Stability Study of a Neuro-Fuzzy Output System Based on Ratio Area Method

Purpose of research is to study the hypothesis about the possibility of changing the type of transition process during training in a neuro-fuzzy inference system based on area ratio method, and to study the properties of weight coefficient influence on its stability.
Methods. An apparatus of fuzzy logic is used for the development of a neuro-fuzzy output system. At the same time, input and output variables are described by triangular membership functions. Mamdani implication model was used in the compositional rule. A linear model of area ratio was used in defasification. The reverse error propagation method was used during training.
Results. In experimental studies, it was found that the proposed neuro-fuzzy model based on area ratio method allows to change the type of transition process, namely, to transform oscillatory process into an aperiodic (monotonic) process. In experimental studies, it was also found that the stability of neuro-fuzzy output system is more influenced by the weight coefficient determined in calculating the total area of membership output functions. Thus, the obtained results prove: first, that the proposed neuro-odd output system ensures the transformation of transfer characteristics, and second, ensures its stability in a given range of weight coefficient characteristics.
Conclusion: The architecture of an adaptive neuro-fuzzy output system based on a linear method of area ratio is described. A distinctive feature of the proposed architecture is the use of an odd system of triangular accessory functions at inputs and outputs. Analysis of the simulation process of its training showed that it s important to ensure stability during training. It is also necessary to establish permissible values of the weight coefficient, numerical values of which in its turn affect the transformation of transfer characteristics of a neuro-fuzzy output system.

1. Shahmoradi S., Shouraki S.B. Evaluation of a novel fuzzy sequential pattern recognition tool (fuzzy elastic matching machine) and its applications in speech and handwriting recognition. Applied Soft Computing, 2018, no. 62, pp. 315-327.

2. Titov V.S., Bobyr M.V., Antsiferov A.V. Adaptivnyi mul'tisetevoi algoritm nechetkologicheskogo vyvoda v zadachakh upravleniya oborudovaniem s ChPU [Adaptive multinetwork fuzzy inference algorithm in problems of control of equipment with CNC]. Mekhatronika, avtomatizatsiya, upravlenie = Mechatronics, Automation, Control. 2013, no. 5, pp. 18-23.

3. Hodgett R.E., Siraj S. SURE: A method for decision-making under uncertainty. Expert Systems with Applications, 2019, no. 115, pp. 684-694.

4. Temur G.T. A novel multi attribute decision making approach for location decision under high uncertainty. Applied Soft Computing, 2016, no. 40, pp. 674-682.

5. Bobyr M.V., Titov V.S., Akulshin G.Yu. Modelirovanie nechetko-logicheskikh sistem upravleniya na osnove myagkikh arifmeticheskikh operatsii [Modeling of fuzzy-logical control systems based on soft arithmetic operations]. Vestnik komp'yuternykh i informatsionnykh tekhnologii = Bulletin of Computer and Information Technologies, 2013, no. 3 (105), pp. 29-35.

6. Annabestani M., Naghavi N. Nonlinear identification of IPMC actuators based on ANFIS-NARX paradigm. Sensors and Actuators, A: Physical, 2014, no. 209, pp. 140-148.

7. A. Piegat Fuzzy Modeling and Control. Physica-Verlag, Heidelberg, 2001.

8. Dolatabadi M., Mehrabpour M., Esfandyari M., Alidadi H., Davoudi M. Modeling of simultaneous adsorption of dye and metal ion by sawdust from aqueous solution using of ANN and ANFIS. Chemometrics and Intelligent Laboratory Systems, 2018, no. 181, pp. 72-78.

9. Bobyr M.V., Milostnaya N.A. Mekhanizm adaptatsii nechetkoi sistemy vyvoda na osnove geneticheskogo algoritma [Adaptation mechanism of a fuzzy inference system based on a genetic algorithm]. Promyshlennye ASU i kontrollery = Industrial ACS and Controllers, 2015, no. 3, pp. 27-32.

10. Rezakazemi M., Dashti A., Asghari M., Shirazian S. H2-selective mixed matrix membranes modeling using ANFIS, PSO-ANFIS, GA-ANFIS. International Journal of Hydrogen Energy, 2017, no. 42, pp. 15211-15225.

11. Mottahedi A., Sereshki F., Ataei M. Overbreak prediction in underground excavations using hybrid ANFIS-PSO model. Bioresource Technology, 2018, no. 267, pp. 634-641.

12. Karaboga D., Kaya E. An adaptive and hybrid artificial bee colony algorithm (ABC) for ANFIS training. Applied Soft Computing, 2016, no. 49, pp. 423-436.

13. Haznedar B., Kalinli A. Training ANFIS structure using simulated annealing algorithm for dynamic systems identification. Neurocomputing,. 2018, no. 302, pp. 66-74.

14. Boulkaibet I., Belarbi K., Bououden S., Chadli M., Marwala T. An adaptive fuzzy predictive control of nonlinear processes based on Multi-Kernel least squares support vector regression. Applied Soft Computing, 2018, no. 73, pp. 572-590.

15. Li L.J., Su H.Y., Chu J. Generalized predictive control with online least squares support vector machines. Acta Automatica Sinica, 2007, no. 33, pp. 1182-1188.

16. Vasileva-Stojanovska T., Vasileva M., Malinovski T., Trajkovik V. An ANFIS model of quality of experience prediction in education. Applied Soft Computing, 2015, no. 34, pp. 129-138.

17. Vemuri N.R. Mutually exchangeable fuzzy implications. Information Sciences, 2015, no. 317, pp. 1-24.

18. Laha A. Building contextual classifiers by integrating fuzzy rule based classification technique and k-nn method for credit scoring. Adv. Eng. Inf., 2007, no, 21, pp. 281-291.

19. Casale G., Pérez J.F., Wang W. QD-AMVA: Evaluating systems with queuedependent service requirements. Perform. Eval., 2015, no.91, pp. 80-98.

20. Bobyr, M.V., Milostnaya, N.A., Kulabuhov, S.A. A method of defuzzification based on the approach of areas ratio. Applied Soft Computing, 2017, no. 59, pp.19-32.

21. Bobyr M.V., Milostnaya N.A. Analiz ispol'zovaniya myagkikh arifmeticheskikh operatsii v strukture nechetko-logicheskogo vyvoda [Analysis of the use of soft arithmetic operations in the structure of fuzzy inference]. Vestnik komp'yuternykh i informatsionnykh tekhnologii = Bulletin of Computer and Information Technologies, 2015, no. 7 (133), pp. 7-15.

22. Bobyr M.V., Emelyanov S.G. A nonlinear method of learning neuro-fuzzy models for dynamic control systems. Applied Soft Computing, 2020, vol. 88, p. 106030.

23. Bobyr M.V., Yakushev A.S., Dorodnykh A.A. Fuzzy devices for cooling the cutting tool of the cnc machine implemented on FPGA. Measurement, 2020, vol. 152, p. 107378.

24. Titov V.S., Bobyr M.V., Antsiferov A.V. Adaptivnyi mul'tisetevoi algo-ritm nechetko-logicheskogo vyvoda v zadachakh upravleniya oborudovaniem S ChPU [Adaptive multi-network fuzzy inference algorithm in control problems for CNC equipment]. Mekhatronika, avtomatizatsiya, upravlenie = Mechatronics, Automation, Control. 2013, no. 5, pp. 18-23.

25. Bobyr M.V. Metody postroeniya funktsii prinadlezhnostei dlya nechetkikh baz znanii [Methods for constructing accessory functions for fuzzy knowledge bases]. Promyshlennye ASU i kontrollery = Industrial ACS and Controllers, 2011, no. 2, pp. 27-32.