Fuzzy Positive Implicative Filter Research Articles

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.

Construction of (n-Fold) EQ-Algebras by Using Fuzzy n-Fold Filters

In this paper, the concept of fuzzy [Formula: see text]-fold (positive implicative, implicative, fantastic) filters in [Formula: see text]-algebras is defined and several results and relation among them are investigated. Then [Formula: see text]-fold (implicative) positive implicative [Formula: see text]-algebras are constructed by using [Formula: see text]-fold fuzzy positive (implicative) filters and suitable congruence relations on [Formula: see text]-algebras.

Fuzzy Positive Implicative Filters of Hoops Based on Fuzzy Points

In this paper, we introduce the notions of ( ∈ , ∈ ) -fuzzy positive implicative filters and ( ∈ , ∈ ∨ q ) -fuzzy positive implicative filters in hoops and investigate their properties. We also define some equivalent definitions of them, and then we use the congruence relation on hoop defined in blue[Aaly Kologani, M.; Mohseni Takallo, M.; Kim, H.S. Fuzzy filters of hoops based on fuzzy points. Mathematics. 2019, 7, 430; doi:10.3390/math7050430] by using an ( ∈ , ∈ ) -fuzzy filter in hoop. We show that the quotient structure of this relation is a Brouwerian semilattice.

Fuzzy 1-type and 2-type positive implicative filters of pseudo-BCK algebras1

The notions of fuzzy 1-type (2-type) positive implicative filter and fuzzy normal filter of pseudo-BCK algebras are introduced, some properties and equivalent conditions are given. By using the new notions, the characterizations of 1-type positive implicative pseudo-BCK algebra and 2-type positive implicative pseudo-BCK algebra (positive implicative BCK-algebra) are displayed. Moreover, some conclusions related with positive implicative filters in previous literature are revised. Finally, the concepts of fuzzy commutative filter and fuzzy implicative filter are proposed, and the relationships among fuzzy 1-type (2-type) positive implicative filters, fuzzy commutative filters and fuzzy implicative filters of pseudo-BCK algebras are investigated.

Some types of falling fuzzy filters of BL-algebras and its applications

The notions of falling fuzzy implicative, positive implicative and fantastic filters of a BL-algebra are introduced based on the theory of falling shadows and fuzzy sets. The relations between fuzzy implicative, positive implicative and fantastic filters and falling fuzzy implicative, positive implicative and fantastic filters are provided. Finally, we apply the concept of falling fuzzy inference relations to BL-algebras and obtain some related results.

On fuzzy positive implicative filters in BE-algebras.

We study several degrees in defining a fuzzy positive implicative filter, which is a generalization of a fuzzy filter in BE-algebras.

Interval-valued intuitionistic (T, S)-fuzzy filters theory on residuated lattices

The aim of this paper is further to develop the filter theory on residuated lattices. Firstly, the notion of interval valued intuitionistic (T, S)-fuzzy filter(IVI (T, S)-fuzzy filter for short) on residuated lattices is introduced by linking the interval valued intuitionistic fuzzy set, t-norm, s-norm and filter theory of residuated lattices; the properties and equivalent characterizations of interval valued intuitionistic (T, S)-fuzzy filter are investigated; the relation between IVI (T, S)-fuzzy filter and filter is studied. Secondly, the notions of interval valued intuitionistic (T, S)-fuzzy implicative filter and interval valued intuitionistic (T, S)-fuzzy Boolean filter are introduced; the properties and equivalent characterizations of them are investigated; the intuitionistic (T, S)-fuzzy implicative filter is proved to be equivalent to the intuitionistic (T, S)-fuzzy Boolean filter in residuated lattices. Finally, the intuitionistic (T, S)-fuzzy positive implicative filter and intuitionistic (T, S)-fuzzy G (MV) filter are introduced; some equivalent characterizations of them are obtained and the relations among these fuzzy filters are investigated.

Intuitionistic fuzzy filter theory of BL-algebras

In this paper, the intuitionistic fuzzy filter theory of BL-algebras is researched. The basic knowledge of BL-algebras and intuitionistic fuzzy sets is firstly reviewed. The notions of intuitionistic fuzzy filters, lattice filters, prime filters, Boolean filters, implicative filters, positive implicative filters, ultra filters and obstinate filters are introduced, respectively. Their important properties are investigated. In intuitionistic fuzzy sets, intuitionistic fuzzy filters, Boolean filters, ultra filters are proved to be equivalent to lattice filters, implicative filters, obstinate filters, respectively. Each intuitionistic fuzzy Boolean filter is an intuitionistic fuzzy positive implicative filter, but the converse may not be true in BL-algebras. The conditions under an intuitionistic fuzzy positive implicative filter being an intuitionistic fuzzy Boolean filter are constructed. Finally, the concepts of the intuitionistic fuzzy ultra and obstinate filters are introduced, and the intuitionistic fuzzy ultra filter is proved to be equivalent to the intuitionistic fuzzy obstinate filter in BL-algebras.

Some kinds of (∈¯,∈¯∨q¯)-fuzzy filters of BL-algebras

The concepts of ( ∈ ¯ , ∈ ¯ ∨ q ¯ ) -fuzzy (implicative, positive implicative and fantastic) filters of B L -algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, ( ∈ , ∈ ∨ q ) -fuzzy (implicative, positive implicative and fantastic) filters and ( ∈ ¯ , ∈ ¯ ∨ q ¯ ) -fuzzy (implicative, positive implicative and fantastic) filters of B L -algebras. Finally, we prove that a fuzzy set F of a B L -algebra L is an ( ∈ ¯ , ∈ ¯ ∨ q ¯ ) -fuzzy implicative filter of L if and only if it is both an ( ∈ ¯ , ∈ ¯ ∨ q ¯ ) -fuzzy positive implicative filter and an ( ∈ ¯ , ∈ ¯ ∨ q ¯ ) -fuzzy fantastic filter.

Some types of generalized fuzzy filters of BL-algebras

The aim of this paper is to introduce the notions of interval valued ( ∈ , ∈ ∨ q ) -fuzzy Boolean (implicative, positive implicative and fantastic) filters in B L -algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued ( ∈ , ∈ ∨ q ) -fuzzy filter in B L -algebras is an interval valued ( ∈ , ∈ ∨ q ) -fuzzy Boolean (implicative) filter if and only if it is both an interval valued ( ∈ , ∈ ∨ q ) -fuzzy positive implicative filter and an interval valued ( ∈ , ∈ ∨ q ) -fuzzy fantastic filter.

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.

On fuzzy fantastic filters of lattice implication algebras

Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.

Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras

We fuzzify the concept of positive implicative filters and associative filters in lattice implication algebras. We prove that (i) every fuzzy positive implicative filter is a fuzzy implicative filter, and (ii) every fuzzy associative filter is a fuzzy filter. We provide equivalent conditions for both fuzzy positive implicative filter and fuzzy associative filter.