Novel Pythagorean fuzzy score function to optimize fuzzy transportation models
Uncertainty in transportation models arises from several factors, including fluctuating demand, variable supply, transportation costs and unpredictable external conditions like market changes or delays. Traditional optimization methods struggle to account for this variability, as they rely on precis...
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Elsevier
2025-03-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590123025001367 |
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| author | Ritu Tarun Kumar Jahnvi Kapil Kumar Nitesh Dhiman M.K. Sharma |
| author_facet | Ritu Tarun Kumar Jahnvi Kapil Kumar Nitesh Dhiman M.K. Sharma |
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| description | Uncertainty in transportation models arises from several factors, including fluctuating demand, variable supply, transportation costs and unpredictable external conditions like market changes or delays. Traditional optimization methods struggle to account for this variability, as they rely on precise inputs. To address the inherent uncertainty in classical transportation problems, fuzzy logic and its extensions such as intuitionistic fuzzy set (IFS), interval valued intuitionistic fuzzy set (IVIFS), Pythagorean fuzzy set (PFS) etc. are employed in the existing literature. This paper utilizes an advanced extension of fuzzy sets, known as Interval-Valued Pythagorean Fuzzy Sets (IVPFS) in transportation models. IVPFS provides a more flexible framework by allowing the MD & NMD to be interval values to capture a wider range of uncertainty. This paper introduces a novel score function dealing with IVPFS to enhance the decision-making processes in uncertain environments. As compare to the other score function of IVPFS, the proposed score function provide us more optimal results. which is also helpful to evaluate more optimal cost of PFTP. Also, the proposed score function integrates these interval values to quantify and rank the alternatives more effectively.However, a notable trade-off is the increased computational complexity due to the use of interval values in the membership and non-membership functions, particularly in larger-scale transportation problems. Furthermore, the different models (Type-1, Type-2 and Type-3) show varied effectiveness in different scenarios: Type-1 performs best when cost uncertainty is primary, Type-2 is suitable when both supply and demand are uncertain and Type-3 addresses all three factors-supply, demand and cost-under uncertainty.Three types of interval valued Pythagorean fuzzy transportation problems (IVPFTP) are examined in this study: Type-1 considers cost in a Pythagorean fuzzy nature, Type-2 addresses both supply and demand in a Pythagorean fuzzy nature and Type-3 incorporates supply, demand and cost all are in a Pythagorean fuzzy nature. Through comprehensive numerical analysis, In Type-1 IVPFTP the cost dropped from 5.19 to 0.675, for Type-2 IVPFTP cost dropped from 0.2615 to 0.001869 and for Type-3 IVPFTP cost dropped from0.17435 to 0.0013879.Thereafter, it was observed that the proposed score function provides a more optimal transportation cost.Also, our findings demonstrate the significant cost reductions and improved decision-making capabilities across different types of IVPFTP models to highlight the efficiency of the proposed score function in handling uncertainty within the transportation problems. |
| format | Article |
| id | doaj-art-808a23037b9f4da58168b3763047e856 |
| institution | Kabale University |
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| language | English |
| publishDate | 2025-03-01 |
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| series | Results in Engineering |
| spelling | doaj-art-808a23037b9f4da58168b3763047e8562025-01-27T04:22:09ZengElsevierResults in Engineering2590-12302025-03-0125104048Novel Pythagorean fuzzy score function to optimize fuzzy transportation models Ritu0Tarun Kumar1 Jahnvi2Kapil Kumar3Nitesh Dhiman4M.K. Sharma5Department of Mathematics, Chaudhary Charan Singh University, Meerut, India, 250004Department of Mathematics, Chaudhary Charan Singh University, Meerut, India, 250004Department of Mathematics, Chaudhary Charan Singh University, Meerut, India, 250004Department of Mathematics, Chaudhary Charan Singh University, Meerut, India, 250004; Department of Mathematics, Atma Ram Sanatan Dharma College (University of Delhi), New Delhi, 110021, IndiaDepartment of Mathematics, Zakir Husain Delhi College, New Delhi, India, 110002Department of Mathematics, Chaudhary Charan Singh University, Meerut, India, 250004; Corresponding author.Uncertainty in transportation models arises from several factors, including fluctuating demand, variable supply, transportation costs and unpredictable external conditions like market changes or delays. Traditional optimization methods struggle to account for this variability, as they rely on precise inputs. To address the inherent uncertainty in classical transportation problems, fuzzy logic and its extensions such as intuitionistic fuzzy set (IFS), interval valued intuitionistic fuzzy set (IVIFS), Pythagorean fuzzy set (PFS) etc. are employed in the existing literature. This paper utilizes an advanced extension of fuzzy sets, known as Interval-Valued Pythagorean Fuzzy Sets (IVPFS) in transportation models. IVPFS provides a more flexible framework by allowing the MD & NMD to be interval values to capture a wider range of uncertainty. This paper introduces a novel score function dealing with IVPFS to enhance the decision-making processes in uncertain environments. As compare to the other score function of IVPFS, the proposed score function provide us more optimal results. which is also helpful to evaluate more optimal cost of PFTP. Also, the proposed score function integrates these interval values to quantify and rank the alternatives more effectively.However, a notable trade-off is the increased computational complexity due to the use of interval values in the membership and non-membership functions, particularly in larger-scale transportation problems. Furthermore, the different models (Type-1, Type-2 and Type-3) show varied effectiveness in different scenarios: Type-1 performs best when cost uncertainty is primary, Type-2 is suitable when both supply and demand are uncertain and Type-3 addresses all three factors-supply, demand and cost-under uncertainty.Three types of interval valued Pythagorean fuzzy transportation problems (IVPFTP) are examined in this study: Type-1 considers cost in a Pythagorean fuzzy nature, Type-2 addresses both supply and demand in a Pythagorean fuzzy nature and Type-3 incorporates supply, demand and cost all are in a Pythagorean fuzzy nature. Through comprehensive numerical analysis, In Type-1 IVPFTP the cost dropped from 5.19 to 0.675, for Type-2 IVPFTP cost dropped from 0.2615 to 0.001869 and for Type-3 IVPFTP cost dropped from0.17435 to 0.0013879.Thereafter, it was observed that the proposed score function provides a more optimal transportation cost.Also, our findings demonstrate the significant cost reductions and improved decision-making capabilities across different types of IVPFTP models to highlight the efficiency of the proposed score function in handling uncertainty within the transportation problems.http://www.sciencedirect.com/science/article/pii/S2590123025001367Intuitionistic fuzzy setPythagorean fuzzy setinterval valued Pythagorean fuzzy setScore functionTransportation problem |
| spellingShingle | Ritu Tarun Kumar Jahnvi Kapil Kumar Nitesh Dhiman M.K. Sharma Novel Pythagorean fuzzy score function to optimize fuzzy transportation models Results in Engineering Intuitionistic fuzzy set Pythagorean fuzzy set interval valued Pythagorean fuzzy set Score function Transportation problem |
| title | Novel Pythagorean fuzzy score function to optimize fuzzy transportation models |
| title_full | Novel Pythagorean fuzzy score function to optimize fuzzy transportation models |
| title_fullStr | Novel Pythagorean fuzzy score function to optimize fuzzy transportation models |
| title_full_unstemmed | Novel Pythagorean fuzzy score function to optimize fuzzy transportation models |
| title_short | Novel Pythagorean fuzzy score function to optimize fuzzy transportation models |
| title_sort | novel pythagorean fuzzy score function to optimize fuzzy transportation models |
| topic | Intuitionistic fuzzy set Pythagorean fuzzy set interval valued Pythagorean fuzzy set Score function Transportation problem |
| url | http://www.sciencedirect.com/science/article/pii/S2590123025001367 |
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