It is not widely acknowledged that none of existing fuzzy β-neighborhood operators satisfies the reflexivity when β≠ 1. To overcome this shortcoming, four types of fuzzy β-neighborhood operators are redefined, which shows that two redefined operators are reflexive. By means of fuzzy logical operators, the (I, T)-fuzzy rough set (ITFRS) model based on the reflexive fuzzy β-neighborhood operators is constructed in this paper. By combining ITFRS models with the classical TOPSIS method, a new decision-making method is proposed to handle multi-criteria decision-making (MCDM) problems under uncertain and fuzzy environments, where the distance between two intuitionistic fuzzy sets (IFSs) is expressed by an intuitionistic fuzzy number (IFN). Meanwhile, both numerical examples with different types of data are given to explain the feasibility of the proposed method and its effectiveness is also illustrated by a comparative analysis. Finally, the stability of the proposed method is further verified based on an experimental analysis in a real-life MCDM problem.