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S-approximation Spaces : A Three-way Decision Approach

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we investigate properties of the lower and upper approximations of an Sapproximation space under different assumptions for its S operator. These assumptions are partial monotonicity, complement compatibility and functional partial monotonicity. We also extend the theory of three way decisions to non-inclusion relations. Also in this work, a new representation for partial monotone S-approximation spaces, called inflections, is introduced. We will also discuss the computational complexity of representing an S-approximation space in terms of inflection sets. Finally, the usefulness of the introduced concepts is illustrated by an example.
Wydawca
Rocznik
Strony
307--328
Opis fizyczny
Bibliogr. 37 poz., rys.
Twórcy
autor
  • Department of Computer Science Yazd University, Yazd, Iran
  • Department of Computer Science Yazd University, Yazd, Iran
Bibliografia
  • [1] Bazan, J., Nguyen, H. S., Szczuka, M.: A View on Rough Set Concept Approximations, Fundamenta Informaticae, 59(2), January 2004, 107–118.
  • [2] Dempster, A.: Upper and lower probabilities induced by a multivalued mapping, The annals of mathematical statistics, 38(2), 1967, 325–339.
  • [3] Gomoliska, A.: Approximation Spaces Based on Relations of Similarity and Dissimilarity of Objects, Fundamenta Informaticae, 79(3), January 2007, 319–333.
  • [4] Gomoliska, A.: On Certain Rough Inclusion Functions, in: Transactions on Rough Sets IX (J. F. Peters, A. Skowron, H. Rybiski, Eds.), number 5390 in Lecture Notes in Computer Science, Springer Berlin Heidelberg, January 2008, ISBN 978-3-540-89875-7, 35–55.
  • [5] Grzymala-Busse, J.: Rough-set and Dempster-Shafer approaches to Knowledge Acquisition under Uncertainty – A Comparison, Technical report, University of Kansas, 1987.
  • [6] Grzymala-Busse, J.W.: Knowledge acquisition under uncertainty a rough set approach, Journal of Intelligent and Robotic Systems, 1(1), March 1988, 3–16, ISSN 0921-0296, 1573-0409.
  • [7] Hooshmandasl, M. R., Shakiba, A., Goharshady, A. K., Karimi, A.: S-Approximation: A New Approach to Algebraic Approximation, Journal of Discrete Mathematics, 2014, April 2014, ISSN 2090-9837.
  • [8] Katzberg, J. D., Ziarko, W.: Variable Precision Extension of Rough Sets, Fundamenta Informaticae, 27(2), January 1996, 155–168.
  • [9] Kopotek, M. A., Wierzcho, S. T.: A New Qualitative Rough-Set Approach to Modeling Belief Functions, in: Rough Sets and Current Trends in Computing (L. Polkowski, A. Skowron, Eds.), number 1424 in Lecture Notes in Computer Science, Springer Berlin Heidelberg, January 1998, ISBN 978-3-540-64655-6, 346–354.
  • [10] Lingras, P.: Combination of evidence in rough set theory, , Fifth International Conference on Computing and Information, 1993. Proceedings ICCI ’93, May 1993.
  • [11] Liu, G.: Rough set theory based on two universal sets and its applications, Knowledge-Based Systems, 23(2), March 2010, 110–115, ISSN 0950-7051.
  • [12] Pawlak, Z.: Rough Sets, International Journal of Computer and Information Sciences, 11, 1982, 341–356.
  • [13] Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data, Theory and decision library: System theory, knowledge engineering, and problem solving, Kluwer Academic Publishers, 1991, ISBN 9780792314721.
  • [14] Pawlak, Z.: Vagueness and uncertainty: a rough set perspective, Computational Intelligence, 11(2), May 1995, 227–232, ISSN 0824-7935.
  • [15] Pawlak, Z.: Rough set theory and its applications to data analysis, Cybernetics & Systems, 29(7), October 1998, 661–688, ISSN 01969722.
  • [16] Pawlak, Z., Skowron, A.: Rough membership functions, in: Advances in the Dempster-Shafer Theory of Evidence (R. Yager, M. Fedrizzi, J. Kacprzyk, Eds.), Wiley, 1994, 251–271.
  • [17] Pawlak, Z., Wong, S., Ziarko, W.: Rough sets: Probabilistic versus deterministic approach, International Journal of Man-Machine Studies, 29, 1988, 81–95.
  • [18] Pei, Z., Xu, Z.: Rough set models on two universes, International Journal of General Systems, 33(5), 2004, 569–581.
  • [19] Polkowski, L.: Rough sets: Mathematical foundations, vol. 15, Physica Verlag, 2002.
  • [20] Polkowski, L., Skowron, A.: Rough mereology, in: Methodologies for Intelligent Systems (Z. W. Ra, M. Zemankova, Eds.), Springer Berlin Heidelberg, January 1994, ISBN 978-3-540-58495-7, 85–94.
  • [21] Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning, International Journal of Approximate Reasoning, 15(4), November 1996, 333–365, ISSN 0888-613X.
  • [22] Shafer, G.: A mathematical theory of evidence, vol. 1, Princeton university press Princeton, 1976.
  • [23] Skowron, A., Grzymala-Busse, J.: From Rough Set Theory to Evidence Theory, in: Advances in the Dempster-Shafer Theory of Evidence (R. Yager, J. Kacprzyk, M. Fedrizzi, Eds.), Wiley, New York, NY, USA, 1994.
  • [24] Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces, Fundamenta Informaticae, 27(2), January 1996, 245–253.
  • [25] Wong, S. K. M., Wang, L. S., Yao, Y. Y.: On modeling uncertainty with interval structures, Computational Intelligence, 11(2), 1995, 406–426.
  • [26] Wong, S. M.,Wang, L. S., Yao, Y. Y.: Interval structure: a framework for representing uncertain information, Morgan Kaufmann Publishers Inc., 1992.
  • [27] Wu, W.Z., Leung, Y., Zhang, W.-X.: Connections between rough set theory and Dempster-Shafer theory of evidence, International Journal of General Systems, 31(4), 2002, 405–430, ISSN 0308-1079.
  • [28] Yao, Y.: Generalized rough set models, in: Rough sets in knowledge discovery 1: Methodology and Approximations (L. Polkowski, A. Skowron, Eds.), vol. 1 of Studies in Fuzziness and Soft Computing, Physica Verlag, Heidelberg, 1998, 286–318.
  • [29] Yao, Y.: Three-way decision: an interpretation of rules in rough set theory, in: Rough Sets and Knowledge Technology, Springer, 2009, 642–649.
  • [30] Yao, Y.: An Outline of a Theory of Three-Way Decisions, in: Rough Sets and Current Trends in Computing (J. Yao, Y. Yang, R. Sowiski, S. Greco, H. Li, S. Mitra, L. Polkowski, Eds.), Springer Berlin Heidelberg, January 2012, ISBN 978-3-642-32114-6, 1–17.
  • [31] Yao, Y., Deng, X.: Quantitative rough sets based on subsethood measures, Information Sciences, 267, May 2014, 306–322, ISSN 0020-0255.
  • [32] Yao, Y., Lin, T.: Generalization of rough sets using modal logic, Intelligent Automation and Soft Computing, 2(2), 1996, 103–120.
  • [33] Yao, Y. Y., Lingras, P. J.: Interpretations of belief functions in the theory of rough sets, Information Sciences, 104(12), January 1998, 81–106, ISSN 0020-0255.
  • [34] Yao, Y. Y., Wong, S. K. M., Wang, L. S.: A non-numeric approach to uncertain reasoning, International Journal of General Systems, 23(4), 1995, 343–359.
  • [35] Zadeh, L.: Fuzzy sets, Information and control, 8(3), 1965, 338–353.
  • [36] Zadeh, L.: The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy sets and Systems, 11(1), 1983, 197–198.
  • [37] Zadeh, L.: A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination, AI magazine, 7(2), 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-074edecf-a92a-47ee-bef9-b21e458a334d
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