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Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority. [ABSTRACT FROM AUTHOR]

Assignment problem (AP) is well-studied and important area in optimization. In this research manuscript, an assignment problem in neutrosophic environment, called as neutrosophic assignment problem (NAP), is introduced. The problem is proposed by using the interval-valued trapezoidal neutrosophic numbers in the elements of cost matrix. As per the concept of score function, the interval-valued trapezoidal neutrosophic assignment problem (IVTNAP) is transformed to the corresponding an interval-valued AP. To optimize the objective function in interval form, we use the order relations. These relations are the representations of choices of decision maker. The maximization (or minimization) model with objective function in interval form is changed to multi- objective based on order relations introduced by the decision makers' preference in case of interval profits (or costs). In the last, we solve a numerical example to support the proposed solution methodology. [ABSTRACT FROM AUTHOR]