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International Journal of General Systems Volume 46, 2017 - Issue 5: Special Issue on Concept Lattices and Their Applications
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Original Articles

Formation of the D-basis from implicational systems using Simplification logic

Estrella Rodríguez-LorenzoApplied Mathematics and Computer Science Department, Universidad de Málaga, Andalucía Tech, Málaga, Spain.View further author information
,
Kira AdarichevaMathematics Department, Hofstra University, New York, NY, USA.View further author information
,
Pablo CorderoApplied Mathematics and Computer Science Department, Universidad de Málaga, Andalucía Tech, Málaga, Spain.View further author information
,
Manuel EncisoApplied Mathematics and Computer Science Department, Universidad de Málaga, Andalucía Tech, Málaga, Spain.View further author information
&
Angel MoraApplied Mathematics and Computer Science Department, Universidad de Málaga, Andalucía Tech, Málaga, Spain.Correspondence [email protected]
View further author information
Pages 547-568 | Received 20 May 2016, Accepted 09 Apr 2017, Published online: 28 Jul 2017

References

  • Adaricheva, K. V., and J. B. Nation. 2014. “On Implicational Bases of Closure Systems with Unique Critical Sets.” Discrete Applied Mathematics 162: 51–69.
  • Adaricheva, K. V., and J. B. Nation. 2016. “Lattice Theory: Special Topics.” Chap. in Bases of Closure Systems, edited by G. Grätzer and F. Wehrung, vol. 2, 181–213. Cham: Springer.
  • Adaricheva, K. V., and J. B. Nation. 2017. “Discovery of the d-basis in Binary Tables Based on Hypergraph Dualization.” Theoretical Computer Science 658 (B): 307–315.
  • Adaricheva, K. V., J. B. Nation, and R. Rand. 2013. “Ordered Direct Implicational Basis of a Finite Closure System.” Discrete Applied Mathematics 161 (6): 707–723.
  • Agrawal, R., T. Imielinski, and A. N. Swami. 1993. “Mining Association Rules between Sets of Items in Large Databases.” In ACM SIGMOD International Conference on Management of Data, Washington, DC, 207–216.
  • Armstrong, W. W., and C. Deobel. 1980. “Decompositions and Functional Dependencies in Relations.” ACM Transactions on Database Systems 5 (4): 404–430.
  • Bertet, K., C. Demko, J.-F. Viaud, and C. Guérin. Forthcoming. “Lattices, Closures Systems and Implication Bases: A Survey of Structural Aspects and Algorithms.” Theoretical Computer Science. doi:10.1016/j.tcs.2016.11.021.
  • Bertet, K., and B. Monjardet. 2010. “The Multiple Facets of the Canonical Direct Unit Implicational Basis.” Theoretical Computer Science 411 (22–24): 2155–2166.
  • Belohlávek, R., and V. Vychodil. 2006a. “Computing Non-redundant Bases of If-then Rules from Data Tables with Graded Attributes.” In 2006 IEEE International Conference on Granular Computing, Atlanta, GA, 205–210.
  • Belohlávek, R., and V. Vychodil. 2006b. “Data tables with Similarity Relations: Functional Dependencies, Complete Rules and Non-redundant Bases.” In Database Systems for Advanced Applications, 11th International Conference, DASFAA, Singapore, 644–658.
  • Cordero, P., A. Mora, M. Enciso, and I. Pérez de Guzmán. 2002. “SLFD Logic: Elimination of Data Redundancy in Knowledge Representation.” Lecture Notes in Computer Science 2527: 141–150.
  • Codd, E. F. 1971. Further Normalization of the Data Base Relational Model. IBM Research Report, San Jose, CA, RJ909.
  • Ganter, B., and R. Wille. 1999. Formal Concept Analysis: Mathematical Foundations. Translated by C. Franzke. New York: Springer-Verlag.
  • Lichman, M. 2013. UCI Machine Learning Repository. Accessed January 12, 2017. http://archive.ics.uci.edu/ml/index.php.
  • Mora, A., M. Enciso, P. Cordero, and I. Fortes. 2012. “Closure via Functional Dependence Simplification.” International Journal of Computer Mathematics 89 (4): 510–526.
  • Rodríguez-Lorenzo, E., K. V. Adaricheva, P. Cordero, M. Enciso, and A. Mora. 2015. “From an Implicational System to its Corresponding d-basis.” In Proceedings of the Twelfth International Conference on Concept Lattices and their Applications, Clermont-Ferrand, France, October 13--16, 217–228.
  • Szathmary, L., P. Valtchev, A. Napoli, and R. Godin. 2009. “Efficient Vertical Mining of Frequent Closures and Generators.” In Advances in Intelligent Data Analysis VIII, 8th International Symposium on Intelligent Data Analysis, IDA, 393–404.

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