Affiliations: Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai, P.R. China | College of Science and Technology, Ningbo University, 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; zhangxh@shmtu.edu.cn
Abstract: Fuzzy logic has become a useful tool for computer science to deal with uncertain information, and various kinds of residuated lattices play an important role in modern fuzzy logic theory because they provide the algebraic frameworks to related fuzzy logic formal systems. The aim of this paper is to investigate the filter theory of residuated lattices. The notions of IMTL-filters (NM-filters, MV-filters) of residuated lattices are introduced, and the characterizations of IMTL-algebras (NM-algebras, MV-algebras) in residuated lattices are presented by these filters. Moreover, fuzzy IMTL(NM, MV)-filters and intuitionistic fuzzy IMTL(NM, MV)-filters are investigated.
