Analysis on the Neutrosophic Fuzzy Rough Multi-objective Quadratic Transportation Problem Using Various Membership Functions

This paper introduces a new variant of fuzzy set called a neutrosophic fuzzy rough set, which is developed by combining both rough set and neutrosophic fuzzy set theory for optimal benefit. An effective optimization of the multi-objective quadratic transportation problem is examined, with a chance of distinct solution vectors for each objective function. This paper employs both neutrosophic fuzzy rough numbers and MOQTP to model Neutrosophic Fuzzy Rough Multi-Objective Quadratic Transportation Problem (NFRMOQTP). In addition, we present a method for solving NFRMOQTP with a numerical example, which involves transforming the model into a single-objective quadratic transportation problem by utilizing various membership functions. Further, in order to verify the suggested approach, we contrast the outcomes with existing technique and the results are discussed.