Solving multi-objective multilevel programming problems using two-phase intuitionistic fuzzy goal programming method

Abstract

This paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective Multilevel Programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.