Game-Theoretic Rough Sets

• Autorzy: Herbert J. P. , Yao J. T.
• Języki publikacji: EN

Abstrakty

EN

This article investigates the Game-theoretic Rough Set (GTRS) model and its capability of analyzing a major decision problem evident in existing probabilistic rough set models. A major challenge in the application of probabilistic rough set models is their inability to formulate a method of decreasing the size of the boundary region through further explorations of the data. To decrease the size of this region, objects must be moved to either the positive or negative regions. Game theory allows a solution to this decision problemby having the regions compete or cooperatewith each other in order to find which is best fit to be selected for the move. There are two approaches discussed in this article. First, the region parameters that define the minimum conditional probabilities for region inclusion can either compete or cooperate in order to increase their size. The second approach is formulated by having classification approximation measures compete against each other. We formulate a learning method using the GTRS model that repeatedly analyzes payoff tables created from approximationmeasures and modified conditional risk strategies to calculate parameter values.

Słowa kluczowe

EN

rough sets; set approximation; game theory; decision-theoretic model; variable precision model; probabilistic rough set model; game-theoretic model

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2011
• Tom: Vol. 108, nr 3/4
• Strony: 267--286
• Opis fizyczny: Bibliogr. 36 poz., tab., wykr.

Twórcy

autor

Herbert J. P.

autor

Yao J. T.

• Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2,

Bibliografia

• [1] Bell,M. G. F.: The use of game theory tomeasure the vulnerability of stochastic networks, IEEE Transactions on Reliability, 52(1), 2003, 63-68.
• [2] Blaszczynski, J., Greco, S., Slowinski, R., Szelg, M.: Monotonic variable consistency rough set approaches, International journal of approximate reasoning, 50(7), 2009, 979-999.
• [3] Ciucci, D.: A Unifying Abstract Approach for Rough Models, Proceedings of Rough Sets and Knowledge Technology (RSKT'08), LNAI 5009, 2008, 371-378.
• [4] Duntsch, I., Gediga, G.: Uncertainty measures of rough set prediction, Artificial Intelligence, 106(1), 1998, 109-137.
• [5] Fischer, J.,Wright, R. N.: An application of game-theoretic techniques to cryptography, Discrete Mathematics and Theoretical Computer Science, 13, 1993, 99-118.
• [6] Fudenberg, D., Tirole, J.: Game Theory, The MIT Press, 1991.
• [7] Greco, S., Matarazzo, B., Slowinski, R.: Parameterized rough set model using rough membership and Bayesian confirmation measures, International Journal of Approximate Reasoning, 49(2), 2008, 285-300.
• [8] Herbert, J. P., Yao, J. T.: A Game-Theoretic Approach to Competitive Learning in Self-Organizing Maps, International Conference on Natural Computation (ICNC'05), LNCS 3610, 2005, 129-138.
• [9] Herbert, J. P., Yao, J. T.: Rough Set Model Selection for Practical Decision Making, Proceedings of Fuzzy Systems and Knowledge Discovery (FSKD'07), Vol. III, 2007, 203-207.
• [10] Herbert, J. P., Yao, J. T.: Game-Theoretic Risk Analysis in Decision-Theoretic Rough Sets, Proceedings of Rough Sets and Knowledge Technology (RSKT'08), LNAI 5009, 2008, 132-139.
• [11] Herbert, J. P., Yao, J. T.: Criteria for choosing a rough set model, Computers and Mathematics with Applications, 57(6), 2009, 908-918.
• [12] Herbert, J. P., Yao, J. T.: Learning Optimal Parameters in Decision-Theoretic Rough Sets, Proceedings of Rough Sets and Knowledge Technology (RSKT'09), LNAI 5589, 2009, 610-617.
• [13] Katzberg, J. D., Ziarko, W.: Variable precision rough sets with asymmetric bounds, Rough Sets, Fuzzy Sets and Knowledge Discovery (W. Ziarko, Ed.), Springer, London, 1994, 167-177.
• [14] Kotlowski,W., Dembczynski, K., Greco, S., Slowinski, R.: Stochastic dominance-based rough set model for ordinal classification, Information Sciences, 178(21), 2008, 4019-4037.
• [15] Li, T. R., Ruan, D., Geert, W., Song, J., Xu, Y.: A rough sets based characteristic relation approach for dynamic attribute generalization in data mining, Knowledge-Based Systems, 20(5), 2007, 485-494.
• [16] Li, Y., Zhang, C., Swanb, J.: Rough set based model in information retrieval and filtering, Proceedings of the 5th International Conference on Information Systems Analysis and Synthesis, 1999, 398-403.
• [17] Nash, J.: The bargaining problem, Econometrica, 18(2), 1950, 155-162.
• [18] Neumann, J. V., Morgenstern, O.: Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944.
• [19] Pawlak, Z.: Rough sets, International Journal of Computer and Information Sciences, 11, 1982, 341-356.
• [20] Roth, A.: The evolution of the labor market for medical interns and residents: a case study in game theory, Political Economy, 92, 1984, 991-1016.
• [21] Slezak, D., Ziarko,W.: The investigation of the Bayesian rough set model, International Journal of Approximate Reasoning, 40(1-2), 2005, 81-91.
• [22] Taylor, S.: Modelling Financial Time Series, JohnWiley & Sons Ltd, 1986.
• [23] Tsumoto, S.: Accuracy and coverage in rough set rule induction, Proceedings of RSCTC'02, LNCS 2475, 2002, 373-380.
• [24] Yao, J. T., Herbert, J. P.: Web-based Support Systems with Rough Set Analysis, Proceedings of Rough Sets and Emerging Intelligent Systems Paradigms (RSEISP'07), LNAI 4585, 2007, 360-370.
• [25] Yao, J. T., Herbert, J. P.: A Game-Theoretic Perspective on Rough Set Analysis, Journal of Chongqing University of Posts and Telecommunications, 20(3), 2008, 291-298.
• [26] Yao, J. T., Herbert, J. P.: Financial time-series analysis with rough sets, Applied Soft Computing, 9(3), 2009, 1000-1007.
• [27] Yao, J. T., Zhang,M.: Feature Selection with Adjustable Criteria, Proceedings of RSFDGrC'05, LNAI 3641, 2005, 204-213.
• [28] Yao, Y. Y.: Probabilistic approaches to rough sets, Expert Systems, 20(5), 2003, 287-297.
• [29] Yao, Y. Y.: Decision-Theoretic Rough Set Models, Proceedings of Rough Sets Knowledge Technology (RSKT'07), LNAI 4481, 2007, 1-12.
• [30] Yao, Y. Y.: Probabilistic rough set approximations, International Journal of Approximate Reasoning, 49(2), 2008, 255-271.
• [31] Yao, Y. Y.: Two Semantic Issues in a Probabilistic Rough Set Model, Fundamenta Informaticae, 108(3-4), 2011, 249-265.
• [32] Yao, Y. Y., Wong, S. K. M., Lingras, P.: A decision-theoretic rough set model, in: Methodologies for Intelligent Systems (Z.W. Ras, M. Zemankova,M. L. Emrich, Eds.), vol. 5, North-Holland, New York, 1990, 17-24.
• [33] Zhou, X., Li, H.: A Multi-view Decision Model Based on Decision-theoretic Rough Set, Proceedings of Rough Sets and Knowledge Technology (RSKT'09), LNAI 5589, 2009, 650-657.
• [34] Ziarko,W.: Variable precision rough set model, Journal of Computer and System Sciences, 46, 1993, 39-59.
• [35] Ziarko, W.: Acquisition of heirarchy-structured probabilitic decision tables and rules from data, Expert Systems, 20, 2003, 305-310.
• [36] Ziarko, W., Fei, X.: VPRSM approach to WEB searching, Proceedings of RSCTC'02, LNCS 2475, 2002, 514-521.