The Structure of Multigranular Rough Sets

• Autorzy: Järvinen Jouni , Radeleczki Sándor

Identyfikatory

DOI

10.3233/FI-2020-1961

• Języki publikacji: EN

Abstrakty

EN

We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called “optimistic” and “pessimistic” multigranular approximation systems are given. We also consider the ordered sets of rough sets determined by these approximation pairs.

Słowa kluczowe

EN

atomistic Boolean lattice; coherence; completely distributive lattice; Dedekind-MacNeille completion; definable set; equivalence relation; irredundant covering; multigranular approximation; rough set; tolerance relation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 176, nr 1
• Strony: 17--41
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Järvinen Jouni

• Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland

autor

Radeleczki Sándor

• Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

Bibliografia

• [1] Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982. 11:341-356. doi:10.1007/BF01001956.
• [2] Yao YY, Lin TY. Generalization of rough sets using modal logics. Intelligent Automation and Soft Computing, 1996. 2:103-120. doi:10.1080/10798587.1996.10750660.
• [3] Järvinen J, Radeleczki S. Irredundant coverings, tolerances, and related algebras. In: Mani A, Cattaneo G, Düntsch I (eds.), Algebraic Methods in General Rough Sets, Trends in Mathematics, pp. 417-457. Birkhäuser, Cham, 2019. doi:10.1007/978-3-030-01162-8_5.
• [4] Burris S, Sankappanavar HP. A Course in Universal Algebra. Number 78 in Graduate Texts in Mathematics. Springer, 1981.
• [5] Järvinen J, Radeleczki S. Rough sets determined by tolerances. International Journal of Approximate Reasoning, 2014. 55:1419-1438. doi:10.1016/j.ijar.2013.12.005.
• [6] Grätzer G. General lattice theory. Springer, 2nd edition, 1998.
• [7] Järvinen J. Knowledge Representation and Rough Sets. Ph.D. dissertation, Department of Mathematics, University of Turku, Finland, 1999. TUCS Dissertations 14.
• [8] Iwiński TB. Algebraic approach to rough sets. Bulletin of Polish Academy of Sciences. Mathematics, 1987. 35:673-683.
• [9] Pomykała J, Pomykała JA. The Stone algebra of rough sets. Bulletin of Polish Academy of Sciences. Mathematics, 1988. 36:495-508.
• [10] Comer SD. On connections between information systems, rough sets, and algebraic logic. In: Algebraic Methods in Logic and Computer Science, number 28 in Banach Center Publications, pp. 117-124. Polish Academy of Scienes, 1993. doi:10.4064/-28-1-117-124.
• [11] Järvinen J, Radeleczki S. Representing regular pseudocomplemented Kleene algebras by tolerance-based rough sets. Journal of the Australian Mathematical Society, 2017. 105:57-78. doi:10.1017/S1446788717000283.
• [12] Qian Y, Liang J, Yao Y, Dang C. MGRS: A multi-granulation rough set. Information Sciences, 2010. 180:949-970. doi:10.1016/j.ins.2009.11.023.
• [13] She Y, He X. On the structure of the multigranulation rough set model. Knowledge-Based Systems, 2012. 36:81-92. doi:10.1016/j.knosys.2012.05.019.
• [14] Schreider JA. Equality, Resemblance, and Order. Mir Publishers, Moskow, 1975.
• [15] Kong Q, Xu W. The comparative study of covering rough sets and multi-granulation rough sets. Soft Computing, 2019. 23:3237-3251. doi:10.1007/s00500-018-3205-y.
• [16] Järvinen J, Kovács L, Radeleczki S. Defining rough sets using tolerances compatible with an equivalence. Information Sciences, 2019. 496:264-283. doi:10.1016/j.ins.2019.05.030.
• [17] Birkhoff G. Lattice Theory, volume XXV of Colloquim publications. American Mathematical Society (AMS), Providence, Rhode Island, third edition, 1995.
• [18] Ganter B, Wille R. Formal Concept Analysis: Mathematical Foundations. Springer, Berlin, Heidelberg, 1999. doi:10.1007/978-3-642-59830-2.
• [19] Davey BA, Priestley HA. Introduction to Lattices and Order. Cambridge University Press, 2nd edition,2002. doi:10.1017/CBO9780511809088.
• [20] Schröder B. Ordered sets: An introduction. Birkhäuser, Boston, 2003. doi:10.1007/978-1-4612-0053-6.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).