Abstract
Linguistic fuzzy modeling that is usually implemented using Mamdani type of fuzzy systems suffers from the lack of accuracy and high computational costs. The paper shows that product-sum inference is an immediate remedy to both problems and that in this case it is sufficient to consider symmetrical output membership functions. For the identification of the latter, a numerically efficient method is suggested and arising interpretational aspects are discussed. Additionally, it is shown that various rule weighting schemes brought into the game to improve accuracy in linguistic modeling only increase computational overhead and can be reduced to the proposed model configuration with no loss of information.
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References
Alonso, J.M., Magdalena, L.: A Conceptual Framework for Understanding a Fuzzy System. In: Joint 2009 IFSA World Congress and EUSFLAT Conference, IFSA-EUSFLAT, pp. 119–124 (2009)
Ishibuchi, H., Kaisho, Y., Nojima, Y.: Complexity, interpretability and explanation capability of fuzzy rule-based classifiers. In: IEEE Int. Conf. Fuzzy Systems, pp. 1730–1735. IEEE Press, New York (2009)
Cordon, O., Herrera, F., Peregrin, A.: Applicability of the fuzzy operators in the design of fuzzy controllers. Fuzzy Sets and Systems 86, 15–41 (1997)
Riid, A., RĂ¼stern, E.: Transparent fuzzy systems and modeling with transparency protection. In: IFAC Symp. on Artificial Intelligence in Real Time Control, pp. 229–234. Elsevier Science, New York (2000)
Zhang, B.S., Edmunds, J.M.: On Fuzzy Logic Controllers. In: IEEE Int. Conf. Control, pp. 961–965. IEEE Press, New York (1991)
Cordon, O., Herrera, F., Hoffmann, F., Magdalena, L. (eds.): Genetic Fuzzy Systems. Evolutionary tuning and learning of fuzzy knowledge bases. World Scientific, Singapore (2001)
Riid, A., RĂ¼stern, E.: Interpretability Improvement of Fuzzy Systems: Reducing the Number of Unique Singletons in Zeroth order Takagi-Sugeno Systems. In: IEEE Int. Conf. Fuzzy Systems, pp. 2013–2018. IEEE Press, New York (2010)
Penrose, R.: A generalized inverse for matrices. Proc. Cambridge Philosophical Society 51, 406–413 (1955)
Golub, G.H., Kahan, W.: Calculating the singular values and pseudo-inverse of a matrix. Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis 2(2), 205–224 (1965)
Riid, A., RĂ¼stern, E.: A Method for Heuristic Fuzzy Modeling in Noisy Environment. In: IEEE Int. Conf. Intelligent Systems, pp. 468–473. IEEE Press, New York (2010)
Pal, N.R., Pal, K.: Handling of inconsistent rules with and extended model of fuzzy reasoning. J. Intelligent and Fuzzy Syst. 7, 55–73 (1999)
Cho, J.S., Park, D.J.: Novel fuzzy logic control based on weighting of partially inconsistent rules using neural network. J. Intelligent and Fuzzy Syst. 8, 99–110 (2000)
Yu, W., Bien, Z.: Design of fuzzy logic systems with inconsistent rule base. J. Intelligent and Fuzzy Syst. 2, 147–159 (1994)
Nauck, D., Kruse, R.: How the Learning of Rule Weights Affects the Interpretability of Fuzzy Systems. In: IEEE Int. Conf. Fuzzy Systems, pp. 1235–1240. IEEE Press, New York (1998)
Ishibuchi, H., Yamamoto, T.: Rule Weight Specification in Fuzzy Rule-Based Classification Systems. IEEE Trans. Fuzzy Systems 13(4), 428–435 (2005)
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Riid, A., RĂ¼stern, E. (2011). Interpretability, Interpolation and Rule Weights in Linguistic Fuzzy Modeling. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2011. Lecture Notes in Computer Science(), vol 6857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23713-3_12
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DOI: https://doi.org/10.1007/978-3-642-23713-3_12
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