness toward the actual application. Pawlak proposed rough sets, which were originally defined in a standard table, however his research in non-standard tables like MVIS and NIS is also seen. Since rough sets have been known to many researchers deeply and several software tools have been proposed until now, it will be necessary to advance from this research on a standard table to research on MVIS and NIS, especially in regards to NIS. In this chapter, previous research is surveyed and new topics toward the actual application of NIS are proposed, namely data mining under various types of uncertainty, rough set-based estimation of an actual value, machine learning by rule generation, information dilution, and an application to privacy-preserving questionnaire, in NIS. Such new topics will further extend the role of Pawlak’s rough sets.

[1]  Yiyu Yao,et al.  Three-way decisions with probabilistic rough sets , 2010, Inf. Sci..

[2]  Saul A. Kripke,et al.  Semantical Considerations on Modal Logic , 2012 .

[3]  Hiroshi Sakai,et al.  Rough Set-Based Information Dilution by Non-deterministic Information , 2013, RSFDGrC.

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

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

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

[7]  Jerzy W. Grzymala-Busse,et al.  A Local Version of the MLEM2 Algorithm for Rule Induction , 2010, Fundam. Informaticae.

[8]  Chenxi Liu,et al.  A Consideration on Learning by Rule Generation from Tables with Missing Values , 2015, 2015 IIAI 4th International Congress on Advanced Applied Informatics.

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

[10]  Hiroshi Sakai,et al.  Applying Rough Sets to Information Tables Containing Possibilistic Values , 2008, Trans. Comput. Sci..

[11]  William Zhu,et al.  Topological approaches to covering rough sets , 2007, Inf. Sci..

[12]  J. Aldrich.  R.A. Fisher and the making of maximum likelihood 1912-1922 , 1997 .

[13]  Shusaku Tsumoto,et al.  Automated extraction of hierarchical decision rules from clinical databases using rough set model , 2003, Expert Syst. Appl..

[14]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

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

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

[17]  Tsau Young Lin,et al.  Introducing the book , 2000 .

[18]  Hiroshi Sakai,et al.  Twofold rough approximations under incomplete information , 2013, Int. J. Gen. Syst..

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

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

[21]  Yiyu Yao,et al.  A Note on Definability and Approximations , 2007, Trans. Rough Sets.

[22]  Makoto Yokoo,et al.  Constraint Satisfaction Problem , 2001 .

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

[24]  Shusaku Tsumoto,et al.  A proposal of a privacy-preserving questionnaire by non-deterministic information and its analysis , 2016, 2016 IEEE International Conference on Big Data (Big Data).

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

[26]  Ramakrishnan Srikant,et al.  Fast Algorithms for Mining Association Rules in Large Databases , 1994, VLDB.

[27]  Yiyu Yao,et al.  Rough set models in multigranulation spaces , 2016, Inf. Sci..

[28]  Hiroshi Sakai,et al.  Apriori-Based Rule Generation in Incomplete Information Databases and Non-Deterministic Information Systems , 2014, Fundam. Informaticae.

[29]  Yiyu Yao,et al.  MGRS: A multi-granulation rough set , 2010, Inf. Sci..

[30]  Hiroshi Sakai,et al.  Non-deterministic Information in Rough Sets: A Survey and Perspective , 2013, RSKT.

[31]  Salvatore Greco,et al.  A Summary and Update of “Granular Computing and Data Mining for Ordered Data: The Dominance-Based Rough Set Approach” , 2010, 2010 IEEE International Conference on Granular Computing.

[32]  Hiroshi Sakai,et al.  The Completeness of NIS-Apriori Algorithm and a Software Tool GetRNIA , 2014, 2014 IIAI 3rd International Conference on Advanced Applied Informatics.

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

[34]  Philip S. Yu,et al.  A General Survey of Privacy-Preserving Data Mining Models and Algorithms , 2008, Privacy-Preserving Data Mining.

[35]  Victor W. Marek,et al.  Information Storage and Retrieval Systems: Mathematical Foundations , 1976, Theor. Comput. Sci..

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

[37]  Zdzislaw Pawlak,et al.  Information systems theoretical foundations , 1981, Inf. Syst..

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

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

[40]  Davide Ciucci,et al.  Generalized rough approximations in PI 1/2 , 2008, Int. J. Approx. Reason..

[41]  Zdzisław Pawlak,et al.  Systemy Informacyjne. Podstawy Teoretyczne , 1983 .

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

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

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

[45]  A. Asuncion,et al.  UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences , 2007 .

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

[47]  Yiyu Yao,et al.  The two sides of the theory of rough sets , 2015, Knowl. Based Syst..