Paper:
Multi-Level Control of Fuzzy-Constraint Propagation in Inference Based on α-Cuts and Generalized Mean
Kiyohiko Uehara* and Kaoru Hirota**
*Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi 316-8511, Japan
**Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
- [1] L. A. Zadeh, “Fuzzy logic = Computing with words,” IEEE Trans. Fuzzy Syst., Vol.4, No.2, pp. 103-111, 1996.
- [2] L. A. Zadeh, “Inference in fuzzy logic via generalized constraint propagation,” Proc. 1996 26th Int. Symposium on Multi-Valued Logic (ISMVL’96), pp. 192-195, 1996.
- [3] A. Kaufmann, “Introduction to the theory of fuzzy subsets,” New York: Academic, Vol.1, 1975.
- [4] N. R. Pal and J. C. Bezdek, “Measuring Fuzzy Uncertainty,” IEEE Trans. Fuzzy Syst., Vol.2, No.2, pp. 107-118, 1994.
- [5] R. R. Yager, “On the specificity of a possibility distribution,” Fuzzy Sets Syst., Vol.50, pp. 279-292, 1992.
- [6] R. R. Yager, “Measuring tranquility and anxiety in decision making: an application of fuzzy sets,” Int. J. General Systems, Vol.8, pp. 139-146, 1982.
- [7] K. Uehara and M. Fujise, “Multistage fuzzy inference formulated as linguistic-truth-value propagation and its learning algorithm based on back-propagating error information,” IEEE Trans. Fuzzy Syst., Vol.1, No.3, pp. 205-221, Aug. 1993.
- [8] H. Maeda, M. Imuro, and S. Murakami, “A study on the spread of fuzziness in multi-fold multi-stage approximating reasoning – Approximate reasoning with triangular type membership function –,” J. of Japan Society for Fuzzy Theory and Systems, Vol.7, No.1, pp. 113-130, 1995 (in Japanese).
- [9] M. Imuro and H. Maeda, “On the spread of fuzziness in multi-fold and multi-stage fuzzy reasoning,” in Proc. 8th Fuzzy System Symposium, Hiroshima, Japan, pp. 221-224, May 1992 (in Japanese).
- [10] G. Cheng and Y. Fu, “Error Estimation of Perturbation under CRI,” IEEE Trans. Fuzzy Syst., Vol.14, No.6, pp. 709-715, Dec. 2006.
- [11] S. Aja-Fernández and C. Alberola-López, “Fast inference using transition matrices: An extension to nonlinear operators,” IEEE Trans. Fuzzy Syst., Vol.13, No.4, pp. 478-490, Aug. 2005.
- [12] S. J. Chen and S. M. Chen, “Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers,” IEEE Trans. Fuzzy Syst., Vol.11, No.1, pp. 45-56, Feb. 2003.
- [13] J. Casillas, O. Cordón, M. J. del Jesus, and F. Herrera, “Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction,” IEEE Trans. on Fuzzy Systems, Vol.13, No.1, Feb. 2005.
- [14] K. Uehara and K. Hirota, “Parallel fuzzy inference based on α-level sets and generalized means,” Int. J. of Information Sciences, Vol.100, No.1-4, pp. 165-206, Aug. 1997.
- [15] K. Uehara, T. Koyama, and K. Hirota, “Fuzzy Inference with Schemes for Guaranteeing Convexity and Symmetricity in Consequences Based on α-Cuts,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.2, pp. 135-149, 2009.
- [16] K. Uehara, T. Koyama, and K. Hirota, “Inference with Governing Schemes for Propagation of Fuzzy Convex Constraints Based on α-Cuts,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.3, pp. 321-330, 2009.
- [17] K. Uehara, T. Koyama, and K. Hirota, “Inference with Governing Schemes for Propagation of Fuzzy Convex Constraints Based on α-Cuts,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.3, pp. 135-149, 2009.
- [18] K. Uehara, T. Koyama, and K. Hirota, “Inference Based on α-Cut and Generalized Mean with Fuzzy Tautological Rules,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.14, No.1, pp. 76-88, 2010.
- [19] K. Uehara, T. Koyama, and K. Hirota, “Suppression Effect ofα-Cut Based Inference on Consequence Deviations,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.14, No.3, pp. 256-271, Apr. 2010.
- [20] K. Uehara, S. Sato, and K. Hirota, “Inference for Nonlinear Mapping with Sparse Fuzzy Rules Based on Multi-Level Interpolation,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.3, pp. 264-287, May 2011.
- [21] M. Mizumoto and H.-J. Zimmermann, “Comparison of Fuzzy Reasoning Methods,” Fuzzy Sets Syst., Vol.8, No.3, pp. 253-283, 1982.
- [22] S. Fukami, M. Mizumoto, and K. Tanaka, “Some Considerations on Fuzzy Conditional Inference,” Fuzzy Sets Syst., Vol.4, No.3, pp. 243-273, 1980.
- [23] K. Uehara and M. Fujise, “Fuzzy Inference Based on Families of α-Level Sets,” IEEE Trans. on Fuzzy Systems, Vol.1, No.2, pp. 111-124, May 1993.
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