Measures of compactness in L-fuzzy pretopological spaces

Article type: Research Article

Authors: Shi, Fu-Gui | Liang, Chengyu

Affiliations: School of Mathematics, Beijing Institute of Technology, Beijing, P.R. China

Note: [] Corresponding author. Chengyu Liang, School of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China. E-mails: liangchengyu87@163.com; fuguishi@bit.edu.cn (F.-G. Shi).

Abstract: In this paper, we introduce the concepts of the degrees of compactness, countable compactness and Lindelöf property in L-fuzzy pretopological spaces by means of implication operator. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. The notions of pre-compactness and semi-compactness in L-fuzzy topological spaces can be viewed as special cases of compactness in L-fuzzy pretopological spaces. Their properties are investigated. Further when L is completely distributive, their characterizations are presented.

Keywords: L-fuzzy pretopology, implication operator, fuzzy compactness degree, countable compactness, Lindelöf property

DOI: 10.3233/IFS-130839

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 3, pp. 1557-1561, 2014