The global community thoroughly evaluates several renewable energy sources but has yet to completely replace conventional energy sources. Thermal power plants (TPPs) are the predominant electrical energy generators among the primary energy sources. Consequently, the researcher had the critical task of conducting a reliability study of TPPs throughout the design and production phase. The evaluation of the TPPs’ system reliability becomes a complex and uncertain challenge owing to the uncertainty associated with the reliability of the TPPs’ components. The assessment of component reliability in a complex system relies on recorded data, which compels technologists to scrutinize the idea of imprecise reliability analysis. This article presents a novel approach to assessing the system’s reliability under uncertain settings. It focuses on performing arithmetic operations on triangular Pythagorean fuzzy numbers (TPFNs) and trapezoidal Pythagorean fuzzy numbers (TrPFNs). TPFNs and TrPFNs are extensions of Pythagorean fuzzy numbers that provide a more precise depiction of uncertainty than standard fuzzy sets. The proposed arithmetic operations evaluate the reliability of different system topologies, including series, parallel, and complex systems. The numerical demonstration is shown by using the suggested processes to assess the reliability of a TPP. The effectiveness of the suggested arithmetic operations on TPFNs and TrPFNs is shown by their ability to decrease uncertainty compared to the conventional approach of using cuts of TPFN and TrPFN.
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