Abstract
The assignment problem (AP) is a linear programming problem (LPP), and it is widely applied in dealing with assignment allocation, transportation system planning, and other practical problems. In the present competitive market, optimization of a single objective AP is not always justified in real-life scenarios. So, in the current situation the decision makers (DMs) are strongly motivated to optimize AP with two objectives known as bi-objective AP (BOAP). In this chapter, neutrosophic BOAP (NBOAP) with single-valued trapezoidal neutrosophic numbers (SVTrNNs) is introduced. To highlight the varied levels of neutrality in NBOAP, we convert the NBOAP into its equivalent BOAP based on the score function and then examine the different approaches with neutrosophic parameters. This study aims to find a pareto-optimal solution (POS) using the two solution approaches based on a neutrosophic decision set (NDS)—fuzzy programming approach (FPA) and neutrosophic FPA (NFPA). A numerical example has been provided to demonstrate the accuracy and appropriateness of FPA and NFPA. Finally, the results from the two approaches are compared, then we conclude that FPA provides the same result as NFPA, and the conclusions are described for future works.
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References
Zadeh, L.A.: Fuzzy sets. Inf. Control. 8(3), 338–353 (1965)
Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)
Tilva, S., Dhodiya, J.: Multi-objective assignment problem solved by hybrid Jaya algorithm. J. Interdiscip Math. 25(1), 109–121 (2022)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Ghosh, S., Roy, S.K., Ebrahimnejad, A., Verdegay, J.L.: Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem. Complex Intell. Syst. 7(2), 1009–1023 (2021)
Smarandache, F.: A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth, USA (1999)
Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), 141–164 (1970)
Khalifa, H.: An approach to the optimization of multi-objective assignment problems with neutrosophic numbers. Int. J. Ind. Eng. Prod. Res. 31(2), 287–294 (2020)
Deli, I., Subas, Y.: Single valued neutrosophic numbers and their applications to multicriteria decision making problem. Neutrosophic Sets and Systems. 2(1), 1–13 (2014)
Harnpornchai, N., Wonggattaleekam, W.: An application of neutrosophic set to relative importance assignment in AHP. Mathematics. 9(20), 2636 (2021)
Ahmad, F., Adhami, A.Y.: Neutrosophic programming approach to multi-objective nonlinear transportation problem with fuzzy parameters. Int. J. Manag. Sci Eng. Manag. 14(3), 218–229 (2019)
Veeramani, C., Edalatpanah, S.A., Sharanya, S.: Solving the multi-objective fractional transportation problem through the neutrosophic goal programming approach. Discret. Dyn. Nat. Soc. 2021, 1–17 (2021)
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Sandhiya, S., Anuradha, D. (2024). Solving Neutrosophic Bi-objective Assignment Problem Using Different Approaches. In: Kamalov, F., Sivaraj, R., Leung, HH. (eds) Advances in Mathematical Modeling and Scientific Computing. ICRDM 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-41420-6_44
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DOI: https://doi.org/10.1007/978-3-031-41420-6_44
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