Fuzzy Prime Filters Research Articles

Fuzzy prime filter theorem in multilattices

This paper mainly focuses on building the fuzzy prime filter theorem for multilattices. Firstly, we introduce the notion of a fuzzy filter generated by a fuzzy subset of a multilattice and we give a characterization. Also, we define four types of fuzzy prime filters and establish some relationships between them. Finally, we state and prove the fuzzy prime filter theorem in distributive multilattices.

Study hoop algebras by fuzzy (n-fold) obstinate filters

Abstract In this article, we introduce the concept of fuzzy (n-fold) obstinate filter on hoop algebras and study some of the properties. We define and study fuzzy prime filter and fuzzy n-fold implicative filter on hoop algebras. Also, the relationship between fuzzy obstinate filter and some other fuzzy filters likeness fuzzy prime and fuzzy positive implicative filters are investigated. Then we show that the quotient of this structure is a Boolean algebra and obtained some condition equivalent with fuzzy n-fold implicative filter. Finally we show that every fuzzy n-fold obstinate filter with some conditions is a fuzzy n-fold implicative filter.

Spectrum of fuzzy prime filters of a 0 - distributive lattice

Stone’s topology on the set of fuzzy prime filters of a bounded 0 - distributive lattice is introduced and many properties of this space of fuzzy prime filters are furnished.

Fuzzy Prime Filters of Lattice Implication Algebras

In this paper, some properties of fuzzy filters are given. Besides, the structure of fuzzy filters are further studied. And finally, the concept of fuzzy prime filter is proposed with some equivalent conditions of fuzzy prime filters obtained.

Fuzzy Filter Spectrum of a BCK Algebra

The notion of fuzzy s‐prime filters of a bounded BCK‐algebra is introduced. We discuss the relation between fuzzy s‐prime filters and fuzzy prime filters. By the fuzzy s‐prime filters of a bounded commutative BCK‐algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s‐prime filters of a bounded commutative BCK‐algebra forms a topological space. Moreover, we show that the set of all fuzzy s‐prime filters of a bounded implicative BCK‐algebra is a Hausdorff space.

On fuzzy filters of pseudo BL-algebras

Abstract We introduce the concept of fuzzy filters of pseudo-BL-algebras and obtain some of their important properties. We further give several kinds of fuzzy filters, such as fuzzy Boolean filter, fuzzy normal filter, fuzzy prime filter, fuzzy ultrafilter and fuzzy obstinate filter and discuss the relations among the above fuzzy filters. We establish the Prime Fuzzy Filter Theorem in pseudo BL-algebras. By studying the relation between fuzzy Boolean filter and fuzzy normal filter in pseudo-BL-algebras, we solve an open problem that whether or not every Boolean filter is normal in pseudo-BL-algebras.

Fuzzy Prime Boolean Filters and Their Operations in IMTL-algebras

Some characterizations of fuzzy prime Boolean filters of IMTL-algebras are given. The lattice operations and the order-reversing involution on the set PB(M) of all fuzzy prime Boolean filters of IMTL-algebras are defined. It is showed that the set PB(M) endowed with these operations is a complete quasi-Boolean algebra (a distributive complete lattice with an order-reversing involution). It is derived that the algebra M/F, which is the set of all cosets of F, is isomorphic to the Boolean algebra {0, 1} if F is a fuzzy prime Boolean filter. By introducing an adjoint pair on PB(M), it is proved that the set PB(M) is also a residuated lattice.

Fuzzy filters and fuzzy prime filters of bounded [formula omitted]-monoids and pseudo BL-algebras

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. The sets of provable formulas in corresponding inference systems from the point of view of uncertain information can be described by fuzzy filters of those algebraic semantics. Bounded residuated lattice ordered monoids ( R ℓ -monoids) are a common generalization of pseudo BL-algebras (and consequently of pseudo MV-algebras) and Heyting algebras, i.e. algebras behind fuzzy and intuitionistic reasoning. In the paper, we introduce and investigate fuzzy filters of bounded R ℓ -monoids and fuzzy prime filters of pseudo BL-algebras.

Fuzzy filters of BL-algebras

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 ∈ Γ), where f i ( i ∈ Γ) are fuzzy prime filters of L.