Filters In BL-algebras Research Articles

New representation for filters of BL-algebras

In this paper, we introduce the concept of TL-filter of BL-algebra and study some basic properties. TL-filter generated by L-subsets and the concept of T-congruence L-relations on BL-algebra are introduced and the relationships between TL-filters and T-congruence L-relations on BL-algebra are studied.

Folding Theory for Fantastic Filters in BL-Algebras

In this paper, the author examines the notion of n-fold fantastic and fuzzy n-fold fantastic filters in BL-algebras. Several characterizations of fuzzy n-fold fantastic filters are given. The author shows that every n-fold (fuzzy n-fold) fantastic filter is a filter (fuzzy filter), but the converse is not true. Using a level set of a fuzzy set in a BL-algebra, the author gives a characterization of fuzzy n-fold fantastic filters. Finally, the author establishes the extension property for n-fold and fuzzy n-fold fantastic filters in BL-algebras. The author also constructs some algorithms for folding theory applied to fantastic filters in BL-algebras.

Fuzzy n-fold obstinate filters in BL-algebras

We define and study the notion of fuzzy n-fold obstinate filters in BL-algebras. Several properties of fuzzy n-fold obstinate filters are given. Using a level set of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold obstinate filters. We prove that the homomorphic image and preimage of fuzzy n-fold obstinate filters are also fuzzy n-fold obstinate filters.

N-Fold obstinate filters in BL-algebras

In this paper, we introduced the notion of n-fold obstinate filter in BL-algebras and we stated and proved some theorems, which determine the relationship between this notion and other types of n-fold filters in a BL-algebra. We proved that if F is a 1-fold obstinate filter, then A/F is a Boolean algebra. Several characterizations of n-fold fantastic filters are given, and we show that A is a n-fold fantastic BL-algebra if A is a MV-algebra (n ≥ 1) and A is a 1-fold positive implicative BL-algebra if A is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and n-fold filters in finite BL-algebras.

Radical of filters in BL -algebras

In this paper, the notion of the radical of a filter in BL-algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV-algebra if and only if Ds(A) ⊆ F. After that we define the notion of semi maximal filter in BL-algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL-algebra. Moreover, we prove that A/F is a semi simple BL-algebra if and only if F is a semi maximal filter of A. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Algorithms and Computations in BL-Algebras

In this paper, the authors study the notion of n-fold implicative and fuzzy n-fold implicative filters, which correspond to various sets of provable formulaes, in BL-algebras. Several characterizations of fuzzy n-fold implicative filters are given and the authors analyse some relationships with various n-fold and fuzzy n-fold filters in BL-algebras, while constructing some algorithms for studying the foldness of filters in BL-algebras. The authors describe the relation between fuzzy n-fold implicative filters and fuzzy (n+1)-fold implicative filters and establish the extension property for fuzzy n-fold implicative filters in BL-algebras.

On filter theory of residuated lattices

The aim of this paper is to develop the filter theory of general residuated lattices. First, we extend some particular types of filters and fuzzy filters in BL-algebras and MTL-algebras naturally to general residuated lattices, and further enumerate some relative results obtained in BL-algebras or MTL-algebras, which still hold in general residuated lattices. Next, we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices, which are two new types of filters and fuzzy filters, and derive some of their characterizations. Finally, we discuss the relations between (fuzzy) regular filters and several other special (fuzzy) filters, and also characterize some special classes of residuated lattices by filters or fuzzy filters.

On ( $$\in, \in \vee q$$ )-Fuzzy Filters of BL-Algebras

The authors introduce the notions of (\(\in, \in \vee q\))-fuzzy Boolean (implicative, positive implicative, and fantastic) filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and describe the relations among these generalized fuzzy filters. It is proved that an (\(\in, \in \vee q\))-fuzzy filter in a BL-algebra is Boolean (implicative) if and only if it is both positive implicative and fantastic.

Generalized fuzzy filters of BL-algebras

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈,∈ Vq)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.

Some Types of Filters in BL Algebras

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters.

Some types of filters in BL algebras

Some types of filters in BL algebras

Fuzzy Boolean and positive implicative filters of [formula omitted]-algebras

The aim of this paper is to introduce the notions of fuzzy Boolean filters and fuzzy positive implicative filters in BL-algebras and to investigate their properties. Several characterizations of fuzzy Boolean filters and fuzzy positive implicative filters are derived. The extension theorems of fuzzy Boolean filters and fuzzy positive implicative filters are obtained. The relation between fuzzy Boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy Boolean filter is a fuzzy positive implicative filter, but the converse may not be true. Furthermore, the conditions under which a fuzzy positive implicative filter is a fuzzy Boolean filter are established.

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.