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    Area of Science:

    • Computational Intelligence
    • Fuzzy Systems Engineering
    • Signal Processing

    Background:

    • Type-3 fuzzy logic systems (T3-FLSs) are increasingly applied in diverse fields, yet their fundamental theory, real-time applications, learning mechanisms, and noise robustness remain underexplored.
    • Existing research primarily focuses on T3-FLS applications, neglecting core theoretical advancements and practical online implementations.

    Purpose of the Study:

    • To simplify T3-FLSs by introducing novel membership functions (MFs) and type reduction methods.
    • To develop new online learning schemes for T3-FLSs, extending the adaptive neuro-fuzzy inference system (ANFIS) concept to T3-FLSs (T3-ANFIS).
    • To enhance robustness against impulsive and non-Gaussian noises using a T3-FLS-based correntropy Kalman filter (CKF).

    Main Methods:

    • Proposed a simplified type reduction for T3-FLSs.
    • Developed a noniterative learning scheme for T3-ANFIS, enabling adaptation of rule and MF parameters.
    • Integrated T3-FLS with a correntropy Kalman filter, featuring an online updated kernel size and nonsingleton fuzzification for improved noise handling.

    Main Results:

    • Demonstrated the feasibility and superiority of the proposed T3-FLS through simulations on real datasets.
    • Verified the enhanced robustness of the T3-FLS-based CKF against impulsive noises compared to traditional Kalman filters.
    • Showcased the effectiveness of the online updated kernel size and nonsingleton fuzzification in improving data noise tolerance.

    Conclusions:

    • The simplified T3-FLS offers advancements in theory and online learning capabilities.
    • The T3-FLS-based CKF provides superior robustness against impulsive noise in real-time applications.
    • The proposed methods represent a significant step towards more reliable and adaptable fuzzy logic systems in noisy environments.