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On improving a weighted additive model for fuzzy goal programming problems. (English) Zbl 1161.90541
Summary: Fuzzy goal programming is a useful tool to deal with problems involving multi objective goals in a fuzzy environment. It is used positively to solve real life problems. To solve fuzzy goal programming problems several weighted additive models are proposed in the literature. A weighted additive model is formulated by R. N. Tiwari, S. Daharmar and J. R. Rao [Fuzzy Sets Syst. 24, 27–34 (1987; Zbl 0627.90073)]. This model is used in the literature and some further research has been carried out based on it. However, there is an oversight within the formulation of this model that sometimes yields suboptimal solutions. The oversight is also repeated in a new research which is done by L.-H. Chen and F.-Ch. Tsai [Eur. J. Oper. Res. 133, No. 3, 548–556 (2001; Zbl 1053.90140)]. This paper explains the lack of precision within the formulation of Tiwari et al.’s model and a correction is suggested to enable it to achieve better solutions. This correction helps us to improve the model to deal with any kind of linear fuzzy goals easily. Illustrative examples are given to support the ideas.

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C29 Multi-objective and goal programming