International Journal of Computational Intelligence Systems

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Volume 14, Issue 1, 2021, Pages 582 - 593

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

Authors
Muhammad Gulzar1, ORCID, M. Haris Mateen2, ORCID, Yu-Ming Chu3, *, ORCID, Dilshad Alghazzawi4, ORCID, Ghazanfar Abbas5
1Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
2Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
3Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
4Department of Mathematics, King Abdulaziz University, Rabigh 21589, Saudi Arabia
5Department of Mathematics and Statistics, Institute of Southern Punjab, Multan 66000, Pakistan
*Corresponding author. Email: chuyuming@zjhu.edu.cn
Corresponding Author
Yu-Ming Chu
Received 2 April 2020, Accepted 28 December 2020, Available Online 15 January 2021.
DOI
10.2991/ijcis.d.210106.001How to use a DOI?
Keywords
Complex intuitionistic fuzzy sets; Complex intuitionistic fuzzy subrings; Product of complex intuitionistic fuzzy subsets; Product of complex intuitionistic fuzzy subrings; Level subsets of complex intuitionistic fuzzy subset
Abstract

The objective of this article is to present the notion of direct product of two complex intuitionistic fuzzy subrings. We show that the direct product of two complex intuitionistic fuzzy subrings is also complex intuitionistic fuzzy subring and discuss its various algebraic aspects. We also define the level subsets of the direct product of two complex intuitionistic fuzzy subsets and prove that the level subset of the direct product of two complex intuitionistic fuzzy subring is subring and prove some fundamental result of this phenomena. We show that the homomorphic image (preimage) of the direct product of complex intuitionistic fuzzy subrings is a complex intuitionistic fuzzy subring by using the notion of classical homomorphism.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
14 - 1
Pages
582 - 593
Publication Date
2021/01/15
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.210106.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Muhammad Gulzar
AU  - M. Haris Mateen
AU  - Yu-Ming Chu
AU  - Dilshad Alghazzawi
AU  - Ghazanfar Abbas
PY  - 2021
DA  - 2021/01/15
TI  - Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings
JO  - International Journal of Computational Intelligence Systems
SP  - 582
EP  - 593
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210106.001
DO  - 10.2991/ijcis.d.210106.001
ID  - Gulzar2021
ER  -