A Comprehensive Study on Pythagorean Fuzzy Normal Subgroups and Pythagorean Fuzzy Isomorphisms

被引:5
作者
Razaq, Abdul [1 ]
Alhamzi, Ghaliah [2 ]
Razzaque, Asima [3 ]
Garg, Harish [4 ,5 ]
机构
[1] Univ Educ, Dept Math, Div Sci & Technol, Lahore 54770, Pakistan
[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh 11564, Saudi Arabia
[3] King Faisal Univ, Dept Basic Sci, Al Hasa 31982, Saudi Arabia
[4] Thapar Inst Engn & Technol Deemed Univ, Sch Math, Patiala 147004, Punjab, India
[5] Graph Era Deemed Univ, Dept Math, Dehra Dun 248002, Uttarakhand, India
来源
SYMMETRY-BASEL | 2022年 / 14卷 / 10期
关键词
Pythagorean fuzzy set; Pythagorean fuzzy subgroup; Pythagorean fuzzy normal subgroup; Pythagorean fuzzy isomorphism; GROUP DECISION-MAKING; MODEL; SETS;
D O I
10.3390/sym14102084
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The Pythagorean fuzzy set is an extension of the intuitionistic fuzzy set used to handle uncertain circumstances in various decisions making problems. Group theory is a mathematical technique for dealing with problems of symmetry. This study deals with Pythagorean fuzzy group theory. In this article, we characterize the notion of a Pythagorean fuzzy subgroup and examine various algebraic properties of this concept. An extensive study on Pythagorean fuzzy cosets of a Pythagorean fuzzy subgroup, Pythagorean fuzzy normal subgroups of a group and Pythagorean fuzzy normal subgroup of a Pythagorean fuzzy subgroup is performed. We define the notions of Pythagorean fuzzy homomorphism and isomorphism and generalize the notion of factor group of a classical group W relative to its normal subgroup S by defining a PFSG of WS. At the end, the Pythagorean fuzzy version of fundamental theorems of isomorphisms is proved.
引用
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页数:19
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