Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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NEW RANKING AND NEW ALGORITHM FOR SOLVING DUAL HESITANT FUZZY TRANSPORTATION PROBLEM

  • K. HEMALATHA (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • VENKATESWARLU. B (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology)
  • Received : 2023.11.16
  • Accepted : 2024.07.16
  • Published : 2024.09.30
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Abstract

In this study, a dual hesitant uncertain setting is employed to study the transportation issue. The dual hesitant fuzzy set handles ambiguous, unreliable, or inaccurate data as well as conditions in real-world practical research queries that are impossible or difficult to solve according to current fuzzy uncertainties. The dual hesitant fuzzy set (DHFS) is composed of a membership hesitant function as well as a non-membership hesitant function. In this investigation, we developed a new scoring formula for converting dual hesitant fuzzy numbers (DHFNs) to crisp values and suggested a novel algorithm called contraharmonic mean for addressing the dual hesitant fuzzy problem of transportation. Excel solver is utilized to find the contraharmonic mean. Additionally, we employed the modified distribution (MODI) method to achieve the best possible result. The recommended approach is then explained using a mathematical instance, and its efficacy can be demonstrated by comparing it to previously used techniques.

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References

  1. J. Ahmed and S. Bashir, Fully Bipolar Single-Valued Neutrosophic Transportation Problems, Mathematical Problems in Engineering 2022 (2022).
  2. F.L. Hitchcock, The distribution of a product from several sources to numerous localities, Journal of mathematics and physics 20 (1941), 224-230.
  3. M.E.A. Raj, G. Sivaraman and P. Vishnukumar, A Novel Kind of Arithmetic Operations on Trapezoidal Fuzzy Numbers and Its Applications to Optimize the Transportation Cost, International Journal of Fuzzy Systems 25 (2023), 1069-1076.
  4. S. Korukoglu and S. Balli, An improved Vogel's approximation method for the transportation problem, Mathematical and Computational Applications 16 (2011), 370-381.
  5. L. Sahoo, Transportation problem in Fermatean fuzzy environment, RAIRO-Operations Research 57 (2023), 145-156.
  6. P.U. Maheswari, V. Vidhya and K. Ganesan, A modified method for finding initial basic feasible solution for fuzzy transportation problems involving generalized trapezoidal fuzzy numbers, In IOP Conference Series: Materials Science and Engineering, 1130, 2021.
  7. L.A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338-353.
  8. R.E. Bellman and L.A. Zadeh, Decision-making in a fuzzy environment, Management science 17 (1970), B-141.
  9. P.S. Kumar and R.J. Hussain, Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems, International Journal of System Assurance Engineering and Management 7 (2016), 90-101.
  10. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986), 87-96.
  11. A. Choudhary and S.P. Yadav, An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2, International Journal of System Assurance Engineering and Management 13 (2022), 2992-3001.
  12. R.M. Rodriguez, L. Martinez, V. Torra, Z.S. Xu and F. Herrera, Hesitant fuzzy sets: state of the art and future directions, International journal of intelligent systems 29 (2014), 495-524.
  13. B. Zhu, Z. Xu, and M. Xia, Dual hesitant fuzzy sets, Journal of Applied Mathematics 2012 (2012).
  14. Z.Q. Liu and S. Miyamoto, Soft computing and human-centered machines, Springer Science & Business Media, 2012.
  15. J. Ye, Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making, Applied Mathematical Modelling 38 (2014), 659-666.
  16. G. Maity, D. Mardanya, S.K. Roy and G.W. Weber, A new approach for solving dualhesitant fuzzy transportation problem with restrictions, Sadhana 44 (2019), 1-11.
  17. A. Kumar, S.S. Appadoo and P. Kaur, Mehar approach for solving dual-hesitant fuzzy transportation problem with restrictions, Sadhana 45 (2020), 1-9.
  18. G. Jothilakshmi, S.K. Prabha and P. Thirumurugan, Application of heuristic method in dual-hesitant fuzzy transportation problem, Adv. Math. Sci. J. 9 (2020), 11133-11140.
  19. S.K. Prabha, K. Jeyalakshmi, M. Thangaraj and K. Subramani, Dual-Hesitant Fuzzy Transportation Problem with ATM, Transportation 7 (2020).
  20. A. Saranya and J.M. Vinotha, Dual Hesitant Multi Objective Fractional Transportation Problem with Non-Linear Discount Cost, Int. J. of Aquatic Science 12 (2021), 3180-3191.
  21. Z.M. Rodzi, A.G. Ahmad, N.S. Ismail, W.N. Mohamad and S. Mohmad, Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making, Math. Sat. 9 (2021), 225-232.
  22. J. Mo and H.L. Huang, Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making, Soft Computing 24 2020, 14721-14733.
  23. H. Garg and G. Kaur, A robust correlation coefficient for probabilistic dual hesitant fuzzy sets and its applications, Neural Computing and Applications 32 (2020), 8847-8866.
  24. R. Yuan and F. Meng, New similarity measures for dual hesitant fuzzy sets and their application, International Journal of Fuzzy Systems 22 (2020), 1851-1867.
  25. H. Fathima, S. Devi, S.K. Prabha, P. Hema and S. Sangeetha, Application of RAM in Dual-Hesitant Fuzzy Transportation Problem, Journal of Algebraic Statistics 13 (2022), 924-930.
  26. V. Torra, Hesitant fuzzy sets, International journal of intelligent systems 25 (2010), 529-539.
  27. S. Ghosh, K.H. Kufer, S.K. Roy, and G.W. Weber, Carbon mechanism on sustainable multi-objective solid transportation problem for waste management in Pythagorean hesitant fuzzy environment, Complex & Intelligent Systems 8 (2022), 4115-4143.
  28. W. Li and X. Deng, Multi-parameter portfolio selection model with some novel scoredeviation under dual hesitant fuzzy environment, International Journal of Fuzzy Systems 22 (2020), 1123-1141.