81
Views
36
CrossRef citations to date
0
Altmetric
Articles

Twofold rough approximations under incomplete information

&
Pages 546-571 | Received 10 Mar 2011, Accepted 18 Feb 2013, Published online: 20 May 2013

References

  • Abiteboul , S. , Hull , R. and Vianu , V. 1995 . Foundations of Databases , New York : Addison-Wesley .
  • ANSI/X3/SPARC Studying Group on Data Base Management Systems. 1975. Interim Report. ACM FDT(Sigmod Records), 7(2).
  • Bell , D. A. , Guan , J. W. and Lee , S. K. 1996 . Generalized Union and Project Operations for Pooling Uncertain and Imprecise Information . Data & Knowledge Engineering , 18 ( 2 ) : 89 – 117 .
  • Bosc , P. , Duval , L. and Pivert , O. 2003 . An Initial Approach to the Evaluation of Possibilistic Queries Addressed to Possibilistic Databases . Fuzzy Sets and Systems , 140 ( 1 ) : 151 – 166 .
  • Couso , I. and Dubois , F. 2011 . Rough Sets, Coverings and Incomplete Information . Fundamenta Informaticae , 108 ( 3–4 ) : 223 – 347 .
  • Ganter , B. and Kuznetsov , S. O. 2008 . Scale Coarsening as Feature Selection . Lecture Notes in Artificial Intelligence , 4933 : 217 – 228 .
  • Grahne, G. 1991. “The Problem of Incomplete Information in Relational Databases.” Lecture Notes in Computer Science 554.
  • Greco , S. , Matarazzo , B. and Slowinski , R. 1999 . Handling Missing Values in Rough Set Analysis of Multi-attribute and Multi-criteria Decision Problem . Lecture Notes in Artificial Intelligence , 1711 : 146 – 157 .
  • Greco , S. , Matarazzo , B. and Slowinski , R. 2001 . Rough Sets Theory for Multicriteria Decision Analysis . European Journal of Operational Research , 129 ( 1 ) : 1 – 47 .
  • Grzymala-Busse , J. W. 2004 . Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction . Transactions on Rough Sets , I : 78 – 95 .
  • Grzymala-Busse , J. W. 2010 . Mining Numerical Data – A Rough Set Approach . Transactions on Rough Sets , XI : 1 – 13 .
  • Guan , Y-Y and Wang , H-K . 2006 . Set-valued Information Systems . Information Sciences , 176 ( 17 ) : 2507 – 2525 .
  • Imielinski , T. 1989 . Incomplete Information in Logical Databases . Data Engineering , 12 : 93 – 104 .
  • Imielinski , T. and Lipski , W. 1984 . Incomplete Information in Relational Databases . Journal of the Association for Computing Machinery , 31 ( 4 ) : 761 – 791 .
  • Kaytoue , M. , Kuznetsov , S. O. , Napoli , A. and Duplessis , S. 2011 . Mining gene expression data with pattern structures in formal concept analysis . Information Sciences , 181 ( 10 ) : 1989 – 2001 .
  • Kryszkiewicz , M. 1999 . Rules in Incomplete Information Systems . Information Sciences , 113 ( 3–4 ) : 271 – 292 .
  • Kuznetsov, S. O., D. Ślȩzak, D. H. Hepting, B. G. Mirkin, eds. 2011. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. Lecture Notes in Artificial Intelligence, 6743.
  • Leung , Y. and Li , D. 2003 . Maximum Consistent Techniques for Rule Acquisition in Incomplete Information Systems . Information Sciences , 153 : 85 – 106 .
  • Li, T., H. S. Nguyen, G. Wang, J. Grzymala-Busse, R. Janicki, A. E. Hassanien, and H. Yu, eds. 2012. Rough Sets and Knowledge Technology. Lecture Notes in Artificial Intelligence, 7414.
  • Lipski , W. 1979 . On Semantics Issues Connected with Incomplete Information Databases . ACM Transactions on Database Systems , 4 ( 3 ) : 262 – 296 .
  • Lipski , W. 1981 . On Databases with Incomplete Information . Journal of the Association for Computing Machinery , 28 ( 1 ) : 41 – 70 .
  • Nakata , M. and Sakai , H. 2005 . Checking Whether or Not Rough-Set-Based Methods to Incomplete Data Satisfy a Correctness Criterion . Lecture Notes in Artificial Intelligence , 3558 : 227 – 239 .
  • Nakata , M. and Sakai , H. 2005 . Rough Sets Handling Missing Values Probabilistically Interpreted . Lecture Notes in Artificial Intelligence , 3641 : 325 – 334 .
  • Nakata , M. and Sakai , H. 2007a . Lower and Upper Approximations in Data Tables Containing Possibilistic Information . Transactions on Rough Sets , VII : 170 – 189 .
  • Nakata , M. and Sakai , H. 2007 . Applying Rough Sets to Information Tables Containing Probabilistic Values . Lecture Notes in Artificial Intelligence , 4617 : 282 – 294 .
  • Nakata, M., and H. Sakai. 2008. “Rough Sets Approximations in Data Tables Containing Missing Values.” In IEEE International Conference on Fuzzy Systems, June 1–6, 2008, Hong Kong, IEEE Press, 673–680.
  • Nakata, M., and H. Sakai. 2010. “Two Rough Approximations for Information Tables Containing Missing Values.” In 2010 IEEE International Conference on Granular Computing, August 14–16, 2010, IEEE Computer Society, 363–368.
  • Nakata , M. and Sakai , H. 2011 . Dual Rough Approximations in Information Tables with Missing Values . Lecture Notes Artificial Intelligence , 6743 : 36 – 43 .
  • Orłowska , E. and Pawlak , Z. 1984 . Representation of Nondeterministic Information . Theoretical Computer Science , 29 ( 1–2 ) : 27 – 39 .
  • Paredaens , J. , Bra , P. , Gyssens , M. and Gucht , D. 1989 . The Structure of the Relational Database Model , Berlin : Springer-Verlag .
  • Parsons , S. 1996 . Current Approaches to Handling Imperfect Information in Data and Knowledge Bases . IEEE Transactions on Knowledge and Data Engineering , 8 ( 3 ) : 353 – 372 .
  • Parsons , S. 1998 . Addendum to Current Approaches to Handling Imperfect Information in Data and Knowledge Bases . IEEE Transactions on Knowledge and Data Engineering , 10 ( 5 ) : 862
  • Pawlak , Z. 1991 . Rough Sets: Theoretical Aspects of Reasoning about Data , Dordrecht : Kluwer Academic .
  • Pawlak , Z. and Skowron , A. 2007 . Rough Sets and Boolean Reasoning . Information Sciences , 177 ( 1 ) : 41 – 73 .
  • Prade , H. and Testemale , C. 1984 . Generalizing Database Relational Algebra for the Treatment of Incomplete or Uncertain Information and Vague Queries . Information Science , 34 ( 2 ) : 115 – 143 .
  • Sakai , H. 2001 . Effective Procedures for Handling Possible Equivalence Relation in Non-deterministic Information Systems . Fundamenta Informaticae , 48 ( 4 ) : 343 – 362 .
  • Sakai, H. 2012. “Examples of Execution by NIS-Apriori based Rule generator in C and Prolog.” Accessed February 18, 2013. http://www.mns.kyutech.ac.jp/ sakai/RNIA/
  • Sakai , H. and Nakata , M. 2006 . An Application of Discernibility Functions to Generating Minimal Rules in Non-deterministic Information Systems . Journal of Advanced Computational Intelligence and Intelligent Informatics , 10 ( 5 ) : 695 – 702 .
  • Sakai , H. and Okuma , A. 2004 . Basic Algorithms and Tools for Rough Non-deterministic Information Systems . Transactions on Rough Sets , I : 209 – 231 .
  • Sakai , H. , Ishibashi , R. , Koba , K. and Nakata , M. 2008 . Rules and Apriori Algorithm in Non-deterministic Information Systems . Transactions on Rough Sets , IX : 328 – 350 .
  • Sakai , H. , Okuma , H. , Nakata , M. and Ślȩzak , D. 2011 . Stable Rule Extraction and Decision Making in Rough Non-deterministic Information Analysis . International Journal on Hybrid Intelligent Systems , 8 ( 1 ) : 41 – 57 .
  • Sakai , H. , Hayashi , K. , Nakata , M. and Ślȩzak , D. 2011 . A Mathematical Extension of Rough Set-based Issues toward Uncertain Information Analysis . New Mathematics and Natural Computation , 7 ( 1 ) : 1 – 28 .
  • Sakai, H., H. Okuma, and M. Nakata. 2013. “Rough Non-deterministic Information Analysis for Uncertain Information.” In The Handbook on Reasoning-Based Intelligent Systems, edited by K. Nakamatsu and L. C. Jain, 81–118. Singapore: World Scientific.
  • Skowron , A. and Stepaniuk , J. 1996 . Tolerance Approximation Spaces . Fundamenta Informaticae , 27 ( 3–4 ) : 245 – 253 .
  • Słowiński , R. and Stefanowski , J. 1989 . Rough Classification in Incomplete Information Systems . Mathematical and Computer Modelling , 12 ( 10–11 ) : 1347 – 1357 .
  • Slowiński , R. and Vanderpooten , D. 2000 . A Generalized Definition of Rough Approximations Based on Similarity . IEEE Transactions on Knowledge and Data Engineering , 12 ( 2 ) : 331 – 336 .
  • Stefanowski , J. and Tsoukiàs , A. 2001 . Incomplete Information Tables and Rough Classification . Computational Intelligence , 17 ( 3 ) : 545 – 566 .
  • Van, N. D., K. Yamada, and M. Unehara. 2011. “Knowledge Reduction in Incomplete Decision Tables Using Probabilistic Similarity-Based Rough set Model”. In 12th International Symposium on Advanced Intelligent Systems, September 28–October 1, 2011, Suwon Korea, 147–150.
  • Yao , Y. Y. 2003 . On Generalizing Rough Set Theory . Lecture Notes in Computer Science , 2639 : 44 – 51 .
  • Yao, J. J., Y. Yang, R. Słowiński, S. Greco, H. Li, S. Mitra, and L. Polkowski, eds. 2012. Rough Sets and Current Trends in Computing. Lecture Notes in Artificial Intelligence, 7413.
  • Zhu , H-D and Li , H-C . 2011 . Extended Rough Set Model Based on Prior Probability and Valued Tolerance Relation . Journal of Electronic Science and Technology , 9 ( 1 ) : 46 – 50 .
  • Zimányi, E., and A. Pirotte. 1997. “Imperfect Information in Relational Databases.” In Uncertainty Management in Information Systems: From Needs to Solutions, edited by A. Motro and P. Smets, 35–87. Dordrecht: Kluwer Academic.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.