Risk Assessment Indicator Weighting for Deep Foundation Pit Construction Using Dual Probabilistic Linguistic Term Sets

In deep foundation pit risk assessment, expert ratings are often aggregated without preserving the dispersion of individual opinions, yet such dispersion directly reflects the reliability of the assessment. To address this shortcoming, this study integrates dual probabilistic linguistic term sets (DPLTS), entropy theory, and the best–worst method (BWM). In this DPLTS framework, the membership set L(p) encodes the central tendency of expert ratings (the assessed risk level), while the non-membership set U(q) encodes the dispersion of ratings, serving as a proxy for expert disagreement—a source of uncertainty that is as critical as the risk level itself for decision-making. The least common multiple expansion method standardizes information length. Secondary indicator weights are determined using fuzzy entropy and cross-entropy, while primary indicator weights are derived via BWM, forming a combined subjective-objective weighting model. Hierarchical aggregation yields the overall risk expectation value. A case study assesses the project as Level III (moderate) risk, with a low variance of 0.0503 indicating strong expert consensus. The risk expectation varies by less than 4% under different entropy measures, confirming robustness. Comparative analysis with fuzzy comprehensive evaluation and CRITIC–Grey system methods shows consistent results, with all three identifying excavation and support as key risk indicators. The proposed method provides not only a reliable risk level but also a quantitative measure of expert agreement, offering enhanced support for targeted risk management.