Abstract
Determining the correct threshold values for probabilistic rough set models has been a heated issue among the community. This article will formulate a game-theoretic approach to calculating these thresholds to ensure correct approximation region size. By finding equilibrium within payoff tables created from approximation measures and modified conditional risk strategies, we provide the user with tolerance levels for their loss functions. Using the tolerance values, new thresholds are calculated to provide correct classification regions. Better informed decisions can be made when utilizing these tolerance values.
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References
Bell, M.G.F.: The use of game theory to measure the vulnerability of stochastic networks. IEEE Transactions on Reliability 52, 63–68 (2003)
Duntsch, I., Gediga, G.: Uncertainty measures of rough set prediction. Artificial Intelligence 106, 109–137 (1998)
Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991)
Gediga, G., Duntsch, I.: Rough approximation quality revisited. Artificial Intelligence 132, 219–234 (2001)
Herbert, J., Yao, J.T.: A game-theoretic approach to competitive learning in self-organizing maps. In: Wang, L., Chen, K., Ong S., Y. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 129–138. Springer, Heidelberg (2005)
Herbert, J., Yao, J.T.: Time-series data analysis with rough sets. In: Proceedings of Computational Intelligence in Economics and Finance (CIEF 2005), pp. 908–911 (2005)
Herbert, J.P., Yao, J.T.: Rough set model selection for practical decision making. In: Proceeding of Fuzzy Systems and Knowledge Discovery (FSKD 2007). III, pp. 203–207 (2007)
Nash, J.: The bargaining problem. Econometrica 18, 155–162 (1950)
Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Roth, A.: The evolution of the labor market for medical interns and residents: a case study in game theory. Political Economy 92, 991–1016 (1984)
Yao, J.T., Herbert, J.P.: Web-based support systems with rough set analysis. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 360–370. Springer, Heidelberg (2007)
Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)
Yao, Y.Y.: Decision-theoretic rough set models. In: Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 1–12. Springer, Heidelberg (2007)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37, 793–809 (1992)
Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, vol. 5, pp. 17–24. North-Holland, New York (1990)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
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Herbert, J.P., Yao, J. (2008). Game-Theoretic Risk Analysis in Decision-Theoretic Rough Sets. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2008. Lecture Notes in Computer Science(), vol 5009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79721-0_22
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DOI: https://doi.org/10.1007/978-3-540-79721-0_22
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