An $m$-polar fuzzy ( $m$F) model offers a practical framework for decision-making by providing higher flexibility in handling uncertainties and preferences. The ability of $m$F sets to tackle multiple reference points permits for a more nuanced analysis, leading to more accurate results in complex decision scenarios. This study was mainly devoted to introducing three novel aggregation operators (AGOs) for multi-criteria decision-making (MCDM) based on generalized geometric Heronian mean (GGHM) operations comprise the concept of $m$F sets. The presented operators consisted of the weighted $m$F power GGHM (W $m$FPGGHM), ordered weighted $m$F power GGHM averaging (OW $m$FPGGHM), and hybrid $m$F power GGHM (H $m$FPGGHM) operators. Some essential fundamental properties of the proposed AGOs were investigated: idempotency, monotonicity, boundedness, and Abelian property. Furthermore, an algorithm based on the initiated W $m$FPGGHM operators was developed to address diverse daily-life MCDM scenarios. Next, to validate the efficiency of the established algorithm, it was implemented in a daily-life MCDM problem involving urban transportation management. At last, a sensitivity analysis of the initiated AGOs was provided with existing $m$F set-based operators involving Dombi, Yager, and Aczel-Alsina's operations-based AGOs.

In this article, we presented two novel approaches for group decision-making (GDM) that were derived from the initiated linguistic $q$-rung orthopair fuzzy Aczel-Alsina weighted arithmetic (L $q$-ROFAAWA) aggregation operator (AgOp) using linguistic $q$-rung orthopair fuzzy numbers (L $q$-ROFNs). To introduce these GDM techniques, we first defined new operational laws for L $q$-ROFNs based on Aczel-Alsina $t$-norm and $t$-conorm. The developed scalar multiplication and addition operations of L $q$-ROFNs addressed the limitations of operations when $q=1$. The first proposed GDM methodology assumed that both experts' weights and attribute weights were fully known, while the second technique assumed that both sets of weights were entirely unknown. We also discussed properties of L $q$-ROFNs under the L $q$-ROFAAWA operators, such as idempotency, boundedness, and monotonicity. Furthermore, we solved problems related to environmental and economic issues, such as ranking countries by air pollution, selecting the best company for bank investments, and choosing the best electric vehicle design. Finally, we validated the proposed GDM approaches using three validity tests and performed a sensitivity analysis to compare them with preexisting models.