A topological structure involving hesitant fuzzy sets

Article type: Research Article

Authors: Deepak, D.^a | Mathew, Bibin^{b; *} | John, Sunil Jacob^b | Garg, Harish^c

Affiliations: [a] TKM College of Engineering, Kollam, India | [b] National Institute of Technology Calicut, Kozhikode, India | [c] School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, India

Correspondence: [*] Corresponding author. Bibin Mathew, National Institute of Technology Calicut, Kozhikode, India. E-mail: bibinmathew777@gmail.com.

Abstract:  This paper addresses an extension of the concept of topological spaces to that of hesitant fuzzy spaces. The topology is established using a conjunction and disjunction operator on hesitant fuzzy sets whose properties are discussed in the beginning. Some examples are discussed before introducing the concepts of interior and closure of a hesitant fuzzy set. The properties of these operators are verified to justify the definitions. The concepts of a hesitant fuzzy subspace topology and continuous mappings on hesitant fuzzy sets are studied. The concepts of connectedness and compactness of hesitant fuzzy topological spaces are studied and various results regarding them are proved.

Keywords: Hesitant Fuzzy Topological Spaces, continuous hesitant fuzzy mappings, connected hesitant fuzzy set, compact hesitant fuzzy topological spaces

DOI: 10.3233/JIFS-182673

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6401-6412, 2019