A solution of mathematical multi‑objective transportation problems using the fermatean fuzzy programming approach

Multi-objective transportation problems (MOTPs) play a crucial role in optimizing logistics, supply chains, and resource allocation, where multiple conflicting objectives must be balanced.
Published in Sustainability
Go to the profile of WAJAHAT ALI
WAJAHAT ALI
Senior Researcher , Aligarh Muslim University
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A solution of mathematical multi-objective transportation problems using the fermatean fuzzy programming approach - International Journal of System Assurance Engineering and Management

In this paper, we present a mathematical model of a traditional transportation problem (TTP) using the fermatean fuzzy parameters (FFPs) and convert it into a crisp form using a new fermatean fuzzy score function (NFFSF). Additionally, we proposed a mathematical model of the multi-objective transportation problem (MOTP) incorporating FFPs, which is similarly transformed into a crisp form using NFFSF under fermatean fuzzy environments (FFE). We extend this approach to develop a mathematical model of a multi-level, multi-objective solid transportation problem (MLMOSTP) using FFPs under FFE. It is also converted into crisp form using NFFSF. The mathematical model of MOTP and MLMOSTP aims to simultaneously minimize three objective functions: total transportation cost, total transportation time, and total carbon emissions. The parameters of mathematical models, including objectives, costs, supply, and demands, are considered as FFPs. The mathematical model of MOTP and MLMOSTP is solved using the fermatean fuzzy programming approach (FFPA) under FFE. The FFPA is particularly suitable for addressing the MOTP and MLMOSTP due to its ability to handle higher uncertainty and vagueness inherent in multi-objective optimization problems. We provided numerical examples to demonstrate the proposed problems’ efficiency and practicality. The SciPy optimization library in Python was used to solve these numerical examples and obtain the best compromise solutions. Managerial and practical implications are discussed.

Multi-objective transportation problems (MOTPs) play a crucial role in optimizing logistics, supply chains, and resource allocation, where multiple conflicting objectives must be balanced. The Fermatean fuzzy programming approach offers an advanced decision-making framework to handle uncertainty and imprecision more effectively than traditional fuzzy methods. By leveraging Fermatean fuzzy sets, which provide higher flexibility in capturing vagueness and hesitancy, this approach enhances the accuracy of transportation models, leading to more realistic and efficient solutions. Researchers and practitioners can apply this method to real-world transportation scenarios, optimizing cost, time, and environmental impact while ensuring robust decision-making in uncertain environments.

Go to the profile of WAJAHAT ALI
WAJAHAT ALI
Senior Researcher , Aligarh Muslim University

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Go to the profile of WAJAHAT ALI
WAJAHAT ALI
about 1 month ago

Future research on multi-objective transportation problems (MOTPs) using the Fermatean fuzzy programming approach can be explored in several key directions:

  1. Hybrid Optimization Techniques – Combining the Fermatean fuzzy approach with metaheuristic algorithms such as genetic algorithms (GA), particle swarm optimization (PSO), or artificial bee colony (ABC) can enhance solution efficiency and scalability for large transportation networks.

  2. Dynamic and Real-Time Applications – Extending this approach to dynamic MOTPs, where transportation parameters (such as demand, supply, and costs) change over time, can help in real-time decision-making for logistics and supply chain management.

  3. Multi-Stage and Multi-Period Models – Future studies can focus on multi-stage transportation problems where decisions at one stage affect subsequent stages. Incorporating time-dependent factors can improve long-term strategic planning.

  4. Sustainability and Green Transportation – Addressing environmental objectives, such as reducing carbon emissions and optimizing energy consumption, within the Fermatean fuzzy framework can support sustainable and eco-friendly transportation solutions.

  5. Integration with Blockchain and IoT – The integration of blockchain technology for secure and transparent transportation data management, along with IoT-enabled real-time monitoring, can further enhance the practical applicability of Fermatean fuzzy-based models.

  6. Decision Support Systems (DSS) – Developing interactive DSS tools that incorporate Fermatean fuzzy logic for transportation managers and policymakers can facilitate better decision-making under uncertainty.

  7. Comparative Analysis with Other Fuzzy Models – Future work should involve a detailed comparison of Fermatean fuzzy programming with intuitionistic, Pythagorean, and other fuzzy set-based approaches to validate its effectiveness in solving MOTPs.

  8. Case Studies and Industry Applications – Conducting real-world case studies in various industries (e.g., healthcare logistics, disaster relief transportation, and perishable goods distribution) can demonstrate the feasibility and advantages of the Fermatean fuzzy programming approach in complex transportation scenarios.

By exploring these research directions, scholars can further enhance the applicability, efficiency, and robustness of Fermatean fuzzy-based MOTP solutions in addressing real-world transportation challenges.

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