FGP approach and Rouben ranking function to bi-level multi-objective quadratic fractional problem with trapezoidal fuzzy numbers and soft fuzzy constraints

Abstract

The requirement of the consistent solution of Bi-level Multi-objective Quadratic Fractional Problem(BLMOQFP) provides the avenue for this research through Fuzzy Goal Programming(FGP) approach. The present study offers to tackle the problems which may have some objectives with infeasible points. Due to having a non-optimal solution of some objective functions, the process becomes complicated to arrive at the solution. This study reveals the way to obtain a consistent solution in such cases. This article disentangles the problem of having Trapezoidal Fuzzy Numbers as coefficients and implements Rouben Ranking Function to transform a fuzzy problem into a crisp one. After that, a new methodology is introduced to convert fractional objectives into non-fractional form. In the last stage, FGP approach is being used to form a single model with linear and simple objective corresponding to initial BLMOQF problem. Present Study deals with soft constraints in the way that Feasible region is also relaxed up to a limit for the betterment of the solution. Soft constraints are transformed into fuzzy goals by defining corresponding membership functions using leniency limits provided by decision-makers. Furthermore, an algorithm and flowchart are also presented to clarify the proposed approach. In addition, a numerical in which most of the objective functions have an infeasible solution is also tested.