Solving Neutrosophic Bi-objective Assignment Problem Using Different Approaches

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.