Solving Bi-objective Assignment Problem under Neutrosophic Environment.

The assignment problem (AP) is a decision-making problem that is used in production planning, industrial organizations, the economy and so on. As the single objective AP is no longer sufficient to handle today's optimization problems, bi-objective AP (BOAP) is considered. This research article introduces BOAP in neutrosophic environment. The neutrosophic BOAP (NBOAP) is formulated by adding the elements of cost matrices with single-valued trapezoidal neutrosophic numbers (SVTrNNs). A new method namely, fixing point approach (FPA) is proposed in this paper. The aim of this study is not only to determine the set of efficient solutions but also to find the optimal compromise solution for NBOAP using FPA. The proposed approach is elucidated with a numerical example and its solutions are plotted in a graph using MATLAB, which demonstrates its efficiency and optimality in practical aspects. This approach is more profitable for decision makers (DMs) and more efficient than other existing approaches because it provides the best optimal compromise solution in a neutrosophic environment. [ABSTRACT FROM AUTHOR]