(Fuzzy) hyperlattices and fuzzy preordered lattices

Article type: Research Article

Authors: He, Pengfei | Xin, Xiaolong | Zhan, Jianming

Affiliations: Department of Mathematics, Northwest University, Xi'an, P.R. China | Department of Mathematics, Hubei University for Nationalities, Enshi, P.R. China

Note: [] Corresponding author. Xiaolong Xin, Department of Mathematics, Northwest University, Xi'an 710127, P.R. China. Tel.: +86 13571952880. E-mails: [email protected]; [email protected] (H.P. He); [email protected] (J.M. Zhan).

Abstract: In this paper, we present some connections between (fuzzy) hyperlattices and fuzzy preordered lattices. We introduce the notion of fuzzy preordered lattices. Then, we construct a hyperlattice associated with it and discuss some relations between hyperlattices and fuzzy preordered lattices. Moreover, using the associated hyperlattices, we obtain a fuzzy hyperlattice and analyze it by fuzzy preordered lattices. Finally, we introduce the fundamental relation on fuzzy hyperlattices and obtain a lattice starting from a fuzzy hyperlattice by it.

Keywords: Fuzzy preordered lattice, hyperlattice, fuzzy hyperlattice, scalar element, order-preserving homomorphism, fundamental relation

DOI: 10.3233/IFS-130908

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp. 2369-2381, 2014