Accurate and robust determination of the electron temperature (Te) and electron density (ne) in atmospheric-pressure non-equilibrium plasmas is often hindered by inconsistencies between values derived independently from continuum and line emission spectra. This study introduces a unified diagnostic framework that resolves this discrepancy through weighted multiobjective optimization. Assuming a two-temperature generalized electron energy distribution function (GEEDF), bremsstrahlung continuum and argon line spectra are fitted simultaneously, with a weight parameter w introduced to balance their respective contributions. The optimal weight is systematically identified using statistical criteria and Pareto analysis, thereby defining a trust region in which both spectral features are reproduced consistently. The method is applied to a closed-channel dielectric barrier discharge (DBD) and an atmospheric-pressure plasma jet (APPJ). The analysis yields a consistent bulk electron temperature of Te ≈ 0.6 eV, which is lower than typical estimates obtained from single-Maxwellian line-ratio assumptions, and an electron density of ne ∼ 10^{12} - 10^{13} cm^{-3} that accurately reflects variations in input voltage and spatial position. These results demonstrate that the weighted unified analysis effectively constrains the EEDF shape, mitigates parameter overestimation, and provides a robust diagnostic tool for characterizing non-equilibrium plasma kinetics.
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