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Design of Discrete Noniterative Algorithms for Center-of-Sets Type Reduction of General Type-2 Fuzzy Logic Systems

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Abstract

According to the alpha-planes expression theory of general type-2 fuzzy sets, this paper completes the center-of-sets (COS) type reduction and defuzzification for general type-2 fuzzy logic systems (GT2 FLSs). In fact, it still remains an open problem by comparing the prevalent Karnik–Mendel (KM) algorithms and other types of alternative noniterative algorithms. The modules of fuzzy inference, COS type reduction, and defuzzification of Mamdani-type GT2 FLSs on the basis of Nagar-Bardini algorithms, Nie-Tan algorithms, and Begian-Melek-Mendel algorithms are also provided. Six simulation examples are provided to illustrate the performances of corresponding noniterative algorithms. In contrast to the KM algorithms, the suggested three types of noniterative algorithms can get faster convergence speeds.

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Acknowledgements

The paper is partially sponsored by the National Natural Science Foundation of China (NSFC) (61973146, 61773107), the Youth Fund of Education Department of Liaoning Province (LJKQZ2021143), the Doctoral Start-up Foundation of Liaoning Province (2021-BS-258), and the Talent Foundation of Liaoning University of Technology (xr2020002). The author is grateful to the well-known scholar J. M. Mendel, who has given many invaluable advices.

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  1. College of Science, Liaoning University of Technology, City of Jinzhou, 121001, China

    Yang Chen, Chenxi Li & Jiaxiu Yang

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  1. Yang Chen
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Correspondence to Yang Chen.

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Chen, Y., Li, C. & Yang, J. Design of Discrete Noniterative Algorithms for Center-of-Sets Type Reduction of General Type-2 Fuzzy Logic Systems. Int. J. Fuzzy Syst. 24, 2024–2035 (2022). https://doi.org/10.1007/s40815-022-01256-5

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