Fuzzy linear programming problem with fuzzy decision variables: A geometrical approach

摘要

Decision making problems force the decision maker to consider fuzzy decision variables in a fuzzy linear programming problem. Therefore, the proposed fuzzy linear programming problem considers a triangular fuzzy decision variable with triangular fuzzy parameters. A defuzzyfication method based on incenter of a triangle, which is formed by joining the vertices of the triangular fuzzy parameters and fuzzy decision variables. The coordinate of the incenter is obtained by using the concept of geometry. In next step, the incenter is considered as a vector quantity. Using the concept of obtaining the magnitude of a vector, the final mathematical model is formulated. The final mathematical programming problem is a crisp non-linear programming problem. The resultant crisp mathematical programming problem is solved by appropriate mathematical software. A numerical example is presented to illustrate the methodology.