Abstract
Choquet-integral-based evaluations by fuzzy rules are comprehensive evaluation methods involving the use of a fuzzy rule table and the Choquet integral. Fuzzy measures are identified from the fuzzy rule table. In this paper, we propose methods for developing fuzzy rule tables for Choquet integral models on the basis of a basic fuzzy rule table and weights of evaluation items.
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References
Choquet, G.: Theory of Capacities. Annales de l’Institut Fourier 5, 131–295 (1954)
Murofushi, T., Sugeno, M.: A theory of fuzzy measures: representations, the Choquet integral, and null sets. J. Math. Anal. Appl. 159(2), 532–549 (1991)
Grabisch, M., Nguyen, H.T., Walker, E.A.: Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer, Dordrecht (1995)
Takahagi, E.: Choquet-integral-based Evaluations by Fuzzy Rules. In: Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, pp. 843–848 (2009)
Tversky, A., Kahneman, D.: Advances in Prospect Theory, Cumulative Representation of Uncertainty. J. of Risk and Uncertainty 5, 297–323 (1992)
Grabisch, M., Labreuche, C.: Bi-capacities — Part I: definition, Möbius transform and interaction. Fuzzy Sets and Systems 151, 211–236 (2005)
Grabisch, M., Labreuche, C.: Bi-capacities — Part II: the Choquet integral. Fuzzy Sets and Systems 151, 237–259 (2005)
Grabisch, M., Labreuche, C.: Capacities on lattices and k-ary capacities. In: 3d Int, Conf. of the European Soc. for Fuzzy Logic and Technology (EUSFLAT 2003), Zittau (2003)
Grabisch, M., Labreuche, C.: Bipolarization of posets and natural interpolationstar. J. of Mathematical Analysis and Applications 343(2), 1080–1097 (2008)
Takahagi, E.: Fuzzy Integral Based Fuzzy Switching Functions. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 129–150. Springer, Heidelberg (2004)
Takahagi, E.: Fuzzy three-valued switching functions using Choquet integral. Journal of Advanced Computational Intelligence and Intelligent Informatics 7(1), 47–52 (2003)
Sugeno, M.: Theory of Fuzzy Integrals and its Applications, doctoral thesis, Tokyo Institute of Technology (1974)
Narukawa, Y., Torra, V.: Fuzzy Measure and Probability Distributions: Distorted Probabilities. IEEE Transactions on Fuzzy Systems 13(5), 617–629 (2005)
Tukamoto, Y.: A Measure Theoretic Approach to Evaluation of Fuzzy Set Defined on Probability Space. Journal of Fuzzy Math 2(3), 89–98 (1982)
Takahagi, E.: A Fuzzy Measure Identification Method by Diamond Pairwise Comparisons and φ s Transformation. Fuzzy Optimization and Decision Making 7(3), 219–232 (2008)
Murofushi, T., Soneda, S.: Techniques for reading fuzzy measures (III): interaction index. In: 9th Fuzzy System Symposium, Sapporo, Japan, pp. 693–696 (1993) (in Japanese)
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Takahagi, E. (2010). Choquet-Integral-Based Evaluations by Fuzzy Rules: Methods for Developing Fuzzy Rule Tables on the Basis of Weights and Interaction Degrees. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_54
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DOI: https://doi.org/10.1007/978-3-642-14055-6_54
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