Abstract
In this paper, we reported a mathematical model using fuzzy relation equations to describe the fault diagnosis based on cause and effect analysis. Generally, with the solution set of the fuzzy relation equations being non-convex, in order to solve such problems, we propose a genetic algorithm and present a computer simulation example to evaluate the performance of the proposed algorithm.
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References
Bowles, J.B., Pelaez, C.E.: Application of fuzzy logic to reliability engineering. Proc. IEEE 83(3), 435–449 (1995)
Peng, Y., Reggia, J.A.: Abductive inference models for diagnostic problem-solving. Springer, New York, Inc (1990)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1975)
Zhang, J., Xu, Y.: Application analysis of fuzzy-relation equation in fault diagnosis. J. China Univ. Min. Technol. 28(5), 209–506 (1999)
Cao, B.Y.: Optimal models and methods with fuzzy quantities. Springer, Berlin Heidelberg (2010)
Wang, P.Z., Zhang, D.Z., Sanchez, E., et al.: Latticized linear programming and fuzzy relation inequalities. J. Math. Anal. Appl. 159(1), 72–87 (1991)
Holland, JH.: Adaptation in natural and artificial system. MIT Press, 1992
De Jong, KA.: An analysis of the behavior of a class of genetic adaptive systems. Ann Arbor Univ. of Mich press, 1975
Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30(1), 38–48 (1976)
Fang, S.C., Li, G.: On the resolution of finite fuzzy relation equations. Int. Math. J. 3(1), 59–72 (2003)
Michalewicz, Z.: Genetic algorithms + data structures = evolution program. Springer, Berlin (1996)
Xueping, W.: A method to solve fuzzy relational equation in lattice [0,1]. Appl. Math. J. Chin. Univ. (Ser. A) 15(2), 127–133 (2000)
Lin, H., Yang, X.: A method for checking the minimal solution of fuzzy equations. J. Sichuan Norm. Univ. (Nat. Sci.) 41(2), 224–229 (2018)
Acknowledgements
We would like to express our appreciation to the editor and the anonymous reviewers for their valuable comments, which have been very helpful in improving the paper. This work is supported by the Natural Science Foundation of Guangdong Province (2016A030307037, 2016A030313552), the General Fund Project of the Ministry of Education and Social Science Research (16YJAZH081).
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This paper is recommended by Yu-bin Zhong who is a professor of Guangzhou University in China.
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Mai, H., Cao, By., Zhou, XG. (2020). The Application of Fuzzy Relational Equations and Genetic Algorithm in Fault Diagnosis Problem. In: Cao, By. (eds) Fuzzy Information and Engineering-2019. Advances in Intelligent Systems and Computing, vol 1094. Springer, Singapore. https://doi.org/10.1007/978-981-15-2459-2_15
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DOI: https://doi.org/10.1007/978-981-15-2459-2_15
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