Rough Granular Computing in Modal Settings : Generalised Approximation Spaces

• Autorzy: Wolski M. , Gomolińska A.

Identyfikatory

DOI

10.3233/FI-2016-1428

• Konferencja: Rough Set Theory Workshop (RST’2015); (6; 29-06-2015; University of Warsaw )
• Języki publikacji: EN

Abstrakty

EN

The paper studies the rough granular computing paradigm within the conceptual settings of multi-modal logic. The main idea is to express a generalised approximation space (U; I; κ), where U is the universe of objects, I is an uncertainty function, and κ is a rough inclusion function, in terms of binary relations, and then to consider the corresponding modal operators. The new modal structure obtained in this way is rich enough to define closure and interior operators corresponding to the classical rough approximation operators and their well-known uni-modal generalisations. In contrast to the standard modal interpretation of rough set approximations, in the new settings one can directly deal with information granules and their properties, which is crucial for granular computing paradigm. More precisely, we are provided with means of describing features of objects and information granules, as well as inclusion degrees between granules.

Słowa kluczowe

EN

rough granular computing; generalised approximation space; modal logic; rough inclusion; topological space; Frechet (V)space

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 148, nr 1/2
• Strony: 157--172
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Wolski M.

• Maria Curie-Skłodowska University, Department of Logic and Cognitive Science, Pl. Marii Curie-Skłodowskiej 4, 20-031 Lublin, Poland

autor

Gomolińska A.

• University of Białystok, Faculty of Mathematics and Informatics, Konstantego Ciołkowskiego 1M, 15-245 Białystok, Poland

Bibliografia

• [1] Alexandrov P. Diskrete Räume. Mat. Sb. (N.S.) (in German) 1937;2(44):501–518. Available from: http://mi.mathnet.ru/msb5579.
• [2] Arenas FG. Alexandroff spaces. Acta Math. Univ. Comenianae. 1999;68(1):17–25. ISSN: 0862-9544. Available from: http://eudml.org/doc/120504.
• [3] Banerjee M, Khan MA. Propositional logics from rough set theory. Transactions on Rough Sets VI. Lecture Notes in Computer Science 4374, 2007; pp. 1–25. doi: 10.1007/978-3-540-71200-8_1.
• [4] Bochvar DA. On a three-valued calculus and its applications to the paradoxes of the classical extended functional calculus. Mathematicheskii Sbornik 4(46):287–308. English translation by M. Bergmann in History and Philosophy of Logic 1981;2:87– 112. doi: 10.1080/01445348108837023.
• [5] Halmos P. Algebraic logic I. Monadic Boolean algebras. Compositio Mathematica 1954-1956;12:217–249. ISSN: 0010-437X. Available from: http://eudml.org/doc/88816.
• [6] Halmos P. The representation of monadic Boolean algebras. Duke Mathematical Journal 1959;26:447–454. Reprinted in Algebraic logic, by Paul R. Halmos, Chelsea Publishing Company, New York 1962, pp. 75–82. doi: 10.2307/2964555. Available from: http://journals.cambridge.org/article_S0022481200118341.
• [7] Kleene SC. On a notation for ordinal numbers. The Journal of Symbolic Logic 1938;3(4):150–155. Available from: http://projecteuclid.org/euclid.jsl/1183385485.
• [8] Khan MA, Banerjee A. A logic for complete information systems. Proceedings of the 10th European Conference, ECSQARU 2009, Verona. Lecture Notes in Computer Science 5590, 2009; pp. 829–840. doi: 10.1007/978-3-642-02906-6_71.
• [9] Lin TY, Liu Q. Rough approximate operators: Axiomatic rough set theory. In Ziarko, W. (Ed.): Rough Sets, Fuzzy Sets and Knowledge Discovery. Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD’93), Banff, Alberta, Canada, 1993; pp. 256–260. doi: 10.1007/978-1-4471-3238-7_31.
• [10] Naturman CA. Interior Algebras and Topology, Ph.D. thesis, University of Cape Town, Department of Mathematics 1991.
• [11] Pagliani P, Chakraborty M. A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns. Trends in Logic 27, Springer-Verlag 2008. ISBN: 1402086210, 9781402086212.
• [12] Pawlak Z. Systemy informacyjne. Podstawy teoretyczne. WNT, Warszawa 1983. Available from: oai: bcpw.bg.pw.edu.pl:1723.
• [13] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publisher, Dordrecht 1991. ISBN: 978-0-7923-1472-1, 978-94-010-5564-2.
• [14] Pawlak Z, Skowron A. Rough sets: Some extensions. Information Sciences 2007;177:28–40. doi: 10. 1016/j.ins.2006.06.006.
• [15] Pedrycz W, Skowron A, Kreinovich V. (Eds.): Handbook of Granular Computing, John Wiley & Sons, Chichester 2008. ISBN: 978-0-470-03554-2.
• [16] Priest G. An Introduction to Non-Classical Logic. Cambridge University Press 2001. ISBN: 9780521854337, 9780521670265. Available from: http://dx.doi.org/10.1017/CBO9780511801174.
• [17] Sierpiński W, Krieger C. General Topology. Courier Corporation 1956. ISBN: 0486411486, 9780486411484.
• [18] Skowron A, Stepaniuk J. Generalized approximation spaces. In: Proc. of 3rd International Workshop on Rough Sets and Soft Computing, San Jose, USA, 1994, pp. 156–163.
• [19] Skowron A, Stepaniuk J. Tolerance approximation spaces. Fundamenta Informaticae 1996;27(2-3):245–253. Available from: http://dl.acm.org/citation.cfm?id=241838.241853.
• [20] Steiner AK. The lattice of topologies: structure and complementation. Transactions of the American Mathematical Society. 1966;122(2):379–398. doi: 10.2307/1994555.
• [21] Stepaniuk J. Rough-Granular Computing in Knowledge Discovery and Data Mining. Studies in Computational Intelligence 152, Springer-Verlag (2008). ISBN: 3540708006, 9783540708001.
• [22] Wiweger A. On topological rough sets. Bulletin of the Polish Academy of Sciences, Mathematics. 1989;37:89–93.
• [23] Yao YY, Lin TY. Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing. 1996;2(2):103–120. doi: 10.1080/10798587.1996.10750660.
• [24] Yao YY. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences. 1998;111(1-4):239–259. doi: 10.1016/S0020-0255(98)10006-3.
• [25] Zadeh L. The key roles of fuzzy information granulation in human reasoning, fuzzy logic and computing with words. 1996. In: Proc. of 5th IEEE International Conference on Fuzzy Systems, p. 1. Available from: http://www.eecs.berkeley.edu/XRG/Summary/Old.summaries/97abstracts/zadeh.1.html
• [26] Zhu W, Wang FY. Reduction and axiomization of covering generalized rough sets. Information Sciences. 2003;152(1):217–230. doi: 10.1016/S0020-0255(03)00056-2.
• [27] Zhu W, Wang FY. Relationships among three types of covering rough sets. Proc. 2006 IEEE International Conference on Granular Computing, 2006, pp. 43–48. doi: 10.1109/GRC.2006.1635755.
• [28] Zhu W, Wang FY. On three types of covering-based rough sets. IEEE Transactions on Knowledge & Data Engineering. 2007;19(8):1131–1144. doi: 10.1109/TKDE.2007.1044.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).