A modified augmented max min model for weighted fuzzy goal programming

Since Narasimhans first application of Fuzzy Set Theory to Goal Programming (GP) in 1980, much research into fuzzy GP has been carried out. In fuzzy GP studies, although several researchers remained loyal to using the traditional GP representation, the majority have followed the fuzzy programming approach. Among fuzzy-programming-based studies, only the studies of Tiwari et al. and Lin seem applicable when the objectives have relative importance. However, both have disadvantages. Because the former model uses the add operator, some of the objectives may not be preferred at the optimal solution even they have heavy weights. The latter model is based on the max-min approach, which does not guarantee a non-dominated solution. In this study, a weighted Fuzzy GP model is presented to overcome these disadvantages, along with the shortcomings of other existing models. The model is modified from Lai and Hwangs augmented max-min model, which is guaranteed to reach a non-dominated solution. The superiority of the model over the existing approaches is demonstrated using numerical examples chosen from the literature.