Vassia Atanassova at 08:28, 22 December 2021

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	\| author = P. K. Sharma		\| author = P. K. Sharma
	\| institution = P.G. ~~department~~ of Mathematics, D.A.V. College		\| institution = P. G. Department of Mathematics, D.A.V. College
	\| address = Jalandhar, Punjab, India		\| address = Jalandhar, Punjab, India
	\| email-before-at = pksharma		\| email-before-at = pksharma

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2021-12-21T16:16:29Z

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
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{{issue/title
| title = Categorical properties of intuitionistic fuzzy groups
| shortcut = nifs/27/4/55-70
}}
{{issue/author
| author = P. K. Sharma
| institution = P.G. department of Mathematics, D.A.V. College
| address = Jalandhar, Punjab, India
| email-before-at = pksharma
| email-after-at = davjalandhar.com
}}
{{issue/author
| author = Chandni
| institution = Lovely Professional University
| address = Phagwara, India
| email-before-at = chandni16041986
| email-after-at = gmail.com
}}
{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/27/4|Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 4]], pages 55-70
| doi = https://doi.org/10.7546/nifs.2021.27.4.55-70
| file = NIFS-27-4-55-70.pdf
| format = PDF
| size = 243
| abstract = The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function ''β'' : Hom(''A'', ''B'') → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups ''A'' and ''B'' of groups ''G'' and ''H'', respectively. We prove that ''β'' is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.
| keywords = Intuitionistic fuzzy group, Intuitionistic fuzzy homomorphism, Category, Covariant functor, Contravariant functor.
| ams = 03E72, 08A72.
| references =
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# Awodey, S. (2005). Category Theory. Oxford University Press, 2 edition.
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# Wyler, O. (1971). On the categories of general topology and topological algebra, Archiv der Mathematik, 22, 7–17.
# Yuan, X.-H., Li, H.-X., & Stanley Lee, E. (2010). On the definition of the intuitionistic fuzzy subgroup, Computers & Mathematics with Applications, 59, 3117-3129.
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# Zhan, J., & Tan, Z. (2004). Intuitionistic M-fuzzy groups. Soochow Journal of Mathematics, 30, 85–90.

| citations =
| see-also =
}}

Issue:Categorical properties of intuitionistic fuzzy groups - Revision history

Vassia Atanassova at 08:28, 22 December 2021

Vassia Atanassova: Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}}..."