First-order logic system $\mathbf{IMTL_{Q}^{*}}$ and triple I method in fuzzy reasoning with linguistic quantifiers

Based on first-order fuzzy logic system $\mathbf{K}^{*}$ and Ying's framework for linguistic quantifiers modeled by Sugeno integrals, a many-sorted first-order logic system $\mathbf{IMTL_{Q}^{*}}$ is constructed. Applying the triple I method, some fuzzy reasoning forms with linguistic quantifiers are investigated.