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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(4): 369-377

Published online December 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.4.369

© The Korean Institute of Intelligent Systems

Topology of the Redefined Intuitionistic Fuzzy Rough Sets

Sang Min Yun , Yeon Seok Eom , and Seok Jong Lee

Department of Mathematics, Chungbuk National University, Cheongju, Korea

Correspondence to :
Seok Jong Lee (sjl@cbnu.ac.kr)

Received: October 15, 2021; Revised: November 19, 2021; Accepted: November 29, 2021

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.

In our previous paper, we proposed a new definition of intuitionistic fuzzy rough sets. In this paper, we propose a topology for redefined intuitionistic fuzzy rough sets and investigate the basic properties of their subspaces, transition spaces, and continuous functions. Moreover, we obtain the adjointness between the categories of fuzzy rough sets and intuitionistic fuzzy rough sets. The results obtained from this new definition differ from those of previous studies.

Keywords: Fuzzy rough set, Intuitionistic fuzzy rough sets, Transition topology, Category

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

Sang Min Yun received his Ph.D. degree from Chungbuk National University in 2015. He is a lecturer at the Department of Mathematics, Chungbuk National University since 2015. His research interests include general topology and fuzzy topology. He is a member of KIIS and KMS.

E-mail: jivesm@naver.com


Yeon Seok Eom received her Ph.D. degree from Chungbuk National University in 2012. She is a lecturer at the Department of Mathematics, Chungbuk National University since 2012. Her research interests include general topology and fuzzy topology. She is a member of KIIS and KMS.

E-mail: math1518@naver.com


Seok Jong Lee received his M.S. and Ph.D. degrees from Yonsei University in 1986 and 1990, respectively. He is a professor at the Department of Mathematics, Chungbuk National University since 1989. He was a visiting scholar in Carleton University from 1995 to 1996, and Wayne State University from 2003 to 2004. His research interests include general topology and fuzzy topology. He is a member of KIIS and KMS.

E-mail: sjl@cbnu.ac.kr


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(4): 369-377

Published online December 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.4.369

Copyright © The Korean Institute of Intelligent Systems.

Topology of the Redefined Intuitionistic Fuzzy Rough Sets

Sang Min Yun , Yeon Seok Eom , and Seok Jong Lee

Department of Mathematics, Chungbuk National University, Cheongju, Korea

Correspondence to:Seok Jong Lee (sjl@cbnu.ac.kr)

Received: October 15, 2021; Revised: November 19, 2021; Accepted: November 29, 2021

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

In our previous paper, we proposed a new definition of intuitionistic fuzzy rough sets. In this paper, we propose a topology for redefined intuitionistic fuzzy rough sets and investigate the basic properties of their subspaces, transition spaces, and continuous functions. Moreover, we obtain the adjointness between the categories of fuzzy rough sets and intuitionistic fuzzy rough sets. The results obtained from this new definition differ from those of previous studies.

Keywords: Fuzzy rough set, Intuitionistic fuzzy rough sets, Transition topology, Category

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