Abstract
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.
Highlights
In 1965, Zadeh [1] introduced the concept of a fuzzy set as a generalization of a crisp set
In 2010, Torra [13] introduced the notion of a hesitant fuzzy set as an extension of a fuzzy set proposed by Zadeh [1] ([14,15])
The purpose of this paper is to investigate the topological properties on hesitant fuzzy sets
Summary
In 1965, Zadeh [1] introduced the concept of a fuzzy set as a generalization of a crisp set. Kim et al [23] gave characterizations of a hesitant fuzzy positive implicative ideal, a hesitant fuzzy implicative ideal, and a hesitant fuzzy commutative ideal, respectively in BCK-algebras They [24] introduced the category HSet( H ) consisting of all hesitant. The purpose of this paper is to investigate the topological properties on hesitant fuzzy sets. We define a hesitant fuzzy topology and base, obtain some of their properties, respectively, and give. We introduce the concepts of a hesitant fuzzy neighborhood, Q-neighborhood, closure, and interior and obtain some of their properties, respectively (in particular, see Propositions 6, 7, 9, and 10). We define a hesitant fuzzy continuous mapping and investigate some of its properties. We introduce the notion of a hesitant fuzzy product space and study some of its properties
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
