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Neutrosophic multi-objective green four-dimensional fixed-charge transportation problem

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Abstract

The main inquisition of this paper is to introduce two methods for solving a multi-objective green 4-dimensional fixed-charge transportation problem (MG4FTP) under neutrosophic environment. The increasing use of transportation vehicles, the condition of roads, vehicle type in daily life to meet our needs that create a lot of problems such as global warming, greenhouse gas (GHG) emissions in the nature. In this paper, we minimize transportation cost, carbon emission and transportation time. In real-life situation, all parameters of transportation problem are not tackled by crisp value, fuzzy numbers and intuitionistic fuzzy numbers, then to accommodate the fact we choice here single valued trapezoidal neutrosophic number (SVTNN) for designing such type of transportation problem. Thereafter we use \(\left( \alpha , \beta , \gamma \right) \)-cut of SVTNN to convert the parameters in interval form of the proposed model. Two new approaches based on neutrosophic programming (NP) and Pythagorean hesitant fuzzy programming (PHFP) are used to extract a better compromise solution of the proposed problem. A comparison is drawn among the compromise solutions that are derived from the programming, by using the score function of SVTNN. Two numerical examples are included to illustrate the applicability and validity of the proposed problem.

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Acknowledgements

The authors are very much grateful to the Editor-in-Chief, Associate Editor and anonymous respective reviewers for their insightful comments that helped us so much to rigorously improve the quality of the manuscript. The author Binoy Krishna Giri is very much grateful to the University Grant Commission of India for supporting financially to continue this research work under JRF (UGC) scheme: Sanctioned letter number [F.NO. 16-9(June 2019)/2019(NET/CSIR)].

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  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721102, India

    Binoy Krishna Giri & Sankar Kumar Roy

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  1. Binoy Krishna Giri
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Correspondence to Sankar Kumar Roy.

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Giri, B.K., Roy, S.K. Neutrosophic multi-objective green four-dimensional fixed-charge transportation problem. Int. J. Mach. Learn. & Cyber. 13, 3089–3112 (2022). https://doi.org/10.1007/s13042-022-01582-y

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