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<p>The dual hesitant Fermatean fuzzy set (DHFFS) as a newfangled generalization of fuzzy set theory, allows for more flexibility in managing ambiguous data during the decision-making process. This article first intrigues the trapezoidal Fermatean hesitant fuzzy number (T-FHFN) as a trapezoidal form of the DHFFS to cope with the uncertainty embedded in real-world optimization issues. Considering environmental, economic, and social assets in a single framework, we devise a sustainable 4-D transportation system to optimize travel cost and time while reducing carbon footprints. For the aforementioned model, T-FHFN is employed to depict uncertainty. In addition, safety constraints are also incorporated into the proposal. Further, we employed fuzzy programming (FP), and a weighted sum technique (WST) to achieve the best answer of the devised model. A case study centred on the shipment of hazardous chemicals is utilized to further explain the significance of the suggested model. To strengthen the study of the suggested sustainable transportation framework, sensitivity evaluations of the parameters involved are also examined. Lastly, conclusions are made along with the future prospects of the model.</p>

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A sustainable 4-dimensional transportation system under dual hesitant Fermatean fuzzy configuration with safety constraints

  • 期刊论文

  • 发表日期：

    2025年4月24日

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  • M. K. Sharma,
  • Sadhna Chaudhary

摘要

The dual hesitant Fermatean fuzzy set (DHFFS) as a newfangled generalization of fuzzy set theory, allows for more flexibility in managing ambiguous data during the decision-making process. This article first intrigues the trapezoidal Fermatean hesitant fuzzy number (T-FHFN) as a trapezoidal form of the DHFFS to cope with the uncertainty embedded in real-world optimization issues. Considering environmental, economic, and social assets in a single framework, we devise a sustainable 4-D transportation system to optimize travel cost and time while reducing carbon footprints. For the aforementioned model, T-FHFN is employed to depict uncertainty. In addition, safety constraints are also incorporated into the proposal. Further, we employed fuzzy programming (FP), and a weighted sum technique (WST) to achieve the best answer of the devised model. A case study centred on the shipment of hazardous chemicals is utilized to further explain the significance of the suggested model. To strengthen the study of the suggested sustainable transportation framework, sensitivity evaluations of the parameters involved are also examined. Lastly, conclusions are made along with the future prospects of the model.