Generalizing TOPSIS for fuzzy multiple-criteria group decision-making

In this paper, we generalize TOPSIS to fuzzy multiple-criteria group decision-making (FMCGDM) in a fuzzy environment. TOPSIS is one of the well-known methods for multiple-criteria decision-making (MCDM). Most of the steps of TOPSIS can be easily generalized to a fuzzy environment, except max and min operations in finding the ideal solution and negative ideal solution. Thus we propose two operators Up and Lo which satisfy the partial ordering relation on fuzzy numbers to the generalization of TOPSIS. In generalized TOPSIS, these two operations (Up and Lo) are employed to find ideal and negative ideal solutions under a fuzzy environment. Then the FMCGDM problem can be solved effectively and efficiently.