PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

An Approach of Proximity in Rough Set Theory

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we have constructed topological structures on rough sets by choosing the path of proximity relations on approximation spaces. So, by this virtue of purpose, we have used rough metric to define nearness concept between rough sets. Some basic results have been proved on this new nearness structure named as rough proximity. The study is well supported by examples. Finally, the theory is developed to construct the compactification of a rough proximity space.
Słowa kluczowe
Wydawca
Rocznik
Strony
251--271
Opis fizyczny
Bibliogr. 44 poz., rys., tab.
Twórcy
  • Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj-211004, India
  • Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj-211004, India
Bibliografia
  • [1] Biswas R. Rough metric spaces. Bull. Pour. Les. Sous. Ens. Flous. Appl. (France). 1996; 68:21-32.
  • [2] Doitchinov D. On completeness in quasi-metric spaces. Topology and its Applications. 1988;30(2):127-148. URL https://doi.org/10.1016/0166-8641(88)90012-0.
  • [3] Efremovič VA. The geometry of proximity I. Mat Sb. 1952; 31(73): 189-200 (in russian); MR 14, 1106. URL http://www.mathnet.ru/eng/sm5526.
  • [4] Hajri MA, Belaid K, Belaid LJ. Scattered spaces, compactification and an application to image classification problem. Tatra Mountains Mathematical Publications. 2016; 66(1):1-12. URL https://doi.org/10.1515/tmmp-2016-0015.
  • [5] Henry C, Peters JF. Image pattern recognition using near sets. In International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing 2007 May 14 (pp. 475-482). Springer, Berlin, Heidelberg. doi:10.1007/978-3-540-72530-5_57.
  • [6] Herrlich H. A concept of nearness. General topology and its application (to appear). 1967; 299:6-25. URL https://doi.org/10.1016/0016-660X(74)90021-X.
  • [7] Kelley JL. General topology. Van Noostrand. 1955. ISBN: 9780387901251.
  • [8] Khare M, Tiwari S. Completion in a common supercategory of Met, UAP, wsAP and Near. Demonstratio Mathematica. 2013; XLVI(1): 209-227. URL https://doi.org/10.1515/dema-2013-0435.
  • [9] Khare M, Tiwari S. Grill determined L-approach merotopological spaces. Fundamenta Informaticae. 2010; 99(1):1-12. doi:10.3233/FI-2010-236.
  • [10] Khare M, Tiwari S. Approach merotopological spaces and their completion. Int J of Math and Mathematical Sc. 2010; Article ID 409804, 16 pages. URL http://dx.doi.org/10.1155/2010/409804.
  • [11] Kondo M, Dudek WA. Topological structures of rough sets induced by equivalence relations. JACIII. 2006; 10(5):621-624. doi:10.20965/jaciii.2006.p0621.
  • [12] Leader S. On clusters in proximity spaces. Fund Math. 1959; 47:205-213. URL http://matwbn.icm.edu.pl/ksiazki/fm/fm47/fm47112.pdf.
  • [13] Leader S. On product of proximity spaces. Math Annalen. 1964; 154(2):185-194. doi:10.1007/BF01360891.
  • [14] Li W, Zhong N, Yao YY, Liu J, Liu C. Developing intelligent applications in social e-mail networks. RSCTC. 2006; LNAI vol. 4259 pp. 776-785. URL https://doi.org/10.1007/11908029_80.
  • [15] Lodato MW. On topologically induced generalized proximity relations II. Pacif J Math. 1966; 15(3):131-135. URL https://projecteuclid.org/euclid.pjm/1102994732.
  • [16] Lodato MW. On topologically induced generalized proximity relations. Proc Amer Math Soc. 1964; 15(3):417-422. URL https://www.jstor.org/stable/2034517.
  • [17] Naimpally SA, Warrack B. Proximity spaces. Cambridge Tract in Mathematics No. 59, Cambridge University Press, Cambridge, UK. 1970. ISBN-13:978-0521091831.
  • [18] Pal SK, Shankar BU, Mitra P. Granular computing, rough entropy and object extraction. Pattern Recogn Lett. 2005; 26(16):2509-2517. URL https://doi.org/10.1016/j.patrec.2005.05.007.
  • [19] Pawlak Z. Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston. 1991. doi:10.1007/978-94-011-3534-4.
  • [20] Pawlak Z. Rough sets. Int J Comput Inf Sci. 1982; 11(5):341-356. doi:10.1007/BF01001956.
  • [21] Peters JF. Proximal relator spaces. Filomat. 2016; 30(2):469-472. doi:10.2298/FIL1602469P.
  • [22] Peters JF. Local Near Sets: Pattern Discovery in Proximity Spaces. Math Comput Sci. 2013; 7(1):87-106. doi:10.1007/s11786-013-0143-z.
  • [23] Peters JF. Classification of perceptual objects by means of features. Int J Info Technol Intell Comput. 2008; 3(2):1-35.
  • [24] Peters JF, Skowron A, Stepaniuk J. Nearness of visual objects. Application of rough sets in proximity spaces. Fund Inform. 2013; 128(1-2):159-176. doi:10.3233/FI-2013-939.
  • [25] Peters JF, Skowron A, Stepaniuk J. Nearness of objects: Extension of approximation space model. Fund Inform. 2007; 79(3-4): 497-512. URL https://content.iospress.com/articles/fundamenta-informaticae/fi79-3-4-18.
  • [26] Peters JF, Tiwari S. Completing extended metric spaces: An alternative approach. Applied Mathematics Letters, 2012; 25(10):1544-1547. URL https://doi.org/10.1016/j.aml.2012.01.012.
  • [27] Peters JF, Tiwari S. Approach merotopies and near filters, theory and application. Gen Math Notes. 2011; 3(1):32-45. URL http://geman.in/yahoo_site_admin/assets/docs/4_GMN-911-V3N1.160123418.pdf.
  • [28] Polkowski L, Skowron A. Rough sets and current trends in computing. Springer, Berlin. 1998; LNCS vol. 1424. ISBN: 9783540646556.
  • [29] Polkowski L, Skowron A. Rough sets in knowledge discovery 1: methodology and applications. Volume 18 of Studies in Fuzziness and Soft Computing. Physica-Verlag, Heidelberg, Germany. 1998. ISBN: 978-3-7908-1884-0.
  • [30] Polkowski L, Skowron A. Rough sets in knowledge discovery 2: applications, case studies and software systems. Volume 19 of Studies in Fuzziness and Soft Computing. Physica-Verlag, Heidelberg, Germany. 1998. ISBN: 978-3-7908-2459-9.
  • [31] Polkowski L, Polkowska MS. Some remarks on sets of communicating sequential processes in topological rough set framework. Fundam Inform. 2004; 60(1-4):291-305. URL https://content.iospress.com/articles/fundamenta-informaticae/fi60-1-4-20.
  • [32] Riesz F. Stetigkeitsbergriff und abstrakte Mengenlehre. Atti IV Congr Intern Mat Roma. 1908; ii: 18-24.
  • [33] Rudin W. Principles of Mathematical Analysis, McGraw-Hill Book Company, 1953. ISBN:9781259064784.
  • [34] Skowron A. On the topology in information systems. Bulletin of the Polish Academy of Sciences Mathematics. 1988; 36(7):477-480.
  • [35] Smirnov YM. On proximity spaces in sense of V. A. Efremovič. Amer Math Soc Translation Ser 2. 1952; 38(1-4):5-35.
  • [36] Száz Á. Basic tools and mild continuities in relator spaces. Acta Math Hungar. 1987; 50(3-4):177-201. MR0918156. URL https://doi.org/10.1007/BF01903935.
  • [37] Throne WJ. Proximity structures and grills. Math Ann. 1973; 206(1):35-62. URL https://doi.org/10.1007/BF01431527.
  • [38] Tiwari S. Ultrafilter completeness in ∈-approach nearness spaces. Math Comput Sci. 2013; 7:107-111. doi: 10.1007/s11786-013-0148-7.
  • [39] Wiweger A. On topological rough sets. Bulletin of the Polish Academy of Sciences Mathematics. 1988; 37:51-62.
  • [40] Wu WZ, Mi JS. Some mathematical structures of generalized rough sets in infinite universes of discourse. Transactions on Rough Sets XIII. 2011; LNCS vol. 6499: pp. 175-206. doi:10.1007/978-3-642-18302-7_11.
  • [41] Wu Q, Wang T, Huang YX, Li JS. Topological theory on rough sets. Transactions on Systems, man and Cybernetics. 2008; 38(1):68-77. doi: doi:10.20965/jaciii.2006.p0621.
  • [42] Yao YY. Relational interpretations of neighborhood operators and rough set approximation operators. Information sciences. 1998; 111(1-4):239-259. URL https://doi.org/10.1016/S0020-0255(98)10006-3.
  • [43] Zhu W. Topological approaches to covering rough sets. Information sciences. 2007; 177(6):1499-1508. URL https://doi.org/10.1016/j.ins.2006.06.009.
  • [44] Zhu W, Wang FY. Covering based granular computing for analysis of conflict. LNCS. 2006; vol.3975 pp. 566-571. doi:10.1007/11760146_58.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-08f17114-1364-48b0-974d-93bebb8357f6
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.