A method for transforming multiple‐objective linear programming problems with trapezoidal Fuzzy coefficients

Abstract

Recently, many methods have been reported for transforming fuzzy multiple‐objective linear programming (MOLP) problems. However, the transformation into a crisp MOLP problem requires an extremely large number of constraints and decision variables which is the main disadvantage of these approaches. This paper proposes that a maximizing MOLP problem with trapezoidal positive fuzzy coefficients can be transformed into a crisp MOLP problem without increasing the number of constraints by basing the two indices on the inequality relation between trapezoidal fuzzy numbers. The usefulness of the proposed method is demonstrated.