Izhar Ahmad

In this study, sufficient optimality criteria for a robust fractional interval-valued optimization problem (RP) is highlighted based on the idea of convexificators. The use of generalized invexity tools to support sufficient optimality conditions is demonstrated by an example. Also, saddle point condition of a Lagrange function is examined for RP. Furthermore, Mond–Weir-type robust dual model is constructed and by employing the concept of generalized invexity, usual duality results are discussed.

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using α-cut of fuzzy numbers wherein the α- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of r∈(0,1] are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.