A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function

This paper investigates the application of tolerance concepts to goal programming in a fuzzy environment. Firstly, the paper presents how the fuzzy goal programming (FGP) problems with unequal weights can be formulated as a single linear programming problem with the concept of tolerances. Next, it illustrates a numerical example to demonstrate how convenient the present model is to solve a FGP problem with unequal weights and unbalanced linear membership functions.