Fuzzy Homomorphism Research Articles

A fuzzy characterization of QF rings

Abstract Let R be a ring. R is called a quasi-Frobenius (QF) ring if R is right artinian and R R is an injective right R-module. In this article, we introduce (weak) fuzzy homomorphisms of modules to obtain a fuzzy characterization of QF rings. We also obtain some fuzzy characterizations of right artinian rings and right CF rings. These results throw new light on the research of QF rings and the related CF conjecture. MSC:03E72, 16L60.

Fuzzy Γ-hypergroups

In this paper, we introduce and analyze fuzzy Γ-hypergroups. We study fuzzy Γ-hypergroups and fuzzy Γ-hypergroup homomorphisms in connections with the associated Γ-hypergroups and Γ-hypergroup homomorphisms, respectively. Finally, since the fuzzy regular relations play an important role in getting quotient Γ-structures, we introduce and analyze fuzzy regular and fuzzy strongly regular relations on fuzzy Γ-hypergroups.

An Algebra of Fuzzy (<i>m</i>, <i>n</i>)-Semihyperrings

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (m, n)-semihyperring, etc. and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (m, n)-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (m, n)-semihyperrings and the relationship between fuzzy (m, n)-semihyperrings and the usual (m, n)-semihyper-rings.

Intuitionistic Fuzzy Soft Rings

In this paper, we initiate the study of intuitionistic fuzzy soft rings by combining soft set theory and intuitionistic fuzzy set theory. The notions of an intuitionistic fuzzy soft ring and an idealistic intuitionistic fuzzy soft ring are defined, and several related properties and structural characteristics are investigated. Then, the definitions of an intuitionistic fuzzy soft function and an intuitionistic fuzzy soft homomorphism are presented, and the theorems on homomorphic image and homomorphic pre-image are given. Finally, we introduce the definition of a normal intuitionistic fuzzy soft ring and examine some of its basic properties.

Intuitionistic Fuzzy Hyperhomomorphism and Intuitionistic Fuzzy Normal Subhypergroups

The purpose of this paper is to introduce some basic concepts of intuitionistic fuzzy hyperalgebra. We continue our study of intuitionistic fuzzy hypergroups, by generalising the concept of fuzzy homomorphism and fuzzy normal subgroup based on fuzzy spaces to intuitionistic fuzzy hyperhomomorphism based on intuitionstic fuzzy spaces. We will introduce the notion of an intuitionistic fuzzy quotient hypergroup induced by an intuitionistic fuzzy normal subhypergroup under intuitionistic fuzzy hyperhomomorphism.

On Fuzzy Homomorphisms Between Hypernear-rings

We focus on the study of the structure of hypernear-rings,in this paper,we recall the basics of crisp homomorphism between hyperstructures,particularly,between hypernear-rings and, then,the notion of fuzzy homomorphism between hypernearrings is established and its main properties are analysed.

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

The aim of this paper is to introduce the notion of fuzzy homomorphism and fuzzy isomorphism between two n-ary hypergroups and to extend the fuzzy results of fundamental equivalence relations to n-ary hypergroups. We study some of their properties and prove the decomposition theorems for fuzzy homomorphism and fuzzy isomorphism.

Fuzzy homomorphisms of algebras

In this paper we consider fuzzy relations compatible with algebraic operations, which are called fuzzy relational morphisms. In particular, we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations, called uniform fuzzy relational morphisms, and those which are partially uniform F-functions, called fuzzy homomorphisms. Both uniform fuzzy relations and partially uniform F-functions were introduced in a recent paper by us. Uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras. We give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms, we establish certain relationships between them and fuzzy congruences, and we prove homomorphism and isomorphism theorems concerning them. We also point to some applications of uniform fuzzy relational morphisms.

Fuzzy hypersemigroups

We introduce the notions of fuzzy hypersemigroup, fuzzy hypergroup, fuzzy hyperideal, homomorphism, hyper congruence, fuzzy homomorphism, fuzzy hypercongruence. The purpose of this note is the study of some characterization of fuzzy hypersemigroup, fuzzy hyperideal of a fuzzy hypersemigroup and homomorphism and hypercongruence on a hypersemigroup.

ON THE FUZZY SHEAF OF THE FUNDAMENTAL GROUPS

Let $X$ be a fuzzy path connected space and $H_{a_{\lambda }}$ be the fundamental group of $X$ based for any $a_{\lambda }\in X$, that is $\pi _{1}(X,a_{\lambda })$. Constructing the fuzzy sheaf of the fundamental groups of $X$, it is shown that there is a covariant functor from the category of fuzzy path connected topological spaces and fuzzy continuous mappings to the category of fuzzy sheaves and fuzzy sheaf homomorphisms.

Algebraic properties of LA-languages

In this study, we introduce the concepts of L-valued regular substitution ( LA-substitution), deterministic L-valued regular substitution ( DLA-substitution), L-valued fuzzy homomorphism and its inverse images, homomorphism and its inverse images for a lattice-ordered monoid L. We also study the properties of LA-languages and DLA-languages under the above-mentioned algebraic operations. The algebraic characterization of the L-valued regular language is given.

Is the class of all fuzzy rings a fuzzy HSP-class?

The aim of this paper is to generalize, the notion of fuzzy subring of a crisp ring to that of a fuzzy ring and the notion of crisp homomorphism between crisp rings with fuzzy direct image and fuzzy inverse image to that of a fuzzy homomorphism between fuzzy rings with truth values in different complete lattices, with fuzzy direct and inverse images, in such a way that the class of all fuzzy rings is in fact a fuzzy HSP-Class. In the process several elementary but important properties that naturally extended, are recorded including Correspondence and Isomorphism Theorems.

Construction of quotient BCI(BCK)-algebra via a fuzzy ideal

The present paper gives a new construction of a quotient BCI(BCK)- algebra X/µ by a fuzzy ideal µ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if µ is a fuzzy ideal (closed fuzzy ideal) of X. then X/µ is a commutative (resp. positive implicative, implicative) BCK(BCI)- algebra if and only if µ is a fuzzy commutative (resp. positive implicative, implicative) ideal of X. Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X. We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especially, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

Completeness and an extension theorem for continuous fuzzy linear order-homomorphisms

In this paper, the notions of λ-Cauchy net and completeness in L-topological vector spaces are introduced, and some of their properties are studied. An extension theorem for continuous fuzzy linear order homomorphisms is proved.

CHOICE OF VARIANTS IN A FUZZY ENVIRONMENT: BINARY RELATIONS AND FUZZY DECOMPOSITION

This paper relates to decision making methods, based on the information of fuzzy preference relations. Various variants of informative interpretation of a fuzzy preference relation and the ways of formal definitions of the fuzzy relation of domination and fuzzy set of nondominated alternatives connected with them, are analyzed. The methods of decomposition of the choice problems in the fuzzy environment are considered in detail. To solve these problems there is offered and analyzed the definition of a fuzzy homomor-phism. Two fuzzy decomposition schemes of a choice of variants are offered: “parallel” and “sequential”. For these schemes conditions ensuring correctness of their application are defined.

Fuzzy homomorphisms

In this paper, we give the definitions of six kinds of fuzzy homomorphisms, and our focal point is to study the relations among the I, II, III, IV homomorphisms by some examples and propositions.

Fuzzy homomorphism and f-fuzzy subgroups generated by a fuzzy subset

The main objects of this paper are 1. (i) to characterise t-level image f t ( H) of a subgroup H ⊂ G 1, under f and t-level inverse image f t −1( H) of a subgroup S ⊂ G 2, and 2. (ii) to study the t-level f-fuzzy subgroup generated by a fuzzy subset ( G 1, v) of G 1 and a fuzzy subset ( G 2, v′) of G 2, where f: G 1 → G 2 is a fuzzy group homomorphism.

Fuzzy homomorphism and fuzzy isomorphism

In this paper, we introduce the concepts of fuzzy homomorphism and fuzzy isomorphism between two fuzzy groups by a natural way, and study some of their properties. We prove the decomposition theorems for fuzzy homomorphism and fuzzy isomorphism. Lastly, using the concept of ϕ-fuzzy quotient group we give the fuzzy homomorphism (isomorphism) theorems of fuzzy groups.

Fuzzy homomorphism and algebraic structures

The object of this paper is to prove an analogue of the Fundamental Theorem of Homomorphism and the Second Isomorphism Theorem for fuzzy homomorphisms. We also study the fuzzy subgroup generated by a fuzzy subset.

Fuzzy homomorphisms of rings

In this paper we introduce the concept of fuzzy homomorphisms of rings. We prove for fuzzy homomorphisms, analogues of the homomorphism theorems of ordinary ring homomorphisms.