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Back to the Beginnings: Pawlak’s Definitions of the Terms Information System and Rough Set

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Thriving Rough Sets

Part of the book series: Studies in Computational Intelligence ((SCI,volume 708))

Abstract

There are several notions and terms in Rough Set Theory not having a crystal clear definition. I discuss here two basic ones: Rough Set and Information System. The discussion will be lead by the two founding papers by Z. Pawlak. We will see that the term Information System has a narrow sense (the most used one in the rough set community) and a wide one (the world wide common use of information system and also Pawlak’s one). In case of the term Rough Set, several definitions are possible, none of them without problems. Some other minor issues related to Pawlak’s papers will be highlighted.

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Notes

  1. 1.

    https://global.britannica.com/topic/information-system

  2. 2.

    Rough Set Database System, http://rsds.univ.rzeszow.pl/

  3. 3.

    https://infobright.com/.

  4. 4.

    A slightly more complex but mathematically equivalent definition can be given inside classical set theory [24].

  5. 5.

    Let me notice that this is done for instance in many valued paraconsistent logics where a proposition can map to 0, 1, both or none of the two values [22].

  6. 6.

    For instance, recently, we had to cancel the Rough Set Theory workshop at ECAI 2016 (European Conference on Artificial Intelligence) due to insufficient participants.

References

  1. Banerjee, M., Chakraborty, M.: Rough sets through algebraic logic. Fundamenta Informaticae 28, 211–221 (1996)

    MathSciNet  MATH  Google Scholar 

  2. Bonikowski, Z.: A certain conception of the calculus of rough sets. Notre Dame J. Formal Logic 33(3), 412–421 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chakraborty, M.K.: On some issues in the foundation of rough sets: the problem of definition. Fundamenta Informaticae (2016) (To appear)

    Google Scholar 

  4. Chakraborty, M.K., Banerjee, M.: Rough sets: some foundational issues. Fundamenta Informaticae 127(1–4), 1–15 (2013)

    MathSciNet  MATH  Google Scholar 

  5. Chiaselotti, G., Ciucci, D., Gentile, T.: Simple graphs in granular computing. Inf. Sci. 340–341, 279–304 (2016)

    Article  MathSciNet  Google Scholar 

  6. Ciucci, D.: Approximation algebra and framework. Fundam. Info. 94(2), 147–161 (2009)

    MathSciNet  MATH  Google Scholar 

  7. Ciucci, D.: Orthopairs and granular computing. Granular Comput. 1, 159–170 (2016)

    Article  Google Scholar 

  8. Ciucci, D., Dubois, D.: Three-valued logics, uncertainty management and rough sets. Trans. Rough Sets XVII, 1–32 (2014)

    Google Scholar 

  9. Ciucci, D., Mihálydeák, T., Csajbók, Z.E.: On definability and approximations in partial approximation spaces. In: Miao, D., Pedrycz, W., Slezak, D., Peters, G., Hu, Q., Wang, R. (eds.) Rough Sets and Knowledge Technology—9th International Conference, RSKT 2014. Proceedings of Lecture Notes in Computer Science, vol. 8818, pp. 15–26. Shanghai, China, 24–26 Oct 2014

    Google Scholar 

  10. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer-Verlag, Berlin Heidelberg (1999)

    Book  MATH  Google Scholar 

  11. Gehrke, M., Walker, E.: On the structure of rough sets. Bull. Pol. Acad. Sci. (Math.) 40, 235–245 (1992)

    MathSciNet  MATH  Google Scholar 

  12. Janicki, R.: Approximations of arbitrary binary relations by partial orders: classical and rough set models. Trans. Rough Sets 13, 17–38 (2011)

    MATH  Google Scholar 

  13. Mani, A.: Dialectics of counting and the mathematics of vagueness. Trans. Rough Sets 15, 122–180 (2012)

    Article  MATH  Google Scholar 

  14. Marek, V.W., Pawlak, Z.: Information storage and retrieval systems: mathematical foundations. Theor. Comput. Sci. 1(4), 331–354 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  15. Orlowska, E., Pawlak, Z.: Measurement and indiscernibility. Bull. Pol. Acad. Sci. Math. 32, 617–624 (1984)

    MathSciNet  MATH  Google Scholar 

  16. Pawlak, Z.: Mathematical foundation of information retrieval. In: Mathematical Foundations of Computer Science: Proceedings of Symposium and Summer School, Strbské Pleso, High Tatras, pp. 135–136. Mathematical Institute of the Slovak Academy of Sciences, Czechoslovakia, 3–8 Sept 1973

    Google Scholar 

  17. Pawlak, Z.: Information systems theoretical foundation. Info. Syst. 6, 205–218 (1981)

    Google Scholar 

  18. Pawlak, Z.: Rough sets. Int. J. Comput. Info. Sci. 11, 341–356 (1982)

    Article  MATH  Google Scholar 

  19. Pawlak, Z.: On discernibility of objects in knowledge representation systems. Bull. Pol. Acad. Sci., Math. Sci. 32, 613–615 (1984)

    Google Scholar 

  20. Pawlak, Z.: Rough sets and some problems of artificial intelligence. Tech. Rep. ICS PAS Reports 565/85, Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland (1985)

    Google Scholar 

  21. Pawlak, Z.: AI and intelligent industrial applications: the rough set perspective. Cybern. Syst. 31(3), 227–252 (2000)

    Article  MATH  Google Scholar 

  22. Priest, G., Tanaka, K., Weber, Z.: Paraconsistent logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Spring 2015 edn. (2015)

    Google Scholar 

  23. Păun, G., Polkowski, L., Skowron, A.: Rough set approximations of languages. Fundamenta Informaticae 32(2), 149–162 (1997)

    MathSciNet  MATH  Google Scholar 

  24. Ramík, J., Vlach, M.: A non-controversial definition of fuzzy sets. Trans. Rough Sets II(3135), 201–207 (2004)

    Google Scholar 

  25. Wang, S., Zhu, Q., Zhu, W., Min, F.: Rough set characterization for 2-circuit matroid. Fundam. Inform. 129(4), 377–393 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Yao, J.T., Yao, Y.Y.: Induction of classification rules by granular computing. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) Rough Sets and Current Trends in Computing, Third International Conference, RSCTC 2002. Proceedings of Lecture Notes in Computer Science vol. 2475, pp. 331–338. Malvern, PA, USA, 14–16 October 2002

    Google Scholar 

  27. Yao, Y.: A note on definability and approximations. Trans. Rough Sets 7, 274–282 (2007)

    MathSciNet  MATH  Google Scholar 

  28. Ziarko, W., Shan, N.: A method for computing all maximally general rules in attribute-value systems. Comput. Intell. 12, 223–234 (1996)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Milano–Bicocca, Milano, Italy

    Davide Ciucci

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  1. Davide Ciucci
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Correspondence to Davide Ciucci .

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Editors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  2. Institute of Mathematics, University of Warsaw Institute of Mathematics, Warsaw, Poland

    Andrzej Skowron

  3. University of Regina, Department of Computer Science University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  4. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. Polish-Japanese Academy IT , Warsaw, Poland

    Lech Polkowski

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Ciucci, D. (2017). Back to the Beginnings: Pawlak’s Definitions of the Terms Information System and Rough Set . In: Wang, G., Skowron, A., Yao, Y., Ślęzak, D., Polkowski, L. (eds) Thriving Rough Sets. Studies in Computational Intelligence, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-319-54966-8_11

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  • DOI: https://doi.org/10.1007/978-3-319-54966-8_11

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