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.
Citation: Ghous Ali, Kholood Alsager. Novel Heronian mean based $ m $-polar fuzzy power geometric aggregation operators and their application to urban transportation management[J]. AIMS Mathematics, 2024, 9(12): 34109-34146. doi: 10.3934/math.20241626
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.
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Ghous Ali, Kholood Alsager. Novel Heronian mean based $ m $-polar fuzzy power geometric aggregation operators and their application to urban transportation management[J]. AIMS Mathematics, 2024, 9(12): 34109-34146. doi: 10.3934/math.20241626
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