Linguistic q-rung orthopair fuzzy group decision-making approach based on new bidirectional projection and generalized knowledge measure

In response to the challenges of handling linguistic uncertainty in multi-criteria group decision-making (MCGDM), this paper introduces a novel decision framework based on linguistic q-rung orthopair fuzzy (Lq-ROF) sets. The motivations from the need to systematically address ambiguity and inconsistency in linguistic evaluations provided by decision-makers. To this end, the study develops three main methodological contributions. Firstly, a normalized bidirectional projection measure (NBDP) and its weighted extension (WNBDP) are proposed to resolve ranking inconsistencies in linguistic environments. Secondly, an axiomatized knowledge entropy measure for Lq-ROF information is established, enabling fine-grained differentiation among linguistic assessments and facilitating dynamic expert weighting. Thirdly, a non-linear programming model is formulated to objectively derive both attribute and expert weights by integrating bidirectional projection with generalized entropy principles. The proposed framework is rigorously evaluated through comparative studies against established methods, including aggregation-based techniques, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Evaluation based on Distance from Average Solution (EDAS), and Complex Proportional Assessment (COPRAS). Results validate the robustness and theoretical advantages of the approach, confirming its effectiveness in quantifying linguistic uncertainty and delivering consistent decision support in complex MCGDM contexts.