M-hazy lattices and its induced fuzzifying convexities

Article type: Research Article

Authors: Liu, Qi | Shi, Fu-Gui^{; *}

Affiliations: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Fu-Gui Shi, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, P.R. China. E-mail: fuguishi@bit.edu.cn

Abstract: In this paper we propose a new approach to the fuzzification of lattices, which is defined from the view of algebraic structure. It is also called an M-hazy lattice. Some properties of M-hazy semilattices and M-hazy lattices are discussed. Besides, we also discuss its relations with M-fuzzifying interval spaces and M-fuzzifying convex spaces.

Keywords: M-fuzzy poset, M-hazy semilattice, M-hazy lattice, M-fuzzifying convexity space

DOI: 10.3233/JIFS-182725

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 2, pp. 2419-2433, 2019