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

Article type: Research Article

Authors: Zhang, Xiaohong | Zeng, Xu

Affiliations: Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai, P.R. China | Department of Mathematics, Faculty of Sciences, Ningbo University, Zhejiang, Ningbo, P.R. China

Note: [] Corresponding author. Xiaohong Zhang, Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, P.R. China. E-mails: zxhonghz@263.net or zhangxh@shmtu.edu.cn

Abstract: 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.

Keywords: Fuzzy logic, linguistic quantifier, fuzzy measure, Sugeno integral, fuzzy reasoning

DOI: 10.3233/IFS-130907

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp. 2359-2367, 2014