Article: A neutrosophic application to the transportation problem with mixed constraints using single-valued trapezoidal neutrosophic numbers Journal: International Journal of Mathematics in Operational Research (IJMOR) 2024 Vol.28 No.4 pp.514 - 525 Abstract: Fuzzy transportation problems have been developed to address the uncertainty in real-world problems. Neutropsohic set plays a vital role in solving uncertainty which is the extension of fuzzy and the intuitionistic set. The defuzzification approach using a proposed ranking function has been considered to convert the fuzzy and neutrosophic data into crisp data. Moreover, this research is proposed a single-valued neutrosophic transportation problem with mixed constraints. The work aims to deal with the transportation problem in terms of neutrosophic nature to obtain optimal results by using a proposed ranking function. The problem explains mixed constraints by employing a conventional approach through numerical illustrations and the obtained results are compared with other ranking approaches. Lastly, it shows the justification of the results and efficiency of the ranking function which gives the optimal transportation cost. Lastly, MATLAB software has been used to show higher accuracy results for various ranking functions, and the proposed ranking function yields the most efficient optimal solution. Inderscience Publishers - linking academia, business and industry through research

Title: A neutrosophic application to the transportation problem with mixed constraints using single-valued trapezoidal neutrosophic numbers

Authors: Kalaivani Kaspar; Palanivel Kaliyaperumal

Addresses: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT), Vellore – 632014. Tamil Nadu, India ' Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT), Vellore – 632014. Tamil Nadu, India

Abstract: Fuzzy transportation problems have been developed to address the uncertainty in real-world problems. Neutropsohic set plays a vital role in solving uncertainty which is the extension of fuzzy and the intuitionistic set. The defuzzification approach using a proposed ranking function has been considered to convert the fuzzy and neutrosophic data into crisp data. Moreover, this research is proposed a single-valued neutrosophic transportation problem with mixed constraints. The work aims to deal with the transportation problem in terms of neutrosophic nature to obtain optimal results by using a proposed ranking function. The problem explains mixed constraints by employing a conventional approach through numerical illustrations and the obtained results are compared with other ranking approaches. Lastly, it shows the justification of the results and efficiency of the ranking function which gives the optimal transportation cost. Lastly, MATLAB software has been used to show higher accuracy results for various ranking functions, and the proposed ranking function yields the most efficient optimal solution.

Keywords: transportation problem; TP; neutrosophic set; NS; single-valued trapezoidal neutrosophic number; SVTNN; mixed constraint transportation problem.

DOI: 10.1504/IJMOR.2024.140349

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.4, pp.514 - 525

Received: 14 Mar 2023
Accepted: 26 Mar 2023
Published online: 05 Aug 2024 *

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Title: A neutrosophic application to the transportation problem with mixed constraints using single-valued trapezoidal neutrosophic numbers

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