Methodology integrating semantic invariance with enhanced TOPSIS for multi-granular unbalanced probabilistic linguistic group decision-making

Purpose This study proposes a methodology incorporating granularity unification, two metrics quantifying distance and fuzziness, and an enhanced technique for order of preference by similarity to ideal solution (TOPSIS) method for multi-granular unbalanced probabilistic linguistic group decision-making. The proposed approach mitigates errors founding in existing granularity unification and simultaneously enhances the discrimination and stability of the decision outcomes. Design/methodology/approach First, a novel cubic-polynomial linguistic scale function is introduced to unify the granularity of multi-granular unbalanced probabilistic linguistic terms (UPLTSs) while preserving semantic invariance. Second, by exploiting this function and the Hellinger distance, two metrics referred to as distance and degree of fuzziness are developed to derive expert weights. Attribute weights are then obtained from a two-stage fuzziness-based procedure that embeds a quadratic programming model. Finally, TOPSIS is enhanced by introducing weighted separations of alternatives from the positive ideal solution and negative ideal solution, and extended to the UPLTS environment. Findings The proposed methodology is first validated through a case study on energy storage technology selection. The results demonstrate its effectiveness compared with the Marcos, CoCoSo, and VIKOR methods. Moreover, it exhibits markedly greater robustness than the classical TOPSIS method. Originality/value A novel granularity-unification method for multi-granular UPLTSs is introduced, while the classical TOPSIS is concurrently enhanced and extended to this setting, with the fuzziness measure embedded in a two-stage weighting framework that integrates a quadratic programming model.