An Improved TOPSIS Method Using Fermatean Fuzzy Sets for Techno-Economic Evaluation of Multi-Type Power Sources

Scientific planning and optimal development of multi-type power sources are critical prerequisites for supporting the robust evolution of emerging power systems. However, existing techno-economic evaluation methods often face challenges such as higher-order uncertainty and weight conflicts, making it difficult to provide reliable support for comparing and selecting power source schemes. To address this, this paper proposes an improved Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on Fermatean Fuzzy Sets (FFS) for techno-economic evaluation of multi-type power sources. First, building on the traditional TOPSIS framework, we introduce Fermatean Fuzzy Sets to construct a FF Hybrid Weighted Distance (FFHWD) measure. This measure simultaneously captures the subjective importance of evaluation indicators and decision-makers’ risk preferences. Second, we design a subjective-objective coupled weighting strategy integrating Fuzzy Analytic Hierarchy Process (FAHP) and Entropy Weight Method (EWM) to achieve dynamic weight balancing, effectively mitigating biases caused by single weighting approaches. Finally, the FFHWD is integrated into the improved TOPSIS framework by defining FF positive and negative ideal solutions. The comprehensive closeness coefficients of each power source scheme are calculated to enable robust ranking and optimal selection of multi-type power source alternatives. Empirical analysis of five representative power generation technologies—thermal power, hydropower, wind power, photovoltaics (PV), and energy storage—demonstrates the following comprehensive techno-economic ranking: hydropower > photovoltaics > thermal power > wind power > energy storage. Hydropower achieves the highest closeness coefficient (−0.4198), whereas energy storage yields the lowest value (−2.8704), effectively illustrating their respective advantages and limitations within the evaluation framework. This research provides scientific decision-making support and methodological references for optimizing multi-type power source configurations and planning new power systems.