Roughness in Substructures of Skew Lattices

Article type: Research Article

Authors: Zhi, Yuan^{a; b} | Zhou, Xiangnan^{b; *}

Affiliations: [a] School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei province, P.R. China | [b] College of Mathematics and Econometrics, Hunan University, Changsha, Hunan province, P.R. China

Correspondence: [*] Corresponding author. Xiangnan Zhou, College of Mathematics and Econometrics, Hunan University, Changsha, Hunan province, P.R. China. E-mail: xnzhou81026@163.com.

Abstract: Skew lattice theory and rough set theory are relatively independent. In this paper, we focus on the relationship between rough sets and skew lattices, a non-commutative generalization of lattices. Motivated by the study on rough ideals in algebraic structures such as lattices, groups and gamma semigroups, we investigate rough substructures of skew lattices, including rough sub-skew lattices and rough sublattices, rough ideals and rough filters, as well as rough s-ideals and rough s-filters.

Keywords: Rough sets, Skew lattices, Ideals, S-ideals, Rough s-ideals, Rough ideals, Homomorphisms

DOI: 10.3233/JIFS-181762

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5959-5972, 2019