A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment
Transportation problems are a crucial area in logistics and operations research that focuses on effectively transporting products and resources from origin to destination. The complex nature of real-world situations requires the utilization of advanced mathematical models and optimization approaches...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2025-03-01
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| Series: | Archives of Control Sciences |
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| Online Access: | https://journals.pan.pl/Content/134371/PDF/art07.pdf |
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| author | Rajkumar Verma Anushri Verma Pranav Dass Chaubey Vishal |
| author_facet | Rajkumar Verma Anushri Verma Pranav Dass Chaubey Vishal |
| author_sort | Rajkumar Verma |
| collection | DOAJ |
| description | Transportation problems are a crucial area in logistics and operations research that focuses on effectively transporting products and resources from origin to destination. The complex nature of real-world situations requires the utilization of advanced mathematical models and optimization approaches to formulate effective solutions. Quantifying the accurate supply, demand, and transportation costs of transportation problems is highly challenging due to the market’s unpredictable economic and environmental conditions. Several methodologies have been proposed to address the issue of transportation problems with uncertain parameters, utilizing fuzzy theory and its derivatives. Complex Pythagorean fuzzy numbers (CPyFNs) are highly suitable and effective for representing uncertain and ambiguous information in real-world scenarios. This article introduces an innovative analysis of transportation problems in the complex Pythagorean fuzzy information framework. Initially,we establish an improved score function value to evaluate the ordering of CPyFNs more precisely and propose several ranking rules. The following section of the study presents mathematical formulations and optimization models for transportation problems, where the parameters are expressed as CPyFNs. The solution approach is formulated using Vogel’s approximation method (VAM) and modified distribution method (MODI) to solve transportation problems in a complex Pythagorean fuzzy setting. An illustrative numerical example is provided to showcase the practicality and effectiveness of the proposed method in real-life scenarios. The significance of the research and the extent of future investigation are also emphasized. |
| format | Article |
| id | doaj-art-89c8cee4014549338b889876b24d95a9 |
| institution | DOAJ |
| issn | 1230-2384 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj-art-89c8cee4014549338b889876b24d95a92025-08-20T03:01:49ZengPolish Academy of SciencesArchives of Control Sciences1230-23842025-03-01Vol. 35No 1155199https://doi.org/10.24425/acs.2025.153962A new score function for optimizing transportation problems in complex Pythagorean fuzzy environmentRajkumar Verma0Anushri Verma1Pranav Dass2Chaubey Vishal3Instituto de Investigación Interdisciplinaria, Universidad de Talca, Talca, Chile; School of Economics and Business, Universidad de Talca, Talca, Chile and Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical Universityfor Women, Kashmere Gate, Delhi-110006, IndiaDepartment of Mathematics, JSS Academy of Technical Education, Noida-201301, Uttar Pradesh, IndiaDepartment of Computer Science, Shyam Lal College, University of Delhi, IndiaDepartment of Mathematics, The Basis Science and Humanities, Pranveer Singh Institute of Technology, Kanpur, Uttar Pradesh, IndiaTransportation problems are a crucial area in logistics and operations research that focuses on effectively transporting products and resources from origin to destination. The complex nature of real-world situations requires the utilization of advanced mathematical models and optimization approaches to formulate effective solutions. Quantifying the accurate supply, demand, and transportation costs of transportation problems is highly challenging due to the market’s unpredictable economic and environmental conditions. Several methodologies have been proposed to address the issue of transportation problems with uncertain parameters, utilizing fuzzy theory and its derivatives. Complex Pythagorean fuzzy numbers (CPyFNs) are highly suitable and effective for representing uncertain and ambiguous information in real-world scenarios. This article introduces an innovative analysis of transportation problems in the complex Pythagorean fuzzy information framework. Initially,we establish an improved score function value to evaluate the ordering of CPyFNs more precisely and propose several ranking rules. The following section of the study presents mathematical formulations and optimization models for transportation problems, where the parameters are expressed as CPyFNs. The solution approach is formulated using Vogel’s approximation method (VAM) and modified distribution method (MODI) to solve transportation problems in a complex Pythagorean fuzzy setting. An illustrative numerical example is provided to showcase the practicality and effectiveness of the proposed method in real-life scenarios. The significance of the research and the extent of future investigation are also emphasized.https://journals.pan.pl/Content/134371/PDF/art07.pdftransportation problem, complex pythagorean fuzzy numbers, minimum transportationcost, vogel’s approximation method, modified distribution method |
| spellingShingle | Rajkumar Verma Anushri Verma Pranav Dass Chaubey Vishal A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment Archives of Control Sciences transportation problem, complex pythagorean fuzzy numbers, minimum transportationcost, vogel’s approximation method, modified distribution method |
| title | A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment |
| title_full | A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment |
| title_fullStr | A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment |
| title_full_unstemmed | A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment |
| title_short | A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment |
| title_sort | new score function for optimizing transportation problems in complex pythagorean fuzzy environment |
| topic | transportation problem, complex pythagorean fuzzy numbers, minimum transportationcost, vogel’s approximation method, modified distribution method |
| url | https://journals.pan.pl/Content/134371/PDF/art07.pdf |
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