Fuzzy group theory: A comparison of different notions of product of fuzzy sets

2000 ◽  
Vol 110 (3) ◽  
pp. 437-446 ◽  
Author(s):  
Naseem Ajmal
Keyword(s):  
Group Theory ◽  
Fuzzy Sets ◽  
Fuzzy Group

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 A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 196075-196085
Author(s):  
Muhammad Gulzar ◽  
M. Haris Mateen ◽  
Dilshad Alghazzawi ◽  
Nasreen Kausar
Keyword(s):  
Group Theory ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Novel Applications

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.

Some Structure Properties of the Cyclic Fuzzy Group Family

2005 ◽  
Vol 12 (03) ◽  
pp. 471-476
Author(s):  
Hacı Aktaş ◽  
Naim Çağman
Keyword(s):  
Fuzzy Sets ◽  
Cyclic Group ◽  
Fuzzy Group ◽  
Classical Notion ◽  
Fuzzy Subgroups ◽  
Group Family ◽  
Structure Properties

In crisp environment, the notion of cyclic group on a set is well known. We study an extension of this classical notion to the fuzzy sets to define the concept of cyclic fuzzy subgroups. By using these cyclic fuzzy subgroups, we then define a cyclic fuzzy group family and investigate its structure properties.

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 RELASI FUZZY PADA GRUP FAKTOR FUZZY

2020 ◽  
Vol 14 (1) ◽  
pp. 33
Author(s):  
Ahmad Madani ◽  
Saman Abdurrahman ◽  
Na'imah Hijriati
Keyword(s):  
Group Theory ◽  
Fuzzy Set ◽  
Fuzzy Relation ◽  
Factor Group ◽  
Fuzzy Relations ◽  
Fuzzy Group ◽  
Congruence Relations ◽  
Fuzzy Congruence ◽  
Fuzzy Subgroups ◽  
Fuzzy Subsets

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 Group Theory

2005 ◽  
Author(s):  
John N. Mordeson ◽  
Kiran R. Bhutani ◽  
Azriel Rosenfeld
Keyword(s):  
Group Theory ◽  
Fuzzy Group
Sign in / Sign up

Export Citation Format

Share Document