A fuzzy multi-criteria decision-making model based on lower and upper boundaries

Many researches generalized classical multi-criteria decision-making (MCDM) methods under uncertain environment for fuzzy multi-criteria decision-making (FMCDM), such that Chen, Liang, Raj and Kumar, and Wang et al. extended TOPSIS into FMCDM methods. However, there are some problems in their methods. For instance, intersection of fuzzy numbers is a null set, calculation is a complex work for approximate triangular fuzzy numbers or trapezoidal fuzzy numbers, or criteria values of ideal/anti-ideal solution may not exist in feasible alternatives. In addition, steps of the methods are too many to realize or apply for decision-makers. To improve above shortcomings, we propose a FMCDM method based on lower and upper boundaries. Practically, the proposed method is not totally generalized TOPSIS under fuzzy environment. Furthermore, the method is aggregated into a FMCDM model to simplify FMCDM computation. Since the FMCDM model can be clearly expressed by a simple formulation, it is easy to utilize the model to solve FMCDM problems.