A New Compromise Decision-making Model Based on TOPSIS and VIKOR forSolving Multi-objective Large-scale Programming Problems with a Block AngularStructure under Uncertainty

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

A New Compromise Decision-making Model Based on TOPSIS and VIKOR forSolving Multi-objective Large-scale Programming Problems with a Block AngularStructure under Uncertainty Keywords:

Multi-objectiveUncertaintyTOPSISVIKOR