scholarly journals On certain properties of fuzzy group product operation

2013 ◽  
Vol 21 ◽  
pp. 153
Author(s):  
V.A. Chupordia ◽  
A.S. Markovs'ka
Keyword(s):  
Group Theory ◽  
Abstract Group ◽  
Product Operation ◽  
Fuzzy Group ◽  
Fuzzy Subgroup ◽  
Group Product

Dedekind's modular law plays a very important role in abstract group theory. We prove modular law for fuzzy groups and obtain conditions for a fuzzy subgroup to have a direct complement.

scholarly journals Complex Fuzzy Groups Based on Rosenfeld’s Approach

2021 ◽  
Vol 20 ◽  
pp. 368-377
Author(s):  
Eman A. Abuhijleh ◽  
Mourad Massa’deh ◽  
Amani Sheimat ◽  
Abdulazeez Alkouri
Keyword(s):  
Group Theory ◽  
Normal Subgroup ◽  
Fuzzy Sets ◽  
Unit Disk ◽  
Mathematical Tool ◽  
Membership Functions ◽  
Fuzzy Group ◽  
Fuzzy Subgroup ◽  
Fuzzy Subgroups

Complex fuzzy sets (CFS) generalize traditional fuzzy sets (FS) since the membership functions of CFS reduces to the membership functions of FS. FS values are always at [0, 1], unlike CFS which has values in the unit disk of C. This paper merges notion and concept in group theory and presents the notion of a complex fuzzy subgroup of a group. This proposed idea represents a more general and better optional mathematical tool as one of the approaches in the fuzzy group. However, this research defines the notion of complex fuzzy subgroupiod, complex fuzzy normal subgroup, and complex fuzzy left(right) ideal. Therefore, the lattice, homomorphic preimage, and image of complex fuzzy subgroupiod and ideal are introduced and studied its properties. Finally, complex fuzzy subgroups and their properties are presented and investigated

On fuzzy spaces and fuzzy group theory

1994 ◽  
Vol 80 (3-4) ◽  
pp. 253-282 ◽  
Author(s):  
K.A. Dib
Keyword(s):  
Group Theory ◽  
Fuzzy Group

scholarly journals Fuzzy Bigroup from another Viewpoint

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
L S Akinola
Keyword(s):  
Group Theory ◽  
Group Algebra ◽  
Cartesian Product ◽  
Basic Properties ◽  
Fuzzy Function ◽  
Fuzzy Group ◽  
Definition Of ◽  
Product Of Groups

In group theory, given two groups G and H, it is possible to construct a new group from the Cartesian product of G and H, G × H. With this as a motivation, we replicate this concept in fuzzy group algebra. In this paper, we take a slight deviation from the familiar definition of fuzzy bigroup by looking at fuzzy bigroup from the idea of Cartesian product of groups. We define Cartesian fuzzy function on groups and give examples. We also define Cartesian fuzzy bigroup and study some of its basic properties.

scholarly journals An Overview of the Foundations of the Hypergroup Theory

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1014
Author(s):  
Christos Massouros ◽  
Gerasimos Massouros
Keyword(s):  
Group Theory ◽  
Abstract Algebra ◽  
Special Issue ◽  
Abstract Group ◽  
Structural Relation ◽  
Fundamental Properties ◽  
Theory Versus ◽  
In The Beginning

This paper is written in the framework of the Special Issue of Mathematics entitled “Hypercompositional Algebra and Applications”, and focuses on the presentation of the essential principles of the hypergroup, which is the prominent structure of hypercompositional algebra. In the beginning, it reveals the structural relation between two fundamental entities of abstract algebra, the group and the hypergroup. Next, it presents the several types of hypergroups, which derive from the enrichment of the hypergroup with additional axioms besides the ones it was initially equipped with, along with their fundamental properties. Furthermore, it analyzes and studies the various subhypergroups that can be defined in hypergroups in combination with their ability to decompose the hypergroups into cosets. The exploration of this far-reaching concept highlights the particularity of the hypergroup theory versus the abstract group theory, and demonstrates the different techniques and special tools that must be developed in order to achieve results on hypercompositional algebra.

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