Abstract
This paper proposes the fuzzy interval bisection method for solving nonlinear fuzzy equations that is applicable to cyber-physical systems. The presented method is based on the authors’ previous research in solving equations that have inaccurate coefficients and expands the interval bisection approach from the interval data to fuzzy one. The proposed method allows the construction of the approximation for the membership function of the equation’s root that involves all available input fuzzy information on the equation’s coefficients. The conceptual details of migrating from ordinary to fuzzy intervals are briefly discussed. The advantages of the new method are considered: the possibility to detect the optimal moment to stop the iterative procedure of fuzzy equation solving and a way to propagate the nested intervals of membership functions when searching the root. An example of approach using is presented for the cyber-physical system containing nonlinear sensors for obtaining information from the object under control.
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Acknowledgments
The study was partially funded by grant No 19–71-00127 of the Russian Science Foundation (fuzzy interval approach for solving fuzzy equations) and by grant No 19–31-90165 of the Russian Foundation for Basic Research (code development, computations carrying out).
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Semenov, K., Tselishcheva, A. (2022). Solving Fuzzy Equations Based on Fuzzy Interval Bisection Method for Intelligent Data Processing in Cyber-Physical Systems. In: Vasiliev, Y.S., Pankratova, N.D., Volkova, V.N., Shipunova, O.D., Lyabakh, N.N. (eds) System Analysis in Engineering and Control. SAEC 2021. Lecture Notes in Networks and Systems, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-030-98832-6_26
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