Approximation operators for semiconcepts

Article type: Research Article

Authors: Mao, Hua^{; *}

Affiliations: Department of Mathematics, Hebei University, China

Correspondence: [*] Corresponding author. Hua Mao, Department of Mathematics, Hebei University, Baoding 071002, China. E-mail: mh@hbu.edu.cn.

Abstract: For a formal context, we define an equivalence relation on the set of attributes. Through this equivalence relation, we define the lower and upper approximation operators relative to the family of semiconcepts of the formal context. We study on the two operators with the further properties that are interesting and valuable in the theory of rough set. In addition, we research on the lattice properties of all of semiconcepts in a formal context. Using this lattice, we set up two operators, and find their approximation properties in the theory of rough set. The two ways for giving approximations generalize the idea of Pawlak rough set approximations from one universal set to two non-related universal sets. We provide examples to exam the correct of the two approximation ways in this paper.

Keywords: Semiconcept, approximation, equivalence relation, lattice, rough set

DOI: 10.3233/JIFS-18104

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3333-3343, 2019