This study introduces a novel group decision-making (GDM) framework under a complex spherical fuzzy environment, extending the golden section (GS) principle from a one-dimensional interval to a high-dimensional data center to address the core challenges of determining decision-maker (DM) weights and ranking alternatives. A rigorous theoretical justification is established, comprising four formal properties (self-similarity, optimal balance, convergence, and geometric center) that mathematically justify the GS ratio as aggregation weights for combining minimum and maximum matrices. An entropy-based method quantifies data quality for DM weight allocation, while a normalized Euclidean distance ranks the options. Eight experimental findings demonstrate the superiority of the GS-based approach: it enhances DM weight stability by a factor of 4.76 (376%) and improves ranking robustness by 8.33% compared to an arithmetic-mean-based center; against a direct extreme-value method, it achieves a 9.74-fold (874%) improvement in weight discrimination and a 0.42% sharper distinction among top alternatives. Dynamic experiments validate that the GS point 0.618 serves as a pivotal partition within $[0, 1]$, with stable ordinal relations over 61.2% of the parameter space. Sensitivity analysis under $\pm50%$ weight variations (18 scenarios) confirms that the optimal alternative remains first in 100% of scenarios with minimal RC variability (std = 0.0013/0.0033). Comparisons with CSFN-TOPSIS and entropy-weighted methods show that the proposed method achieves the highest ranking discrimination (RDI = 0.8777). The proposed framework provides a robust, theoretically grounded methodology for reliable decision support in applications such as software quality assessment.
Citation: Chuan Yue. A golden-section-Based group decision framework for software quality assessment under complex spherical fuzzy environments[J]. AIMS Mathematics, 2026, 11(7): 20815-20874. doi: 10.3934/math.2026846
This study introduces a novel group decision-making (GDM) framework under a complex spherical fuzzy environment, extending the golden section (GS) principle from a one-dimensional interval to a high-dimensional data center to address the core challenges of determining decision-maker (DM) weights and ranking alternatives. A rigorous theoretical justification is established, comprising four formal properties (self-similarity, optimal balance, convergence, and geometric center) that mathematically justify the GS ratio as aggregation weights for combining minimum and maximum matrices. An entropy-based method quantifies data quality for DM weight allocation, while a normalized Euclidean distance ranks the options. Eight experimental findings demonstrate the superiority of the GS-based approach: it enhances DM weight stability by a factor of 4.76 (376%) and improves ranking robustness by 8.33% compared to an arithmetic-mean-based center; against a direct extreme-value method, it achieves a 9.74-fold (874%) improvement in weight discrimination and a 0.42% sharper distinction among top alternatives. Dynamic experiments validate that the GS point 0.618 serves as a pivotal partition within $[0, 1]$, with stable ordinal relations over 61.2% of the parameter space. Sensitivity analysis under $\pm50%$ weight variations (18 scenarios) confirms that the optimal alternative remains first in 100% of scenarios with minimal RC variability (std = 0.0013/0.0033). Comparisons with CSFN-TOPSIS and entropy-weighted methods show that the proposed method achieves the highest ranking discrimination (RDI = 0.8777). The proposed framework provides a robust, theoretically grounded methodology for reliable decision support in applications such as software quality assessment.
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Chuan Yue. A golden-section-Based group decision framework for software quality assessment under complex spherical fuzzy environments[J]. AIMS Mathematics, 2026, 11(7): 20815-20874. doi: 10.3934/math.2026846
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