In Dynamic Systems with Fuzzy α - Cutting Determination of Membership Function Ranges

Abstract

Uncertainties and inaccuracies in the membership function value ranges defined by the expert in dynamic systems cause serious errors in system output. In this study, fuzzy α-cutting technique was used to determine the ranges of membership functions on the universal cluster and neighborhood values of normal values were calculated for different α cutting coefficients and then neighborhood values were adjusted according to determined step values. Thus, while determining the value range of membership function in dynamic systems, it will be possible to talk about its neighborhood in the values that serve the same purpose. Operation in the dynamic process as wind power installation for Turkey wind energy interval value set in the potential atlas used and α cutting techniques of the gap on the universal set of the determined value with re-calculation and determination are provided.

Keywords

• Dynamic systems,α - Cutting technique,Fuzzy cluster,Membership function

References

1. [1] Kandil, A., El-Tantawy, O.A., El-Sheikh, S.A., El-Sayed, Sawsan S.S. (2017). Fuzzy soft connected sets in fuzzy soft topological spaces II, Journal of the Egyptian Mathematical Society, 25, 171–177.
2. [2] Alan, A.Y. (2003). Nispi Mantik (Fuzzy Logic), International Seminar Group, Ludwigshaven, Germany
3. [3] Kissi, M., Ramdani, M., Tollabi, M. and Zakarya, D. (2004). Determination of fuzzy logic membership functions using genetic algorithms: application to structure-odor modeling, Journal of Molecular Modeling, 10 (5-6): 335-341.
4. [4] Kim, J.W., Kim, B.M. and Kim, J.Y. (1998). Genetic algorithm simulation approach to determine membership functions of fuzzy traffic controller, Electronics Letters, 34 (20): 1982- 1983.
5. [5] Mondelli, G., Castellano, G., Attolico, V. and Distante, C. (1998). Parallel genetic evolution of membership functions and rules for a fuzzy controller, High-Performance Computing and Networking Lecture Notes in Computer Science, 1401, 922-924.
6. [6] Kim, J.H., Seo, J.Y. and Kim, G.C. (1996). Estimating membership functions in a fuzzy network model for part-of-speech tagging, Journal of Intelligent & Fuzzy Systems, 4 (4): 309-320.
7. [7] Singpurwalla, N.D. (2004). Membershipfunctions and probability measures of fuzzy ets – Rejoinder, Journal of the American Statistical Association, 99 (467): 884-889.
8. [8] Lindley, D.V. (2004). Membership functions and probability measures of fuzzy sets – Comment, Journal of the American Statistical Association, 99 (467): 877-879.

9. [9] Simon, D. (2002). Sum normal optimization of fuzzy membership functions, International Journal of Uncertainty fuzzyness and Knowledge-Based Systems, 10 (4): 363-384.
10. [10] Sancho-Royo, A. and Verdegay, J.L. (1999). Methods for the construction of membership functions, International Journal of Intelligent Systems, 14 (12): 1213-1230.
11. [11] Chen, S.M., Kao, C.H. and Yu, C.H. (2002). Generating fuzzy rules from training data containing noise for handling classification problem, Cybernetics and Systems, 33 (7): 723-748.
12. [12] Cho, Y., Lee, K., Yoo, J. and Park, M. (1998). Autogeneration of fuzzy rules and membership functions for fuzzy modelling using rough set theory, IEE Proceedings-Control Theory and Applications, 145 (5): 437-442.
13. [13] Lin, C.J. and Ho, W.H. (2005). An asymmetrysimilarity- measure-based neural fuzzy inference system, Fuzzy Sets and Systems, 152 (3): 535- 551.
14. [14] Wu, T.P. and Chen, S.M. (1999). A new method for constructing membership functions and fuzzy rules from training examples, IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 29 (1): 25-40.
15. [15] Halgamuge, S.K., Poechmueller, W. and Glesner, M. (1995). An alternative approach for generation of membership functions and fuzzy rules based on radial and cubic basis functions networks, International Journal of Approximate Reasoning, 12 (3-4): 279-298.
16. [16] Abebe, A. J., GUİNOT, V. and Solomatine, D. P. (2000). Fuzzy alpha-cut vs. Monte Carlo techniques in assessing uncertainty in model parameters, Proc. 4-th International Conference on Hydroinformatics, Iowa City, USA.
17. [17] Turnbull, H. and Omenzetter, P. (2017). Fuzzy finite element model updating of a laboratory wind turbine blade for structural modification detection, Procedia Engineering, 199, 2274–2281.
18. [18] Bojadziev, G. and Bojadziev, M. (1991). Fuzzy Sets, Fuzzy Logic, Applications, World Scientific, London.
19. [19] Bai, Y. and Wang, D. (2006). Fundamentals of Fuzzy Logic Kontrol Fuzzy Sets,Fuzzy Rules and Defuzzifications, Advanced Fuzzy Logic Technologies InIndustrial Applications, Springer.
20. [20] Internet: General Directorate of Meteorology, (2017). https://www.mgm.gov.tr/genel/ruzgar-atlasi.aspx