Modification of Near Sets Theory

• Autorzy: Marei E. A. , Abd El-Monsef M. E. , Abu-Donia H. M.

Identyfikatory

DOI

10.3233/FI-2015-1186

• Języki publikacji: EN

Abstrakty

EN

Most real life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subsets without coding or using assumption. The aim of this paper is to introduce different approaches to near sets by using general relations and special neighborhoods. Some fundamental properties and characterizations are given. We obtain a comparison between these new approximations and traditional approximations introduced by Peters [23].

Słowa kluczowe

EN

information system; topological space; rough sets; near sets; open set β

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2015
• Tom: Vol. 137, nr 3
• Strony: 387--402
• Opis fizyczny: Bibliogr. 37 poz., tab.

Twórcy

autor

Marei E. A.

• Department of Mathematics, Faculty of Science and Art Shaqra University, Saudi Arabia

autor

Abd El-Monsef M. E.

• Department of Mathematics, Faculty of Science Tanta University, Egypt Hassan M. Abu-Donia

autor

Abu-Donia H. M.

• Department of Mathematics, Faculty of Science Zagazig University, Egypt

Bibliografia

• [1] M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud: β-open sets and β-continuous mappings, Bull. Fac. Assiut Uni. (1983)77-90.
• [2] M. E. Abd El-Monsef, A. M. Kozae, M. J. Iqelan: Near Approximations in Topological Spaces, Int.Jornal of Math.Analysis. (2010)279-290.
• [3] H. M. Abu-Donia, A. A. Nasef, E. A. Marei: Finite Information Systems, Applied Mathematics and Information Sciences. (2007)13-21.
• [4] A. Galton: A generalized topological view of motion in discrete space, Theor. Comput. Sci. (2002).
• [5] S. Greco, B. Matarazzo, R. Slowinski: Rough approximation by dominance relation, International Journal of Intelligent Systems. (2002)153-171.
• [6] J. Kelley: General topology, Van Nostrand Company. (1955).
• [7] M. Kryszkiewicz: Rules in incomplete information systems, Information Sciences. (1999)271-292.
• [8] C. Largeron, S. Bonnevay: A Pretopological Approach for Structural Analysis, Information Sci. (2002)185-196.
• [9] Y. Leung, D.-Y. Li: Maximal consistent block technique for rule acquisition in incomplete information systems, Information Sciences. (2003)85-106.
• [10] T.Y. Lin, Y.Y. Yao: Mining soft rules using rough sets and neighborhoods, In: Proceedings of the Symposium on Modelling, Analysis and Simulation, Computational Engineering in Systems Applications (CESA’96), IMASCS Multiconference, Lille, France, July 912. (1996)1095-1100.
• [11] P. J. Lingras, Y. Y. Yao: Data mining using extension of rough set model, Journal of American Society of Information Science. (1998)415-422.
• [12] S. Naimpally, J.F. Peters: Topologywith Applications: Topological Spaces via Near and Far, World Scientific, Sinapore. (2012), , to appear.
• [13] E. Orlowska, Z. Pawlak: Representation of nondeterministic information, Theoretical Computer Science. (1987)27-39.
• [14] M. Pavel: Fundamentals of Pattern Recognition, 2nd Edition. Marcel Dekker, Inc., NY (1993).
• [15] Z. Pawlak: Rough sets, International Journal of Computer and Information Sciences. (1982)341-356.
• [16] Z. Pawlak, A. Skowran: Rough membership functions in fuzzy logic for the Managment of Uncertainty, (L. A. Zadah and J. Kacprzyk, Eds.), Johnwily and Sons, New York. (1994)251-271.
• [17] Z. Pawlak, R. Slowinski: Rough set approach to multi-attribute decision analysis, Invited Review, European Journal of Operational Research. (1994)443-459.
• [18] J.F. Peters, A. Skowron, J. Stepaniuk: Nearness in approximation spaces, G. Lindemann, H. Schlilngloff et al. (Eds.), Proc. Concurrency, Specification & Programming (CS&P’2006). Informatik-Berichte Nr. 206, Humboldt-Universitat zu Berlin (2006)434-445.
• [19] J.F. Peters, S. Ramanna, Feature selection: a near set approach, in: ECML & PKDD Workshop on Mining Complex Data, Warsaw. (2007)1-12.
• [20] J.F. Peters: Near sets: Special theory about nearness of objects, Fundamenta Informaticae. (2007)1-28.
• [21] J.F. Peters: Classification of objects by means of features, In: Proc. IEEE Symposium Series on Foundations of Computational Intelligence. (2007)1-8.
• [22] J.F. Peters, A. Skowron, J. Stepaniuk: Nearness of Objects: Extension of Approximation Space Model, Fundamenta Informaticae. (2007)1-24.
• [23] J.F. Peters: Near sets: general theory about nearness of objects, Appl.Math. Sci. (2007)2609-2629.
• [24] J.F. Peters: Tolerance near sets and image correspondence, Int. J. Bio-Inspired Comput. (2008)239-245.
• [25] J.F. Peters, C. Henry: Reinforcement learning with approximation spaces, Fundam. Inform. (2009)323-349.
• [26] J.F. Peters: Corrigenda and addenda: tolerance near sets and image correspondence. 2(5)(2010)310-318.
• [27] J.F. Peters, S. Naimpally: Applications of near sets, Notices of the Amer. Math. Soc. 59(4)(2012)536-542.
• [28] J.F. Peters, P. Wasilewski: Tolerance spaces: Origins, theoretical aspects and applications, Information Sciences. 195(2012)211-225.
• [29] A. Skowron, C. Rauszer: The discernibility matrices and functions in information systems. in: Slowinski, R. (Ed.), Intelligent Decision Support: Handbook of Applications and Advances of Rough Sets Theory. Kluwer Academic Publisher, Dordrecht. (1992)331-362.
• [30] A. Skowron, J. Stepaniuk: Generalized approximation space. In: Lin, T.Y., Wildberger, A.M. (Eds.), Soft Computing, Simulation Councils, San Diego. (1995)18-21.
• [31] A. Skowron, J. Stepaniuk: Tolerance approximation spaces, Fundamenta Informaticae. (1996)245-253.
• [32] R. Slowinski, D. Vanderpooten: A generalized definition of rough approximations based on similarity, IEEE Transactions on Knowledge and Data Engineering. (2000)331-336.
• [33] B.M.R. Stadler, P.F. Stadler: Generalized topological spaces in evolutionary theory and combinatorial chemistry, J. Chem. Inf. Comput. Sci. (2002)577-585.
• [34] Y. Y. Yao, S. K. M. Wong: Generalization of rough sets using relationships between attribute values. In: Proceedings of the 2nd Annual Joint Conference on Information Sciences. (1995)30-33.
• [35] Y.Y. Yao: Two views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning. (1996)291-317.
• [36] Y.Y. Yao: Relational interpretation of neighborhood operators and rough set approximation operator, Information Sciences. (1998)239-259.
• [37] W. -X. Zhang, J. -S. Mi, W. -Z. Wu: Approaches to knowledge reducts in inconsistent systems, International Journal of Intelligent Systems. (2003)989-1000.