Interval-valued $\mathcal{T}$-fuzzy filters and interval-valued $\mathcal{T}$-fuzzy congruences on residuated lattices

Authors:
Yi Liu;Yang Xu;Xiaoyan Qin
Affiliations:
College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan province, P.R. China and Intelligent Control Development Center, Southwest Jiaotong University, Chengd ...;Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan province, P.R. China;Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan province, P.R. China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2014

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Abstract

The aim of this paper is further to develop the fuzzy filter theory and fuzzy congruence relation on a residuated lattice. First, we introduce the concepts of interval-valued $\mathcal{T}$-fuzzy implicative, positive implicative, MV, regular filters with respect to a t-norm $\mathcal{T}$ on D[0,1] and investigate their properties, and some equivalent characterizations of these generalized fuzzy filters are derived. Next, we introduce the concept of interval-valued $\mathcal{T}$-fuzzy congruence relation on a residuated lattice, and the relation between interval-valued $\mathcal{T}$-fuzzy congruences and interval-valued $\mathcal{T}$-fuzzy filters are investigated. Finally, we construct a new residuated lattice which induced by interval-valued $\mathcal{T}$-fuzzy congruences, the homomorphism theorem is given.