In this article, a novel fuzzy <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-neighborhood operator with reflexivity is constructed and a new fuzzy rough set model based on the fuzzy <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-neighborhood operator is proposed. Aiming at decision-making in information systems with real-valued information systems (RVISs), we first utilize data normalization method to effectively transform RVISs into information systems with fuzzy-valued information systems (FVISs). Then, we use the fuzzy <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-neighborhood-based fuzzy rough set model to convert FVISs into information systems with intuitionistic fuzzy-valued information systems (IFVISs). By adopting the idea of the PROMETHEE II method, we develop three different sorting decision-making schemes on IFVISs, which consist of the subtraction of intuitionistic fuzzy numbers, sorting functions, and intimacy coefficients. Finally, numerical experiments demonstrate the effectiveness of our method. Comparative studies and Spearman rank correlation analyses explain the superiority of our schemes. Experimental results verify the stability of the performance of our strategy.