A Compromise Decision-Making Model Based on TOPSIS and VIKOR for Multi-Objective Large- Scale Nonlinear Programming Problems with A Block Angular Structure under Fuzzy Environment

This paper proposes a compromise model, based on a new method, to solve the multiobjective large scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and farther from fuzzy negative ideal solution (FNIS). Second of them is that the proposed method provides a maximum ‘‘group utility’’ for the ‘‘majority’’ and a minimum of an individual regret for the ‘‘opponent’’. In proposed method, the decomposition algorithm is utilized to reduce the large-dimensional objective space. A multi objective identical crisp linear programming derived from the fuzzy linear model for solving the problem. Then, a compromise solution method is applied to solve each sub problem based on TOPSIS and VIKOR simultaneously. Finally, to illustrate the proposed method, an illustrative example is provided.