IMTLMV-filters and fuzzy IMTLMV-filters of residuated lattices

Authors:
Xiaohong Zhang;Huijie Zhou;Xiaoyan Mao
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;College of Science and Technology, Ningbo University, Ningbo, P.R. China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2014

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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 IMTLNM, MV-filters and intuitionistic fuzzy IMTLNM, MV-filters are investigated.