Novel Heronian mean based $m$-polar fuzzy power geometric aggregation operators and their application to urban transportation management

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.