L-fuzzy multigranulation rough set based on residuated lattices

Article type: Research Article

Authors: Le, Van Thien^{a; b} | Hu, Bao Qing^{a; *}

Affiliations: [a] School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China | [b] University of Pedagogy, HoChiMinh City, Vietnam

Correspondence: [*] Corresponding author. Bao Qing Hu, School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China. Tel.: +86 27 68775350; Fax: +86 27 68752256; E-mail: [email protected].

Abstract: This paper studies L-fuzzy multigranulation rough set based on residuted lattices, which is considered as an extension of the classical L-fuzzy rough set. Two models of L-fuzzy optimistic multigrannulation rough set and L-fuzzy pessimistic multigrannulation rough set based on residuted latteices are suggested. Then, we mainly investigate some fundamental properties of the L-fuzzy multigranulation rough set model. With regards to residuated lattices’ topology, we study the topological and the lattice structure in the L-fuzzy optimistic multigranulation rough set model and L-fuzzy pessimistic multigranulation rough set model, respectively.

Keywords: Residuated lattice, ℒ-fuzzy multigranulation rough sets, optimistic-lower/upper set, pessimistic-lower/upper set, Topology

DOI: 10.3233/IFS-152071

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 5, pp. 2821-2831, 2016