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PID Controller Fuzzy Reliability for Hydropower System under Intuitionistic Fuzzy Environment

  • Vidhi Tiwari ORCID logo , Akshay Kumar ORCID logo and Mangey Ram ORCID logo EMAIL logo
Published/Copyright: November 19, 2025
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Abstract

This work considers the intuitionistic fuzzy approach, using the Rayleigh distribution to define failure parameters and trapezoidal intuitionistic fuzzy numbers (TrIFNs) to characterize fuzzy variables. We calculate the reliability function using the universal (probability) generating function. We further apply the method to a hydropower system subjected to a PID (proportional-integral-derivative) controller by evaluating intuitionistic fuzzy reliability and the sensitivity of fuzzy reliability. We also use the average operator of TrIFNs with equal weights to analyze intuitionistic fuzzy reliability and sensitivity more effectively. We present the results in graphical and tabular form for greater clarity.

MSC 2020: 90B25; 68M15

Acknowledgements

We would like to thank Graphic Era Deemed to be University, Dehradun, India for their valuable contribution and support in the completion of this research.

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Received: 2025-02-04
Revised: 2025-10-28
Accepted: 2025-11-06
Published Online: 2025-11-19

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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