Duality of multi-objective fractional Bi-level programming problem and its application

Fractional programming is used in several fields of study. The critical cause of interest in fractional programming is the idea that by taking factors like return on investment maximization, cost/time minimization, return/risk maximization, etc., into account, programming models can better match real-world problems. Bi-level programming problems are used to study hierarchical systems. The bi-level fractional programming problem is an emerging branch of optimization used to study two-level ratio problems. In this paper, we consider a multi-objective fractional bi-level programming problem, and as its application, we establish a Mond-Weir type dual. The relationship between the two is studied via weak and strong duality results under the assumption of \(\partial ^*\) ${\partial }^{\ast }$ -pseudoconvexity and \(\partial ^*\) ${\partial }^{\ast }$ -quasiconvexity. An application is provided to validate the weak duality theorem.