An analysis of fully fuzzy linear programming with fuzzy decision variables through logistics network design problem

Recently, there is a growing attention by the researchers to solve and interpret the analysis of fully fuzzy linear programming problems in which all of the parameters as well as the decision variables are considered as fuzzy numbers. Under a fully uncertain environment where all of the data are stated as fuzzy, presenting the reasonable range of values for the decision variables may be comparatively better than the currently available crisp solutions so as to provide ranges of flexibility to decision makers. However, there is still a scarcity of solution methodologies on fuzzy mathematical programs with fuzzy decision variables. Based on this motivation, a new parametric method which is mainly based on α-cut representation of fuzzy intervals is proposed in this paper by incorporating the decision maker's attitude toward risk. In order to illustrate validity and practicality of the proposed method, it is applied to a generic reverse logistics network design model including fuzzy decision variables. To the best of our knowledge, this is the first study in the literature which presents fuzzy efficient solutions and analysis for a fully fuzzy reverse logistics network design problem with fuzzy decision variables. The provided solutions by the proposed method are also compared to the available solution methodologies from the literature in terms of computational efficiency, solution quality and ease of use. By using the proposed method, the decision makers can be supported by yielding fuzzy efficient solutions under different uncertainty levels and risk attitudes. The computational results have also shown that more reliable and necessarily precise solutions can be generated by the proposed method for a risk-averse decision maker.