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
TL-filters of integral residuated l-monoids
Information Sciences: an International Journal
On v-filters and normal v-filters of a residuated lattice with a weak vt-operator
Information Sciences: an International Journal
Some types of generalized fuzzy filters of BL-algebras
Computers & Mathematics with Applications
The pseudo-linear semantics of interval-valued fuzzy logics
Information Sciences: an International Journal
The radical of a perfect residuated structure
Information Sciences: an International Journal
Some kinds of View the -fuzzy filters of BL-algebras
Computers & Mathematics with Applications
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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/ff(1), where ff(1) = {x ∈ L|f(x) =f(1)}. Moreover, each BL-algebra L is a subdirect product of linearly ordered BL-algebras L/fi (i ∈ Γ). where fi (i ∈ Γ) are fuzzy prime filters of L.