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In this article we present three inclusion functions which characterise the nearness relation between finite sets of objects defined in line with J. F. Peters, A. Skowron, and J. Stepaniuk [26]. By means of these functions we extend the notion of nearness to the graded case where one can measure the degree to which one set is near to another one.
Wydawca
Czasopismo
Rocznik
Tom
Strony
301--317
Opis fizyczny
Bibliogr. 42 poz., tab.
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autor
autor
- Institute of Mathematics, Białystok University ul. Akademicka 2, 15-267 Białystok, Poland, anna.gom@math.uwb.edu.pl
Bibliografia
- [1] Arkhangel'skii, A. V., Fedorchuk, V. V.: The basic concepts and constructions of general topology, in: General Topology I (A. V. Arkhangel'skii, L. S. Pontryagin, Eds.), Springer, New York, 1990.
- [2] Drwal, G., Mrózek, A.: System RClass - software implementation of a rough classifier, Proc. 7th Int. Symp. Intelligent Information Systems (IIS'1998), Malbork, Poland, June 1998 (M. A. Kłopotek, M. Michalewicz, Z. W. Ra´s, Eds.), PAS Institute of Computer Science, Warszawa, 1998, 392-395.
- [3] Efremovich, V. A.: The geometry of proximity I (in Russian), Mat. Sb., 31(73), 1952, 189-200.
- [4] Gomolińska, A.: On three closely related rough inclusion functions, Lecture Notes in AI, 4585, 2007, 142-151.
- [5] Gomolińska, A.: On certain rough inclusion functions, Transactions on Rough Sets IX: journal subline of LNCS, 5390, 2008, 35-55.
- [6] Gomolińska, A.: Rough approximation based on weak q-RIFs, Transactions on Rough Sets X: journal subline of LNCS, 5656, 2009, 117-135.
- [7] Gomolińska, A.: A logic-algebraic approach to graded inclusion, Fundamenta Informaticae, 109(3), 2011, 265-279.
- [8] Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach as a proper way of handling graduality in rough set theory, Transactions on Rough Sets VII: journal subline of LNCS, 4400, 2007, 36-52.
- [9] Greco, S., Matarazzo, B., Słowiński, R.: Granular computing for reasoning about ordered data: The dominance-based rough set approach, in: Handbook of Granular Computing (W. Pedrycz, A. Skowron, V. Kreinovich, Eds.), John Wiley & Sons, Chichester, 2008, 347-373.
- [10] Henry, C. J.: Near Sets: Theory and Applications, Ph. D. dissertation, University of Manitoba, Winnipeg, Canada, 2010.
- [11] Herrlich, H.: A concept of nearness, General Topology and Applications, 4, 1974, 191-212.
- [12] Herrlich, H.: Topological structures, Mathematical Centre Tracts, 52, 1974, 59-122.
- [13] Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, Kraków, 1913, English transl. in [2], pages 16-63.
- [14] Naimpally, S. A., Warrack, B. D.: Proximity Spaces, Cambridge University Press, Cambridge, UK, 1970.
- [15] Pawlak, Z.: Information systems - theoretical foundations, Information Systems, 6(3), 1981, 205-218.
- [16] Pawlak, Z.: Rough sets, Int. J. Computer and Information Sciences, 11, 1982, 341-356.
- [17] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht, 1991.
- [18] Pawlak, Z., Skowron, A.: Rough membership functions, in: Fuzzy Logic for the Management of Uncertainty (M. Fedrizzi, J. Kacprzyk, R. R. Yager, Eds.), John Wiley & Sons, New York, 1994, 251-271.
- [19] Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning, Information Sciences, 177, 2007, 41-73.
- [20] Pawlak, Z., Skowron, A.: Rough sets: Some extensions, Information Sciences, 177, 2007, 28-40.
- [21] Pawlak, Z., Skowron, A.: Rudiments of rough sets, Information Sciences, 177, 2007, 3-27.
- [22] Peters, J. F.: Classification of objects by means of features, Proc. 1st IEEE Symp. Foundations of Computational Intelligence (FOCI'2007), Honolulu, Hawaii, April 2007 (D. Fogel, J. Mendel, X. Yao, T. Omori, Eds.), 2007, 1-8.
- [23] Peters, J. F.: Near sets. Special theory about nearness of objects, Fundamenta Informaticae, 75(1-4), 2007, 407-433.
- [24] Peters, J. F.: Sufficiently near sets of neighbourhoods, Lecture Notes in AI, 6954, 2011, 17-24.
- [25] Peters, J. F., Naimpally, S. A.: Applications of near sets, Notices of the AMS, 59(4), 2012, 536-542.
- [26] Peters, J. F., Skowron, A., Stepaniuk, J.: Nearness of objects: Extension of approximation space model, Fundamenta Informaticae, 79(3-4), 2007, 497-512.
- [27] Peters, J. F., Wasilewski, P.: Foundations of near sets, Information Sciences, 179(18), 2009, 3091-3109.
- [28] Polkowski, L.: Reasoning by Parts: An Outline of Rough Mereology, Warszawa, 2011, ISBN 978-83-931192-0-2.
- [29] Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning, Int. J. Approximated Reasoning, 15(4), 1996, 333-365.
- [30] Polkowski, L., Skowron, A.: Rough mereology in information systems. A case study: Qualitative spatial reasoning, in: [32], 2001, 89-135.
- [31] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces, Fundamenta Informaticae, 27, 1996, 245-253.
- [32] Skowron, A., Stepaniuk, J., Swiniarski, R.: Modelling rough granular computing based on approximation spaces, Information Sciences, 184, 2012, 20-43.
- [33] Słowiński, R., Greco, S., Matarazzo, B.: Rough sets in decision making, in: Encyclopedia of Complexity and Systems Science (R. A. Meyers, Ed.), Springer Science + Business Media, New York, 2009, 7753-7786.
- [34] Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations, in: Advances in Machine Intelligence and Soft Computing (P. P. Wang, Ed.), vol. 4, Duke University Press, 1997, 17-33.
- [35] Stepaniuk, J.: Knowledge discovery by application of rough set models, in: [32], 2001, 137-233.
- [36] Surma, S. J., Srzednicki, J. T., Barnett, J. D., Eds.: Stanisław Le´sniewski Collected Works, Kluwer/Polish Scientific Publ., Dordrecht/Warszawa, 1992.
- [37] Szczuka, M., Skowron, A., Stepaniuk, J.: Function approximation and quality measures in rough-granular systems, Fundamenta Informaticae, 109(3), 2011, 339-354.
- [38] Wasilewski, P., Peters, J. F., Ramanna, S.: Perceptual tolerance intersection, Lecture Notes in AI, 6086, 2010, 277-286.
- [39] Wolski, M.: Approximation spaces and nearness type structures, Fundamenta Informaticae, 79(3-4), 2007, 567-577.
- [40] Zadeh, L. A.: Outline of a new approach to the analysis of complex system and decision processes, IEEE Trans. on Systems, Man, and Cybernetics, 3, 1973, 28-44.
- [41] Ziarko, W.: Variable precision rough set model, J. Computer and System Sciences, 46(1), 1993, 39-59.
- [42] Ziarko, W.: Stochastic approach to rough set theory, Lecture Notes in AI, 4259, 2006, 38-48.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0029-0007