An improved hybrid defuzzification method for fuzzy controllers

Mourad  Nachaoui; Abdeljalil  Nachaoui; R. Y.  Shikhlinskaya; Abdelali Elmoufidi

doi:10.19139/soic-2310-5070-1706

Mourad Nachaoui Equipe de Mathematiques et Interactions Universite Sultan Moulay slimane, Faculte des Sciences et Techniques
Abdeljalil Nachaoui Laboratoire de Mathematiques Jean Leray CNRS / Universite de Nantes UMR6629 2 rue de la Houssiniere,
R. Y. Shikhlinskaya Z1148, Z.Khalilov, 23, Baku State University, Institute Applied Mathematics
Abdelali Elmoufidi Equipe de Mathematiques et Interactions Universite Sultan Moulay slimane, Faculte des Sciences et Techniques

DOI: https://doi.org/10.19139/soic-2310-5070-1706

Keywords: Fuzzy sets, Fuzzy Logic, fuzzy controllers, inference, defuzzification, WABL Method

Abstract

This paper deals with fuzzy logic controllers. Our interest is in studying different techniques of defuzzification methods. In particular, we propose a generalization of the WABL method to the multiple output system controller. We give a numerical realization, and we show the advantages of this method compared to other defuzzification methods (MOM, COG, WAF,\ldots) through an application for intelligent control of air conditioners.

References

Berenji, Hamid R. "Fuzzy logic controllers." An introduction to fuzzy logic applications in intelligent systems. Springer, Boston, MA, 1992. 69-96.

Bounabi, M., Karim EL Moutaouakil, and Khalid Satori. The Optimal Inference Rules Selection for Unstructured Data Multi-Classification. Statistics, Optimization & Information Computing, Vol. 10, no. 1, Feb. 2022, pp. 225-3, doi:10.19139/soic-2310-5070-1131.

B. Carse, T. C. Fogarty, and A. Munro, "Evolving fuzzy rule based controllers using genetic algorithms," Fuzzy Sets and Systems, vol. 80, no. 3, pp. 273-293, Jun. 1996.

Sain, Debdoot, and B. M. Mohan. "Modeling, simulation and experimental realization of a new nonlinear fuzzy PID controller using Center of Gravity defuzzification." ISA transactions 110 (2021): 319-327.

Ganascia, Jean-Gabriel. Le Mythe de la Singularité. Faut-il craindre l'intelligence artificielle?. Le Seuil, 2017.

Gilda, K. S., and S. L. Satarkar. "Maxima-Based Defuzzification Methods Proposed for Fuzzy Systems." Proceedings of Integrated Intelligence Enable Networks and Computing. Springer, Singapore, 2021. 629-639.

H. Hellendoorn and C. Thomas, "Defuzzification in fuzzy controllers," Journal of Intelligent and Fuzzy Systems, vol. 1, no. 2, pp. 109-123, 1993.

Iqbal, Shafqat, et al. "A new fuzzy time series forecasting method based on clustering and weighted average approach." Journal of Intelligent & Fuzzy Systems 38.5 (2020): 6089-6098.

Khanali, H., and B. Vaziri. Similarity Technique Effectiveness of Optimized Fuzzy C-Means Clustering Based on Fuzzy Support Vector Machine for Noisy Data. Statistics, Optimization & Information Computing, Vol. 9, no. 3, July 2021, pp. 618-29, doi:10.19139/soic-2310-5070-1035.

G. Klir and T. Folgers, Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, 1988.

Y. Lin, G. A. Cunningham III, and S. V. Coggeshall, "Using fuzzy partitions to create fuzzy systems from input-output data and set the initial weights in a fuzzy neural network," IEEE Trans. Fuzzy Systems, vol. 5, no. 4, pp. 614-621, Nov. 1997.

Lyaqini, S., M. Nachaoui, and M. Quafafou. "Non-smooth classification model based on new smoothing technique." Journal of Physics: Conference Series. Vol. 1743. No. 1. IOP Publishing, 2021.

Lyaqini, S., M. Nachaoui, and A. Hadri. "An efficient primal-dual method for solving non-smooth machine learning problem." Chaos, Solitons & Fractals 155 (2022): 111754.

Lyaqini, S., and M. Nachaoui. "Identification of Genuine from Fake Banknotes Using an Enhanced Machine Learning Approach." International Conference on Numerical Analysis and Optimization Days. Springer, Cham, 2021.

E. H. Mamdani, H. J. Efstathiou, and K. Sugiyama, "Developments in fuzzy logic control, " in Proc. 23rd Conf. on Decision and Control, pp. 888-893, Las Vegas, V, Dec. 1984.

Nachaoui, M. , 'Etude th'eorique et approximation num'erique d'un probl`eme inverse de transfert de la chaleur (Doctoral dissertation, Universit'e de Nantes (2011)).

Nachaoui, M., A. Chakib, and A. Nachaoui. "An efficient evolutionary algorithm for a shape optimization problem." Applied and Computational Mathematics 19.2 (2020): 220-244.

Nasiboglu, Resmiye, and Rahila Abdullayeva. "Analytical Formulations for the Level Based Weighted Average Value of Discrete Trapezoidal Fuzzy Numbers." arXiv preprint arXiv:1810.05110 (2018).

Nasibov, Efendi N., and Ali Mert. "On methods of defuzzification of parametrically represented fuzzy numbers." Automatic Control and Computer Sciences 41.5 (2007): 265-273.

Yager, Ronald R., and Lotfi A. Zadeh, eds. An introduction to fuzzy logic applications in intelligent systems. Vol. 165. Springer Science & Business Media, 2012.

K. Sugiyama, "Rule-based self-organizing controller," Fuzzy Computing Theory, Hardware and Applications, by M.M. Gupta and T. Yamakawa, Editors, Elsevier Science Pubs., pp. 341-353,1988.

C. Von Altrock, B. Krause, and H. -J. Zimmermann, "Advanced fuzzy logic control of a model car in extreme situations," Fuzzy Sets and Systems, vol. 48, no. 1, pp. 41-52, 26 May 1992.

M. Delgado, A. F. G. Skarmita, and F. Martin, "A fuzzy clusteringbased rapid prototyping for fuzzy rule-based

modelling," IEEE Trans. Fuzzy Systems, vol. 5, no. 2, pp. 223-233, May 1997.

Pattnaik, M. Fuzzy Economic Order Quantity (FEOQ) Model With Units Lost Due to Deterioration. Statistics, Optimization & Information Computing, Vol. 2, no. 3, Aug. 2014, pp. 257-73, doi:10.19139/soic.v2i3.40.

Dijkman, J. G.; van Haeringen, H.; de Lange, S. J. "Fuzzy numbers." J. Math. Anal. Appl. 92 (1983), no. 2, 301-341.

R. R. Yager, "Implementing fuzzy logic controllers using a neural network framework," Fuzzy Sets and Systems, vol. 48, pp. 53-64, 1999.

SHIKHLINSKAYA R. Y. ON A SOLUTION OF ONE FUZZY LOGIC PROBLEM, arXiv:0811.3809v1 [math.LO] 24 Nov 2008

S. Roychowdhury and B. -H. Wang, "Cooperative neighbors in defuzzification," Fuzzy Sets and Systems, vol. 78, no. 1, pp. 37-49, 26 Feb. 1996.

T. J. Procyk and E. H. Mamdani, "A linguistic self-organizing process controller," Automatica, vol. 15, pp. 15-30, 1979.

T. Takagi and M. Sugeno, "Fuzzy identification of systems and its application to modeling and control," IEEE Trans. Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116-132, Jan./Feb. 1985.

W. Pedrycz, Fuzzy Control and Fuzzy Systems, Second Extended Edition, Research Studies Press, England, 1993.

L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, pp. 338-353, 1965.

L. A. Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes," IEEE Trans. Systems, Man and Cybernetics, vol. 3, no. 1, pp. 28-44, Jan. 1973.

L. A. Zadeh, "Fuzzy logic and approximate reasoning," Synthese, vol. 30pp. 407-428, 1975.

L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning," Information Sciences, vol. 8, pp. 199- 249, 1975.

L. A. Zadeh, "Making computers think like people," IEEE Spectrum, vol. 21, no. 8, pp. 26-32, Aug. 1984.

H. -J. Zimmermann, Fuzzy Set Theory and its Applications, 2nd Edition, Kluwer Academic Publishers, 1991.