A Solution Algorithm for Finding the Best and the Worst Fuzzy Compromise Solutions of Fuzzy Rough Linear Programming Problem with Triangular Fuzzy Rough Number Coefficients

Abstract

An algorithm for the solution of the fuzzy rough linear programming (FRLP) problems with triangular fuzzy rough number parameters is proposed to overcome the uncertainty in decision-making problems. While the costs of the objective function and the coefficients of constraints are triangular fuzzy rough numbers, the variables are in the triangular fuzzy form. Fuzzy optimal solutions are found by solving two distinct fully fuzzy linear programming (FFLP) problems, obtained from the lower and upper approximations of the FRLP problem. These solutions are utilized to evaluate different fuzzy objective function values, and these values are compared according to their supports to specify the worst and the best fuzzy rough compromise solutions. The decision-maker (DM) can make a final decision within the bounds of these supports according to the direction of the optimization. Also, the algorithm yields approximate fuzzy rough compromise solutions in the infeasibility case of the FFLP problems. To demonstrate the efficiency of the algorithm, some numerical examples are illustrated.