A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

Muhammad Gulzar; M. Haris Mateen; Dilshad Alghazzawi; Nasreen Kausar

doi:10.1109/ACCESS.2020.3034626

A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

Muhammad Gulzar^*
, M. Haris Mateen
, Dilshad Alghazzawi
, Nasreen Kausar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

90 Scopus citations

Abstract

In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre-image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.

Original language	English
Article number	9244057
Pages (from-to)	196075-196085
Number of pages	11
Journal	IEEE Access
Volume	8
DOIs	https://doi.org/10.1109/ACCESS.2020.3034626
State	Published - 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2013 IEEE.

Keywords

Complex intuitionistic fuzzy set
complex intuitionistic fuzzy subgroup
level subsets
product of complex intuitionistic fuzzy sets
product of complex intuitionistic fuzzy subgroups

ASJC Scopus subject areas

General Computer Science
General Materials Science
General Engineering

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10.1109/ACCESS.2020.3034626

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title = "A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory",

abstract = "In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre-image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.",

keywords = "Complex intuitionistic fuzzy set, complex intuitionistic fuzzy subgroup, level subsets, product of complex intuitionistic fuzzy sets, product of complex intuitionistic fuzzy subgroups",

author = "Muhammad Gulzar and Mateen, \{M. Haris\} and Dilshad Alghazzawi and Nasreen Kausar",

note = "Publisher Copyright: {\textcopyright} 2013 IEEE.",

year = "2020",

doi = "10.1109/ACCESS.2020.3034626",

language = "English",

volume = "8",

pages = "196075--196085",

journal = "IEEE Access",

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AU - Gulzar, Muhammad

AU - Mateen, M. Haris

AU - Alghazzawi, Dilshad

AU - Kausar, Nasreen

PY - 2020

Y1 - 2020

N2 - In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre-image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.

AB - In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre-image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.

KW - Complex intuitionistic fuzzy set

KW - complex intuitionistic fuzzy subgroup

KW - level subsets

KW - product of complex intuitionistic fuzzy sets

KW - product of complex intuitionistic fuzzy subgroups

UR - https://www.scopus.com/pages/publications/85096302688

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DO - 10.1109/ACCESS.2020.3034626

M3 - Article

AN - SCOPUS:85096302688

SN - 2169-3536

VL - 8

SP - 196075

EP - 196085

JO - IEEE Access

JF - IEEE Access

M1 - 9244057

ER -

A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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