International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(1): 59-68
Published online March 25, 2022
https://doi.org/10.5391/IJFIS.2022.22.1.59
© The Korean Institute of Intelligent Systems
Yousef Al-Qudah1 , Khaleed Alhazaymeh2, Nasruddin Hassan3, Hamza Qoqazeh1, Mohammad Almousa1, and Mohammad Alaroud1
1Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, Jordan
2Department of Basic Sciences and Mathematics, Faculty of Science, Philadelphia University, Amman, Jordan
3School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia
Correspondence to :
Yousef Al-Qudah (alquyousef82@gmail.com)
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.
A vague soft set is a mapping from a parameter set to the collection of vague subsets of the universal set. In this study, a vague soft relation is presented based on the Cartesian product of vague soft sets. The basic properties of these relations are studied to explain the concept of transitive closure of a vague soft relation. The symmetric, reflexive, and transitive closures of a vague soft set are introduced followed by examples to illustrate these relations. The concepts are further extended by proposing some of their properties. The existence and uniqueness of the transitive closure of a vague soft relation are established, and an algorithm to compute the transitive closure of a vague soft relation is also provided.
Keywords: Vague soft set, Transitive closure, Symmetric closure, Fuzzy set
No potential conflict of interest relevant to this article was reported.
E-mail: alquyousef82@gmail.com
International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(1): 59-68
Published online March 25, 2022 https://doi.org/10.5391/IJFIS.2022.22.1.59
Copyright © The Korean Institute of Intelligent Systems.
Yousef Al-Qudah1 , Khaleed Alhazaymeh2, Nasruddin Hassan3, Hamza Qoqazeh1, Mohammad Almousa1, and Mohammad Alaroud1
1Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, Jordan
2Department of Basic Sciences and Mathematics, Faculty of Science, Philadelphia University, Amman, Jordan
3School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia
Correspondence to:Yousef Al-Qudah (alquyousef82@gmail.com)
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.
A vague soft set is a mapping from a parameter set to the collection of vague subsets of the universal set. In this study, a vague soft relation is presented based on the Cartesian product of vague soft sets. The basic properties of these relations are studied to explain the concept of transitive closure of a vague soft relation. The symmetric, reflexive, and transitive closures of a vague soft set are introduced followed by examples to illustrate these relations. The concepts are further extended by proposing some of their properties. The existence and uniqueness of the transitive closure of a vague soft relation are established, and an algorithm to compute the transitive closure of a vague soft relation is also provided.
Keywords: Vague soft set, Transitive closure, Symmetric closure, Fuzzy set
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