Inference with Governing Schemes for Propagation of Fuzzy Convex Constraints Based on α-Cuts
Kiyohiko Uehara*, Takumi Koyama*, and Kaoru Hirota**
*Ibaraki University, Hitachi 316-8511, Japan
**Tokyo Institute of Technology, Yokohama 226-8502, Japan
A governing scheme is proposed for fuzzy constraint propagation from given facts to consequences in convex forms, which is applied to the inference method based on α-cuts and generalized mean. The governing is performed by self-tuning which can reflect the distribution forms of fuzzy sets in consequent parts to the forms of deduced consequences. Thereby, the proposed scheme can solve the problems in the conventional inference based on the compositional rule of inference that deduces fuzzy sets with excessive fuzziness increase and specificity decrease. In simulations, it is confirmed that the proposed scheme can effectively perform the constraint propagation from given facts to consequences in convex forms while reflecting fuzzy-set distributions in consequent parts. It is also demonstrated that consequences are deduced without excessively large fuzziness and small specificity.
-  L. A. Zadeh, “Fuzzy logic = Computing with words,” IEEE Trans. Fuzzy Syst., Vol.4, No.2, pp. 103-111, 1996.
-  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.
-  I. B. Turksen and Y. Tian, “Combination of rules or their consequences in fuzzy expert systems,” Fuzzy Sets Syst., Vol.58, No.1, pp. 3-40, 1993.
-  G. Cheng and Y. Fu, “Error estimation of perturbation under CRI,” IEEE Trans. Fuzzy Syst., Vol.14, No.6, pp. 709-715, Dec. 2006.
-  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.
-  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 –,” Journal of Japan Society for Fuzzy Theory and Systems, Vol.7, No.1, pp. 113-130, 1995 (in Japanese).
-  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, May 1992, pp. 221-224 (in Japanese).
-  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.
-  V. G. Kaburlasos, “FINs: lattice theoretic tools for improving prediction of sugar production from populations of measurements,” IEEE Trans. Syst., Man, Cybern. B, Cybern., Vol.34, No.2, pp. 1017-1030, Apr. 2004.
-  V. G. Kaburlasos and A. Kehagias, “Novel fuzzy inference system (FIS) analysis and design based on lattice theory. part I: working principles,” Int. Journal of General Systems, Vol.35, No.1, pp. 45-67, Feb. 2006.
-  V. G. Kaburlasos and A. Kehagias, “Novel fuzzy inference system (FIS) analysis and design based on lattice theory,” IEEE Trans. Fuzzy Systems, Vol.15, No.2, pp. 243-260, Apr. 2007.
-  V. G. Kaburlasos and S. E. Papadakis, “Granular self-organizing map (grSOM) for structure identification,” Neural Networks, Vol.19, pp. 623-643, 2006.
-  S.-Q. Fan, W.-X. Zhanga, and W. Xu, “Fuzzy inference based on fuzzy concept lattice,” Fuzzy Sets and Systems, Vol.157, pp. 3177-3187, Dec. 2006.
-  Y.-Z. Zhang and H.-X. Li, “Variable weighted synthesis inference method for fuzzy reasoning and fuzzy systems,” Computers and Mathematics with Applications, Vol.52, pp. 305-322, 2006.
-  Z. Huang and Q. Shen, “Fuzzy interpolative reasoning via scale and move transformation,” IEEE Trans. Fuzzy Syst., Vol.14, No.2, pp. 340-359, Apr. 2006.
-  K. W. Wong, D. Tikk, T. D. Gedeon, and L. T. Kóczy, “Fuzzy rule interpolation for multidimensional input spaces with applications: A case study,” IEEE Trans. Fuzzy Syst., Vol.13, No.6, pp. 809-819, Dec. 2005.
-  K. Uehara and K. Hirota, “Parallel fuzzy inference based on α-level sets and generalized means,” Int. Journal of Information Sciences, Vol.100, No.1-4, pp. 165-206, Aug. 1997.
-  K. Uehara and K. Hirota, “Fuzzy connection admission control for ATM networks based on possibility distribution of cell loss ratio,” IEEE Journal on Selected Areas in Communications, Vol.15, No.2, pp. 179-190, Feb. 1997.
-  K. Uehara, T. Koyama, and K. Hirota, “Fuzzy Inference with Schemes for Guaranteeing Convexity and Symmetricity in Consequences Based on α-Cuts,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.2, pp. 135-149, 2009.
-  A. Kaufmann, “Introduction to the theory of fuzzy subsets,” New York: Academic, Vol.1, 1975.
-  N. R. Pal and J. C. Bezdek, “Measuring Fuzzy Uncertainty,” IEEE Trans. Fuzzy Syst., Vol.2, No.2, pp. 107-118, 1994.
-  R. R. Yager, “On the specificity of a possibility distribution,” Fuzzy Sets Syst., Vol.50, pp. 279-292, 1992.
-  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.
-  M. Mizumoto and H. J. Zimmermann, “Comparison of fuzzy reasoning methods,” Fuzzy Sets Syst., Vol.8, pp. 253-283, 1982.
-  S. Fukami, M. Mizumoto, and K. Tanaka, “Some considerations on fuzzy conditional inference,” Fuzzy Sets Syst., Vol.4, pp. 243-273, 1980.
-  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.
-  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 Transactions on Fuzzy Systems, Vol.13, No.1, Feb. 2005.
-  L. A. Zadeh, “The concept of a linguistic truth variable and its application to approximate reasoning – I, II, III,” Informat. Sci., Vol.8, pp. 199-249, pp. 301-357, Vol.9, pp. 43-80, 1975.
-  K. Uehara, “Fuzzy inference based on a weighted average of fuzzy sets and its learning algorithm for fuzzy exemplars,” in Proc. of the Int. Joint Conf. of the Fourth IEEE Int. Conf. on Fuzzy Systems and the Second Int. Fuzzy Engineering Symposium, FUZZ-IEEE/IFES'95 (Yokohama, Japan), 1995, Vol.IV, pp. 2253-2260.
-  K. Uehara and M. Fujise, “Fuzzy inference based on families of α-level sets,” IEEE Trans. Fuzzy Syst., Vol.1, No.2, pp. 111-124, May 1993.
-  K. Uehara and K. Hirota, “Parallel and multistage fuzzy inference based on families of α-level sets,” Int. Journal of Information Sciences, Vol.106, No.1-2, Apr. 1998.
-  K. Uehara and M. Fujise, “Learning of fuzzy-inference criteria with artificial neural network,” in Proc. of Int. Conf. on Fuzzy Logic & Neural Networks, IIZUKA '90, Vol.1, Iizuka, Japan, Jul. 1990, pp. 193-198.
-  K. Uehara, E. Taguchi, T. Watahiki, and T. Miyata, “A data converter for analog/fuzzy-logic interface,” The Transactions of the Institute of Electronics and Communication Engineers, J67-C, 4, pp. 391-396, 1984 (in Japanese).
-  L. T. Kóczy and K. Hirota, “Approximate reasoning by linear rule interpolation and general approximation,” Int. J. Approx. Reason., Vol.9, No.3, pp. 197-225, 1993.
-  L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Syst. Man Cybern., Vol.SMC-3, No.1, pp. 28-44, 1973.
-  P. T. Chang and K. C. Hung, “α-cut fuzzy arithmetic: Simplifying rules and a fuzzy function optimization with a decision variable,” IEEE Trans. Fuzzy Syst., Vol.14, No.4, pp. 496-510, Aug. 2006.
-  P. T. Chang, K. C. Hung, K. P. Lin, and C. H. Chang, “A comparison of discrete algorithms for fuzzy weighted average,” IEEE Trans. Fuzzy Syst., Vol.14, No.5, pp. 809-819, 2006.