Fuzzy rough bi-level multi-objective nonlinear programming problem (FRBMNPP)
moved toward becoming rise normally in various real applications. In this article we develop bilevel
multi-objective nonlinear programming problem (BMNPP), in which the objective functions
have fuzzy nature and the constraints represented as a rough set. The fuzzy objective functions converted
into deterministic ones by utilizing the a-cut methodology. Thus the FRBMNPP become a
rough BMNPP which is transformed into two problems corresponding to the upper and lower
approximation models. The Karush-Kuhn-Tucker (KKT) method and two models of technique
of order preferences by similarity to ideal solution (TOPSIS) approach are developed to solve such
problem. At last, applicability and efficiency of the two TOPSIS models and KKT method, suggested
in this study, are presented through an algorithm and a numerical illustration.