Soft Homomorphism Research Articles

An Abstract Context to Lattice-Based Ideals (Filters) with Multi-Fuzzy Soft Settings

In this study, multi-fuzzy soft ideals (filters) are introduced over the lattice-ordered multi-fuzzy soft set ([Formula: see text]) and their results are shown. The ideas of lattice-ordered multi-fuzzy soft homomorphism ([Formula: see text]) between two [Formula: see text]s are then introduced, along with those of lattice-ordered multi-fuzzy soft isotone map [Formula: see text], lattice-ordered multi-fuzzy soft isomorphism ([Formula: see text]), and kernel of [Formula: see text]. We also look at the principal ideal and soft prime ideal of [Formula: see text].

η-Intuitionistic Fuzzy Soft Groups

In this research, we present the idea of the intuitionistic fuzzy soft group defined on the intuitionistic fuzzy soft set. The main purpose of this research is to create a new concept, which is an intuitionistic fuzzy group. To achieve this, we combine the concept of intuitionistic fuzzy group and intuitionistic fuzzy soft group. As the main result, we prove the correlation between the intuitionistic fuzzy soft group and intuitionistic fuzzy soft group along with some properties of intuitionistic fuzzy soft groups. Also, we prove some properties of a subgroup of an intuitionistic fuzzy soft group. An intuitionistic fuzzy soft homomorphism is also proved.

Nilpotent soft polygroups

In this paper, we introduce nilpotent soft (sub)polygroups. In addition, nilpotency of intersection, extended intersection, restricted union of two nilpotent soft polygroups are studied. Espesialy, a necessary and suficient condition between nilpotency of a polygroup and soft polygroups is obtained. Finally, we define two new soft polygroups (Sα)A∪{c} and (Qα)_A derived from a soft polygroup α_A and study on nilpotency of these structures. Also, we extend a soft homomorphism of groups to polygroups. This helps us to extend some properties of groups to polygroups.

RP-T-Fuzzy Soft Subrings and Ideals of Soft Rings

In this paper we introduce a concept which is called RP-T-fuzzysoft subring and examine some properties of the restricted intersection, therestricted union, the ∧-intersection and the product of their families. A con-dition to make the restricted union of RP-T-fuzzy soft subrings of a soft ringto be RP-T-fuzzy soft subring of this soft ring is determined. A correlationbetween the RP-T-fuzzy soft subring of a soft ring and α-level sets of this softring is demonstrated. The RP-T-fuzzy soft subrings under some binary opera-tions are investigated. Moreover, the image and pre-image of RP-T-fuzzy softsubrings under fuzzy soft homomorphisms is examined. Finally, we present theconcept of RP-T-fuzzy soft ideal and we investigate the analogue propertiesfor them.

Bipolar-value fuzzy soft lie subalgebras

In this paper, the notions of bipolar-value fuzzy soft Lie subalgebras are given, some of their properties are studied. Furthermore, we shall define the definition of bipolar-value fuzzy soft homomorphism of bipolar-value fuzzy soft Lie subalgebras and show that the theorem of bipolar-value fuzzy soft homomorphic pre-image of bipolar-value fuzzy soft Lie subalgebra, we shall give a counterexample which the image of a bipolar-value fuzzy soft Lie subalgebra under bipolar-value fuzzy soft homomorphism needs not be bipolar-value fuzzy soft Lie subalgebra.

Soft Set and Soft Group from Classical View Point

It is shown that a soft set can be represented as a crisp set of soft elements and a soft group as a ordinary group of soft elements. From this view point it is immediate that soft group share the properties of ordinary group. Also using soft elements the definitions of soft co-sets, soft homomorphism and cyclic soft groups are presented and their properties are studied.

On Neutrosophic Normal Soft Groups

The concepts of neutrosophic normal soft group,neutrosophic soft cosets, neutrosophic soft homomorphism are introduced and illustrated by suitable examples in this paper. Several related properties and structural characteristics are investigated. Some of their basic theorems are also established.

On Neutrosophic Normal Soft Groups

The concepts of neutrosophic normal soft group, neutrosophic soft cosets, neutrosophic soft homomorphism are introduced and illustrated by suitable examples in this paper. Several related properties and structural characteristics are investigated. Some of their basic theorems are also established.

A study on soft Z-congruence relations over hemirings

Soft set theory was first proposed by Molodtsov in 1999 as a general mathematical tool for dealing with uncertainties. In this paper, we introduce the notion of soft Z-congruence relations and investigate several related properties. Furthermore, we obtain a one-to-one correspondence between soft Z-congruence relations and strong h-idealistic soft hemirings and a one-to-one correspondence between soft Z-congruence relations and soft strong h-ideals. Moreover, we show that the relationships between fuzzy congruence relations and soft congruence relations. Finally, we show that soft homomorphisms of soft hemirings and establish homomorphism theorems for soft hemirings by using soft Z-congruence relations.

On Normalistic Vague Soft Groups and Normalistic Vague Soft Group Homomorphism

We further develop the theory of vague soft groups by establishing the concept of normalistic vague soft groups and normalistic vague soft group homomorphism as a continuation to the notion of vague soft groups and vague soft homomorphism. The properties and structural characteristics of these concepts as well as the structures that are preserved under the normalistic vague soft group homomorphism are studied and discussed.

Soft relations applied to semigroups

Binary relations, in particular, equivalence relations play an important role in both mathematics and information sciences. The concept of soft sets was initiated by Molodtsov as a general mathematical framework for dealing with uncertainty. The present paper establishes a possible connection between binary relations and soft sets. The concept of soft binary relations is introduced and some related properties are investigated. It is shown that any fuzzy relation may be considered as a soft binary relation. Moreover, we discuss the application of soft binary relations in semigroup theory. We consider soft congruence relations over semigroups and show that all soft congruence relations over a semigroup with a fixed parameter set form a lattice. Finally, the notion of soft homomorphisms is presented and isomorphism theorems for soft semigroups are established based on soft congruence relations.

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.

On Fuzzy Soft Groups

Molodtsov introduced the concept of soft set theory which can be used as generic mathematical tool for dealing with uncertainty. In this paper, we discuss fuzzy soft sets algebraic structure and give the definition of fuzzy soft group. We define operations on fuzzy soft groups and prove some results on them. Furthermore, definitions of fuzzy soft function and fuzzy soft homomorphism are defined and the theorems on homomorphic image and homomorphic pre image are given. After that, the definition of normal fuzzy soft group is given and some of its basic properties are studied.

Introduction to fuzzy soft groups

In this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied. Furthermore, definitions of fuzzy soft function and fuzzy soft homomorphism are defined and the theorems of homomorphic image and homomorphic pre-image are given. After that, the definition of normal fuzzy soft group is given and some of its basic properties are studied.