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International Journal of Fuzzy Logic and Intelligent Systems 2023; 23(1): 79-90

Published online March 25, 2023

https://doi.org/10.5391/IJFIS.2023.23.1.79

© The Korean Institute of Intelligent Systems

Conormal Product for Intutionistic Anti-Fuzzy Graphs

K. Kalaiarasi1 , L. Mahalakshmi1, Nasreen Kausar2, and A. B. M. Saiful Islam3

1Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tamil Nadu, India
2Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, Turkey
3Department of Civil & Construction Engineering, College of Engineering, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

Correspondence to :
K. Kalaiarasi (kalaishruthi1201@gmail.com)

Received: October 22, 2021; Revised: November 29, 2022; Accepted: January 4, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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This study introduces and analyzes the conormal product of intuitionistic anti-fuzzy graphs (IAFGs) and analyzes certain fundamental theorems and applications. Further, new notions on complete and regular IAFGs were introduced, and the conormal product operation was applied to these IAFGs. We showed that the conormal product of two IAFGs could be used and analyzed important results showing that the conormal product of complete, regular, and strong IAFGs is an IAFG.

Keywords: Conormal product of IFGs, Conormal product of IAFGs, Conormal product of complete IAFGs, Conormal product of regular IAFGs, Conormal product of strong IAFGs

Conflict of Interest

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No potential conflict of interest relevant to this article was reported.

Biographies

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K. Kalaiarasi received a Ph.D. degree in Mathematics from Manonmanium University, Thirunelveli. She is currently an assistant professor of Mathematics in faculty of PG and Research Department of Mathematics, Cauvery College for Women, Trichy. Her research interests include fuzzy inventory models, operations research, data science, and machine learning.

E-mail: kalaishruthi1201@gmail.com

L. Mahalakshmi received a Ph.D degree in Mathematics from Cauvery College for Women Autonomous and affiliated to Bharathidasan University, Tiruchirappalli. She is currently an assistant professor of Mathematics in Faculty of PG and Research Department of Mathematics, Cauvery College for Women, Trichy. Her research interests are associative and commutative (non-associative and non-commutative fuzzy graphs and its applications on fuzzy graphs).

E-mail: mahaparthi19@gmail.com

Nasreen Kausar received a Ph.D. degree in Mathematics from Quaid-i-Azam university Islamabad, Pakistan. She is currently an assistant professor of Mathematics in Faculty of Arts and Science, Yildiz Technical University, Istanbul, Tur-key. Her research interests are associative and commutative (non-associative and non-commutative algebraic structure and its applications on fuzzy structures.

E-mail: nkausar@yildiz.edu.tr

A. B. M. Saiful Islam received a Ph.D. in Structural Engineering with an excellence award from the Department of Civil Engineering, University of Malaya (UM), Malaysia. He did his Post-Doc as a High Impact Research Bright Sparks (HIR BSP) and earlier he obtained a Master of Science in Structural Engineering and Bachelor of Science in Civil Engineering from Bangladesh University of Engineering and Technology (BUET). His research interests include nonlinear dynamics, offshore structures, structural retrofitting, base isolation and lightweight concrete. Dr. Islam authored/coauthored 100+ referred publications. Currently, he is an associate professor in the Department of Civil & Construction Engineering, College of Engineering, Imam Abdulrahman Bin Faisal University (IAU), Saudi Arabia. His involvement includes as Editor-in-Chief/Editor of 4 journals and reviewer of 60+ journals.

E-mail: abm.saiful@gmail.com

Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2023; 23(1): 79-90

Published online March 25, 2023 https://doi.org/10.5391/IJFIS.2023.23.1.79

Copyright © The Korean Institute of Intelligent Systems.

Conormal Product for Intutionistic Anti-Fuzzy Graphs

K. Kalaiarasi1 , L. Mahalakshmi1, Nasreen Kausar2, and A. B. M. Saiful Islam3

1Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tamil Nadu, India
2Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, Turkey
3Department of Civil & Construction Engineering, College of Engineering, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

Correspondence to:K. Kalaiarasi (kalaishruthi1201@gmail.com)

Received: October 22, 2021; Revised: November 29, 2022; Accepted: January 4, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study introduces and analyzes the conormal product of intuitionistic anti-fuzzy graphs (IAFGs) and analyzes certain fundamental theorems and applications. Further, new notions on complete and regular IAFGs were introduced, and the conormal product operation was applied to these IAFGs. We showed that the conormal product of two IAFGs could be used and analyzed important results showing that the conormal product of complete, regular, and strong IAFGs is an IAFG.

Keywords: Conormal product of IFGs, Conormal product of IAFGs, Conormal product of complete IAFGs, Conormal product of regular IAFGs, Conormal product of strong IAFGs

Fig 1.

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Figure 1.

Conormal product of two IAFGs.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 2.

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Figure 2.

Conormal product of complete IAFGs.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 3.

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Figure 3.

Conormal product of complete IAFGs.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 4.

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Figure 4.

Conormal product of complete IAFGs.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 5.

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Figure 5.

Conormal product of strong IAFGs.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 6.

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Figure 6.

Conormal product of regular IAFGs.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 7.

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Figure 7.

Conormal product of regular IAFG.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

Fig 8.

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Figure 8.

Regular IAFG.

The International Journal of Fuzzy Logic and Intelligent Systems 2023; 23: 79-90https://doi.org/10.5391/IJFIS.2023.23.1.79

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