In this paper, we propose a new fuzzy interpolative reasoning (FIR) method on the basis of representative values (RVs) and characteristic points (CPs) of rough-fuzzy sets (RFSs). Firstly, it calculates the Euclidean distance between the antecedent polygonal RFS ${\widetilde A_{ij}}$ and the observation polygonal RFS ${\widetilde A_j^\ast}$ based on the RVs $Rep{(\tilde A_j^\ast)_x}$ and $Rep{(\tilde A_j^\ast)_y}$ of antecedent polygonal RFS $\widetilde A_j^\ast$ in the ${X}$-axis and ${Y}$-axis, respectively, and the RVs $Rep{(\tilde A_j^\ast)_x}$ and $Rep\,{(\tilde A_j^\ast)_y}$ of the observation polygonal RFS $\widetilde A_j^\ast$ in the X-axis and Y-axis, respectively, where ${1 \leq i \leq q}$ and ${1 \leq j \leq m}$. Then, it calculates the weight $w_{ij}^{\prime}$ and the normalized weight $w_{ij}$ of the ${j}$th antecedent variable of fuzzy rule ${R_{i}}$ and calculates the weight ${w_{i}}$ of fuzzy rule ${R_{i}}$, which are used to calculate the RVs $Rep{(\underline {{{\widetilde B}^\ast}})_x}$ and $Rep{(\overline {{{\tilde B}^\ast}})_x}$ of the lower approximate polygonal fuzzy set $\underline {{{\tilde B}^\ast}}$ and the upper approximate polygonal fuzzy set (UAPFS) ${\overline {\tilde B}^\ast}$ of the interpolated consequence polygonal ${{\tilde B}^\ast}$ in the X-axis, respectively. Then, it calculates the CPs of the LAPFS $\underline {{{\tilde B}^\ast}}$ and calculates the CPs of the $\overline {{{\tilde B}^\ast}}$ of the interpolated consequence RFS ${{\tilde B}^\ast}$ based on the obtained RVs $Rep{(\underline {{{\tilde B}^\ast}})_x}$ and $Rep{(\overline {{{\tilde B}^\ast}})_x}$ of the LAPFS $\underline {{{\tilde B}^\ast}}$ and the UAPFS $\overline {{{\tilde B}^\ast}}$ of the interpolated consequence polygonal RFS ${{{\tilde B}^\ast}}$ in the ${X}$-axis, respectively. Finally, it calculates the membership degree (MD) $\underline {\mu _g^\ast}$ of the gth CP $\underline {b_g^\ast}$ of the LAPFS $\underline {{{\tilde B}^\ast}}$ and calculates the MD $\...