Fully intuitionistic fuzzy multi-level linear fractional programming problem

Abstract

In many real situations, it is frequently difficult to accurately determine the membership and non-membership degrees related to an element of the set with complete satisfaction because of the ambiguity in the input data. In instances like these, intuitionistic fuzzy (IF) numbers are crucial. We present a simple approach in this paper to solve the fully intuitionistic fuzzy multi-level linear fractional programming (FIFMLLFP) problem. By applying the new suggested approach to the problem under consideration, each level of the FIFMLLFP problem is converted into five crisp linear (MLMOLFP) problems, where each crisp problem has an additional bounded variables constraint and the upper problems' optimization variables are treated as parameters. This is done by using an iterative technique for linearizing fractional objectives. We converted the MLMOLFP problem into a multilevel multiobjective linear programming (MLMOLP) problem, in addition to the ε-constraint method that is used to reduce MLMOLP problem to a single objective linear programming problem. The method is demonstrated step-by-step with a numerical example.