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Open AccessArticle

Hesitant Fuzzy Topological Spaces

by Jeong-Gon Lee 1,* and Kul Hur 2
1
Division of Applied Mathematics, Nanoscale Science and Technology Institute, Wonkwang University, Iksan 54538, Korea
2
Department of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 188; https://doi.org/10.3390/math8020188
Received: 1 January 2020 / Revised: 28 January 2020 / Accepted: 30 January 2020 / Published: 4 February 2020
(This article belongs to the Special Issue Fuzziness and Mathematical Logic )
In this study, we define a hesitant fuzzy topology and base, obtain some of their properties, respectively, and give some examples. Next, we introduce the concepts of a hesitant fuzzy neighborhood, Q-neighborhood, closure, and interior and obtain some of their properties, respectively. Furthermore, we define a hesitant fuzzy continuous mapping and investigate some of its properties. Furthermore, we define a hesitant fuzzy subspace and obtain some of its properties. In particular, we obtain the Pasting lemma. We investigate the concept of hesitant fuzzy product space and study some of its properties.
Keywords: hesitant fuzzy set; hesitant fuzzy topology; hesitant fuzzy bees; hesitant fuzzy neighborhood and Q-neighborhood; hesitant fuzzy closure; hesitant fuzzy interior; hesitant fuzzy continuous mapping; hesitant fuzzy subspace; hesitant fuzzy product space hesitant fuzzy set; hesitant fuzzy topology; hesitant fuzzy bees; hesitant fuzzy neighborhood and Q-neighborhood; hesitant fuzzy closure; hesitant fuzzy interior; hesitant fuzzy continuous mapping; hesitant fuzzy subspace; hesitant fuzzy product space
MDPI and ACS Style

Lee, J.-G.; Hur, K. Hesitant Fuzzy Topological Spaces. Mathematics 2020, 8, 188.

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