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On the Structure of Indiscernibility Relations Compatible with a Partially Ordered Set

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Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7268))

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Abstract

In a recently published work the author investigates indiscernibility relations on information systems with a partially ordered universe. Specifically, he introduces a notion of compatibility between the (partially ordered) universe and an indiscernibility relation on its support, and establishes a criterion for compatibility. In this paper we make a first step in the direction of investigating the structure of all the indiscernibility relations which satisfy such a compatibility criterion.

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References

  1. Codara, P.: A theory of partitions of partially ordered sets. PhD thesis, Università degli Studi di Milano, Italy (2008)

    Google Scholar 

  2. Codara, P.: Partitions of a Finite Partially Ordered Set. In: Damiani, E., D’Antona, O., Marra, V., Palombi, F. (eds.) From Combinatorics to Philosophy. The Legacy of G.-C. Rota, pp. 45–59. Springer, US (2009)

    Chapter  Google Scholar 

  3. Codara, P.: Indiscernibility Relations on Partially Ordered Sets. In: IEEE International Conference on Granular Computing, GrC 2011, pp. 150–155 (2011)

    Google Scholar 

  4. Codara, P., D’Antona, O.M., Marra, V.: Open Partitions and Probability Assignments in Gödel Logic. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS (LNAI), vol. 5590, pp. 911–922. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jelonek, J., Krawiec, K., Slowinski, R.: Rough set reduction of attributes and their domains for neural networks. Computational Intelligence 11, 339–347 (1995)

    Article  Google Scholar 

  7. Kryszkiewicz, M.: Rough set approach to incomplete information systems. Inform. Sci. 112(1-4), 39–49 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu, G., Zhu, W.: The algebraic structures of generalized rough set theory. Inform. Sci. 178(21), 4105–4113 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Mac Lane, S.: Categories for the working mathematician, 2nd edn. Graduate Texts in Mathematics, vol. 5. Springer, New York (1998)

    MATH  Google Scholar 

  10. Orłowska, E. (ed.): Incomplete information: rough set analysis. STUDFUZZ, vol. 13. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  11. Pagliani, P., Chakraborty, M.: A geometry of approximation. Trends in Logic—Studia Logica Library, vol. 27. Springer, New York (2008)

    Book  MATH  Google Scholar 

  12. Pawlak, Z.: Rough sets. Internat. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pawlak, Z.: Rough set approach to knowledge-based decision support. European Journal of Operational Research 99, 48–57 (1995)

    Article  Google Scholar 

  14. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177(1), 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yao, Y.Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16(1), 87–104 (2001)

    Article  MATH  Google Scholar 

  16. Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15, 291–317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Via Comelico 39, I-20135, Milan, Italy

    Pietro Codara

Authors
  1. Pietro Codara
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Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, Computer Science Division, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

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© 2012 Springer-Verlag Berlin Heidelberg

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Codara, P. (2012). On the Structure of Indiscernibility Relations Compatible with a Partially Ordered Set. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29350-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-29350-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29349-8

  • Online ISBN: 978-3-642-29350-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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