Fuzzy Sets and Systems
Fuzzy ideals of BCI and MV-algebras
Fuzzy Sets and Systems
Fuzzy maximal ideals of BCI and MV algebras
Information Sciences—Intelligent Systems: An International Journal
Fuzzy implicative and Boolean ideals of MV-algebras
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy Boolean and positive implicative filters of BL-algebras
Fuzzy Sets and Systems
Soft BL-algebras based on fuzzy sets
Computers & Mathematics with Applications
Filters of residuated lattices and triangle algebras
Information Sciences: an International Journal
On filter theory of residuated lattices
Information Sciences: an International Journal
New types of fuzzy filters of BL-algebras
Computers & Mathematics with Applications
On fuzzy filters of pseudo BL-algebras
Fuzzy Sets and Systems
Algorithms and Computations in BL-Algebras
International Journal of Artificial Life Research
Folding Theory for Fantastic Filters in BL-Algebras
International Journal of Artificial Life Research
Anti Fuzzy Deductive Systems of BL-Algebras
International Journal of Artificial Life Research
Some types of falling fuzzy filters of BL-algebras and its applications
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
New representation for filters of BL-algebras
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
IMTLMV-filters and fuzzy IMTLMV-filters of residuated lattices
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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The aim of this paper is to introduce the notions of fuzzy filters, fuzzy prime filters and the cosets of a fuzzy filter in BL-algebras and investigate some of their properties. The fuzzy filter generated by a fuzzy set is discussed. Some characterizations of fuzzy filters and fuzzy prime filters are derived. The extension theorem of fuzzy prime filters and the fuzzy prime filters theorem are established. Finally, we prove that the algebra L/f which is the set of all cosets of f is a BL-algebra, and is isomorphic to the BL-algebra L/f"f"("1"), where f"f"("1")={x@?L|f(x)=f(1)}. Moreover, each BL-algebra L is a subdirect product of linearly ordered BL-algebras L/f"i (i@?@C), where f"i (i@?@C) are fuzzy prime filters of L.