Hedge algebra is a powerful and flexible tool for handling linguistic information, enabling precise quantitative computations and enhancing the effectiveness of multi-criteria decision-making (MCDM). This study proposes a novel integrated fuzzy MCDM approach that combines an enhanced fuzzy analytic hierarchy process (EFAHP) with a 4-tuple hedge algebra semantics model to assess digital transformation in retail enterprises. In this approach, the EFAHP method is integrated with hedge algebra to determine the priorities of pillars and criteria while providing a rigorous mathematical mechanism to transform ambiguous linguistic evaluations into numerical values. This transformation leverages the semantic structure of linguistic variable domains and incorporates fuzziness measures for both atomic words and intensity-modifying words (hedges). Furthermore, a new consistency index formula is introduced to evaluate the reliability of the EFAHP results, with validation being limited to the case study dataset. The 4-tuple hedge algebra semantic model is then employed to assess and rank the digital transformation levels of retail enterprises in Vietnam. Finally, a sensitivity analysis verifies the robustness of the proposed approach by illustrating how variations in pillar and criterion weights influence enterprise rankings.

Dynamic multi-criteria group decision-making (MCGDM) is widely applied in complex real-world settings where multiple experts evaluate alternatives across diverse criteria under uncertain and evolving conditions. This study proposes a transparent and interpretable linguistic (L-) framework for dynamic MCGDM grounded in hedge algebras (HA), a mathematical formalism that provides explicit algebraic and semantic structures for L-domains. A novel binary L-aggregation operator is developed using the 4-tuple semantic representation of HA, ensuring closure, commutativity, monotonicity, partial associativity, the existence of an identity element, and semantic consistency throughout the aggregation process. Using this operator, a two-stage dynamic decision-making model is developed—(i) L-FAHP for determining the criterion weights in dynamic environments, and (ii) L-FTOPSIS for ranking alternatives—where both methods are formulated on HA L-scales. To address temporal dynamics, a dynamic L-aggregation mechanism is further proposed to integrate current expert judgments with historical evaluations through a semantic decay factor, enabling the controlled attenuation of outdated information. A case study on enterprise digital transformation readiness illustrates that the proposed framework enhances semantic interpretability, maintains stability under uncertainty, and more accurately captures the temporal evolution of expert assessments. These results underscore the practical value and applicability of the HA-based dynamic L-approach in complex decision environments where expert knowledge and temporal variability are critical.