A Matrix Norm-Based Pythagorean Fuzzy Metric and its Application in Merec-Swara-Vikor Framework for Solar Panel Selection

Due to the escalating electricity demand from industrialization and modernization, it is imperative to explore clean and sustainable energy sources. Solar energy has become a feasible solution for this surging demand. Solar panels, vital components of solar power systems, are crucial in converting sunlight into electricity. However, selecting the most suitable solar panel is a complex task involving subjective and measurable parameters involving uncertainties. To address the uncertainties and ambiguities in real-life problems, the theory of Pythagorean fuzzy sets with distance measures has emerged as a flexible and superior tool. Nevertheless, many existing distance functions often fail to meet necessary metric conditions, leading to inaccurate and unreasonable outcomes. These Limitations are being pointed out by many literature. In addition, we observe a serious drawback of parameter dependency of some existing measures. This paper proposes a novel metric for Pythagorean fuzzy sets using the matrix norm to overcome these drawbacks. Additionally, we discuss various mathematical properties and provide geometrical representations for the proposed distance measure. To demonstrate the superiority of the proposed measure, we conduct a comparative study against existing distance measures. Furthermore, we develop a Pythagorean fuzzy-Method based on the Removal Effects of Criteria- Stepwise Weight Assessment Ratio Analysis-Vlse Kriterijumska Optimizacija Kompromisno Resenje (PF-MEREC-SWARA-VIKOR) method for selecting solar panel systems. Our approach incorporates the MEREC method for objective criteria, utilizes the SWARA method to calculate subjective weights, and employs the VIKOR method in the Pythagorean fuzzy context to determine the preference order of alternatives. We conduct sensitivity analysis and comparative studies with existing developed methods to validate our method. The results highlight the effectiveness and advantages of our novel approach in selecting solar panels