Formalizing Two Generalized Approximation Operators

Adam Grabowski; Michał Sielwiesiuk

doi:10.2478/forma-2018-0016

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Formalizing Two Generalized Approximation Operators

Formalized Mathematics

Volume 26 (2018): Issue 2 (July 2018)

By: Adam Grabowski and Michał Sielwiesiuk

Open Access

|Dec 2018

Abstract

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article we give the formal characterization of two closely related rough approximations, along the lines proposed in a paper by Gomolińska [2]. We continue the formalization of rough sets in Mizar [1] started in [6].

References

[1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17
Open DOI Search in Google Scholar Back to article
[2] Anna Gomolińska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103–119, 2002.
Search in Google Scholar Back to article
[3] Adam Grabowski. Automated discovery of properties of rough sets. Fundamenta Informaticae, 128:65–79, 2013. doi:10.3233/FI-2013-933.10.3233/FI-2013-933
Open DOI Search in Google Scholar Back to article
[4] Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.10.3233/FI-2016-1406
Open DOI Search in Google Scholar Back to article
[5] Adam Grabowski. Formalization of generalized almost distributive lattices. Formalized Mathematics, 22(3):257–267, 2014. doi:10.2478/forma-2014-0026.10.2478/forma-2014-0026
Open DOI Search in Google Scholar Back to article
[6] Adam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21–28, 2004.
Search in Google Scholar Back to article
[7] Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.10.2478/forma-2013-0006
Open DOI Search in Google Scholar Back to article
[8] Adam Grabowski. Binary relations-based rough sets – an automated approach. Formalized Mathematics, 24(2):143–155, 2016. doi:10.1515/forma-2016-0011.10.1515/forma-2016-0011
Search in Google Scholar Back to article
[9] Adam Grabowski and Magdalena Jastrzębska. A note on a formal approach to rough operators. In Marcin S. Szczuka and Marzena Kryszkiewicz et al., editors, Rough Sets and Current Trends in Computing – 7th International Conference, RSCTC 2010, Warsaw, Poland, June 28-30, 2010. Proceedings, volume 6086 of Lecture Notes in Computer Science, pages 307–316. Springer, 2010. doi:10.1007/978-3-642-13529-3_33.10.1007/978-3-642-13529-3_33
Open DOI Search in Google Scholar Back to article
[10] Adam Grabowski and Magdalena Jastrzębska. Rough set theory from a math-assistant perspective. In Rough Sets and Intelligent Systems Paradigms, International Conference, RSEISP 2007, Warsaw, Poland, June 28–30, 2007, Proceedings, pages 152–161, 2007. doi:10.1007/978-3-540-73451-2_17.10.1007/978-3-540-73451-2_17
Search in Google Scholar Back to article
[11] Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.10.1007/978-3-642-14128-7_26
Search in Google Scholar Back to article
[12] Adam Grabowski and Christoph Schwarzweller. Rough Concept Analysis - theory development in the Mizar system. In Asperti, Andrea and Bancerek, Grzegorz and Trybulec, Andrzej, editor, Mathematical Knowledge Management, Third International Conference, MKM 2004, Bialowieza, Poland, September 19–21, 2004, Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 130–144, 2004. doi:10.1007/978-3-540-27818-4_10. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19-21, 2004.10.1007/978-3-540-27818-4_10.3rdSep.19-212004
Open DOI Search in Google Scholar Back to article
[13] Jouni Järvinen. Lattice theory for rough sets. Transactions of Rough Sets, VI, Lecture Notes in Computer Science, 4374:400–498, 2007.10.1007/978-3-540-71200-8_22
Search in Google Scholar Back to article
[14] Eliza Niewiadomska and Adam Grabowski. Introduction to formal preference spaces. Formalized Mathematics, 21(3):223–233, 2013. doi:10.2478/forma-2013-0024.10.2478/forma-2013-0024
Open DOI Search in Google Scholar Back to article
[15] Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.10.1007/BF01001956
Open DOI Search in Google Scholar Back to article
[16] Y.Y. Yao. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning, 15(4):291–317, 1996. doi:10.1016/S0888-613X(96)00071-0.10.1016/S0888-613X(96)00071-0
Open DOI Search in Google Scholar Back to article
[17] William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.10.1016/j.ins.2007.05.037
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/forma-2018-0016 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 183 - 191

Accepted on: Jun 29, 2018

Published on: Dec 24, 2018

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

rough approximation,

rough set,

generalized approximation operator

Related subjects:

Mathematics,

General mathematics,

Computer sciences,

Computer sciences, other

© 2018 Adam Grabowski, Michał Sielwiesiuk, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 26 (2018): Issue 2 (July 2018)