Fuzzy Congruence Relation Research Articles

On fuzzy congruence relation in residuated lattices

In this paper, we characterize some properties of fuzzy congruence relations and obtain a fuzzy congruence relation generated by a fuzzy relation in residuated lattices. For this purpose, two various types of fuzzy relations (regular and irregular) are introduced. In order to obtain a fuzzy congruence relation generated by an irregular fuzzy relation it must convert to a regular fuzzy relation.

Fuzzy congruence relation on pseudo-UP algebra

Fuzzy congruence relation on pseudo-UP algebra

Fuzzy congruence relation on fuzzy lattice

Fuzzy congruence relation on fuzzy lattice

Properties of <i>R<sub>0</sub></i>-algebra based on hesitant fuzzy MP filters and congruence relations

<abstract><p>The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of <italic>R<sub>0</sub></italic>-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in <italic>R<sub>0</sub></italic>-algebra.</p></abstract>

Properties of <i>R<sub>0</sub></i>-algebra based on hesitant fuzzy MP filters and congruence relations

<abstract><p>The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of <italic>R<sub>0</sub></italic>-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in <italic>R<sub>0</sub></italic>-algebra.</p></abstract>

Fuzzy Congruence Relations in Generalized Almost Distributive Fuzzy Lattices

This paper defines the fuzzy congruence relation of GADFL (Generalized nearly distributive fuzzy lattices). The ideas of θ - ideal and θ - Prime ideal are introduced in GADFL, and the fuzzy congruence relation is used to explain these ideals.AMS subject classification: 06D72, 06F15, 08A72.

Norms over intuitionistic fuzzy congruence relations on rings

In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.

L‐fuzzy congruence classes in universal algebras

In this paper, we study fuzzy congruence relations and their classes; so-called fuzzy congruence classes in universal algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Fuzzy congruence relations generated by a fuzzy relation are fully characterized in different ways. The main result in this paper is that, we give several Mal'cev-type characterizations for a fuzzy subset of an algebra A in a given variety to be a class of some fuzzy congruence on A. Some equivalent conditions are also given for a variety of algebras to possess fuzzy congruence classes which are also fuzzy subuniverses. Special fuzzy congruence classes called fuzzy congruence kernels are characterized in a more general context in universal algebras.

L-Fuzzy Congruences and L-Fuzzy Kernel Ideals in Ockham Algebras

In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebraA,f, whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebraAto become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence onAhaving a given fuzzy ideal as its kernel.

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.

Isomorphism Theorems on Intuitionistic Fuzzy Abstract Algebras

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017. In this study, homomorphism between intuitionistic fuzzy abstract algebras is defined, intuitionistic fuzzy function is examined and then intuitionistic fuzzy congruence relations are defined on intuitionistic fuzzy abstract algebra. First and third isomorphism theorems on intuitionistic abstract algebras are introduced.

Fuzziness in L-algebras

The aim of this paper is to introduce fuzzy ideals and fuzzy (weak) congruence relations of L-algebras. We give a sufficient and necessary condition for a fuzzy set to be a fuzzy ideal of an L-algebra. After obtaining a necessary condition for a fuzzy set to be a fuzzy ideal of L-algebras, we construct an example to show that the condition is not sufficient. For CKL-algebras, however, we prove that it is both necessary and sufficient. Then we give a process to generate a fuzzy ideal by a fuzzy set of CKL-algebras. Finally, we establish a correspondence between fuzzy ideals and fuzzy weak congruence relations of L-algebras, and get homomorphism theorems induced by fuzzy congruence relations.

The Commutator of Fuzzy Congruences in Universal Algebras

We develop the commutator theory for fuzzy congruence relations of general universal algebras. In particular, for algebras in modular varieties, we characterize the commutator of fuzzy congruences using the Day’s terms.

On Fuzzy Deductive Systems of Hilbert Algebras

In this paper, we study fuzzy deductive systems of Hilbert algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Several characterizations are obtained for fuzzy deductive systems generated by a fuzzy set. It is also proved that the class of all fuzzy deductive systems of a Hilbert algebra forms an algebraic closure fuzzy set system. Furthermore, we obtain a lattice isomorphism between the class of fuzzy deductive systems and the class of fuzzy congruence relations in the variety of Hilbert algebras.

RELASI FUZZY PADA GRUP FAKTOR FUZZY

Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation if and if is a fuzzy congruence relations on fuzzy group and a fuzzy relation defined of is a fuzzy congruence relations on fuzzy factor group.

Fuzzy congruence relations on pseudo BE-algebras

In this paper, we introduce the concept of fuzzy congruence relations on a pseudo BE-algebra and some of properties are investigated. We show that the set of all fuzzy congruence relations is a modular lattice and the quotient structure induced by fuzzy congruence relations is studied.

Fuzzy congruence on product lattices under T-norms

In this paper, by using T-norms, we define the concept of fuzzy congruence on lattice X and if Y be another lattice, then we introduce the concept of fuzzy congruence on the product X × Y under T-norms. Alsobyusing T-norms, we prove that for every fuzzy congruence relation ρ on X × Y the fuzzy congruences ρ X and ρ Y can be defined on X and Y respectively such that ρ = ρ X × ρ Y

Anti Fuzzy Equivalence Relation on Rings with Respect to t-conorm C

In this paper, by using t-conorms, we define the concept of anti fuzzy equivalence relation and anti fuzzy congruence relation on ring R and we investigate some of their basic properties. Also we define fuzzy ideals of ring R under t-conorms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring. Next we investigate this concept under homomorphism of new introduced ring.

Birkhoff Center of a Quotient of Almost Distributive Fuzzy Lattices

The concept of a fuzzy congruence relation is introduced, and we also prove quotient isomorphism in Almost Distributive Fuzzy lattice.

Fuzzy congruence relation generated by a fuzzy relation in vector spaces

Fuzzy congruence relation generated by a fuzzy relation in vector spaces