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Proceedings of the 18th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 35

Rough Sets: Introduction, History and Selected Applications (Tutorial Lecture — Extended Abstract)

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DOI: http://dx.doi.org/10.15439/2023F0003

Citation: Proceedings of the 18th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 35, pages 69–70 ()

Full text

Abstract. The aim of this tutorial is to present a brief overview of the theory of rough sets from the perspective of its mathematical foundations, history of development, as well as connections with other branches of mathematics and informatics. The content concerns both the theoretical and practical aspects of applications. The above mentioned target of the tutorial will be covered in two parts. In the first part we would aim to present the introduction to rough sets and the second part will focus on the connections with other branches of mathematics and informatics. In particular, in the second part, we will discuss the connections of rough sets with logics, topology and algebra, and graph theory (when it comes to mathematics), as well as knowledge representation, machine learning and data mining, and theoretical computer science (when it comes to informatics).

References

  1. Z. Pawlak, “Rough sets,” Int. J. Inform. Comput. Sci., vol. 11, pp. 341–356, 1982.
  2. ——, Rough sets - theoretical aspects of reasoning about data, ser. Theory and decision library : series D. Kluwer, 1991, vol. 9.
  3. E. Orlowska, “A logic of indiscernibility relations,” ser. Lecture Notes in Computer Sciences. Berlin: Springer-Verlag, 1985, no. 208, pp. 177–186.
  4. D. Ciucci and D. Dubois, “Three-valued logics, uncertainty management and rough sets,” Trans. Rough Sets, vol. 17, pp. 1–32, 2014. [Online]. Available: https://doi.org/10.1007/978-3-642-54756-0_1
  5. M. Banerjee, “Logic for rough truth,” Fundam. Informaticae, vol. 71, no. 2-3, pp. 139–151, 2006.
  6. P. K. Singh and S. Tiwari, “Topological structures in rough set theory: A survey,” Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, pp. 1270 – 1294, 2020.
  7. G. Cattaneo and D. Ciucci, “Lattices with interior and closure operators and abstract approximation spaces,” Trans. Rough Sets, vol. 10, pp. 67–116, 2009.
  8. G. Chiaselotti, D. Ciucci, T. Gentile, and F. Infusino, “Generalizations of rough set tools inspired by graph theory,” Fundam. Informaticae, vol. 148, no. 1-2, pp. 207–227, 2016.
  9. M. Inuiguchi, W.-Z. Wu, C. Cornelis, and N. Verbiest, Fuzzy-Rough Hybridization. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015, pp. 425–451.
  10. A. Campagner, D. Ciucci, and T. Denoeux, “Belief functions and rough sets: Survey and new insights,” Int. J. Approx. Reason., vol. 143, pp. 192–215, 2022.
  11. R. Bello and R. Falcon, Rough Sets in Machine Learning: A Review. Cham: Springer International Publishing, 2017, pp. 87–118.
  12. D. Slezak, P. Synak, A. Wojna, and J. Wroblewski, “Two database related interpretations of rough approximations: Data organization and query execution,” Fundam. Informaticae, vol. 127, no. 1-4, pp. 445–459, 2013.
  13. D. Bianucci and G. Cattaneo, “Information entropy and granulation coentropy of partitions and coverings: A summary,” Trans. Rough Sets, vol. 10, pp. 15–66, 2009.
  14. D. Slęzak, “Approximate entropy reducts,” Fundam. Informaticae, vol. 53, no. 3-4, pp. 365–390, 2002.
  15. A. Campagner, D. Ciucci, and V. Dorigatti, “Uncertainty representation in dynamical systems using rough set theory,” Theor. Comput. Sci., vol. 908, pp. 28–42, 2022.