A Method for Fuzzy Multiple Objective Linear Programming Problems with Relationship Between Coefficients

Abstract

Fuzzy mathematical programming problems are convenient for decision making under uncertainty. Therefore, a lot of formulations for them have been proposed in the recent decade. We get optimal solutions easily, because many problems are transformed into linear programming problems. But, they can hardly deal with some of relationship between uncertain coefficients. In this paper, in order to improve these defects, we suggest a new method using scenarios which are used in stochastic linear programming. In usual methods, scenarios are composed of crisp numbers. However, in this case, there are some defects that the size of problems become very large and uncertainty of problems are not described well in a small number of scenarios. So, we suggest new scenarios composed of fuzzy numbers and a new method for solving multiple objective linear programming problems which can get the solutions considering the balance of all scenarios, all goals, optimistic viewpoints and pessimistic ones.