The relations between Alexandrov L-fuzzy pre-uniformities and approximation operators

Article type: Research Article

Authors: Oh, Ju-Mok | Chan Kim, Yong^{; *; 1}

Affiliations: Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, Korea

Correspondence: [*] Corresponding author. Yong Chan Kim, Department ofMathematics, Gangneung-Wonju National University, Gangneung, Gangwondo 25457, Korea. Tel.: +82 33 640 2270; Fax: +82 33 647 3256; E-mail: yck@gwnu.ac.kr.

Note: [1] This work was supported by Research Fund of Gangneung-Wonju National University in 2016.

Abstract: We introduce the concepts of Alexandrov L-fuzzy pre-uniformities in complete residuated lattices. We obtain Alexandrov L-fuzzy topologies, L-lower approximation operators and L-upper approximation operators induced by Alexandrov L-fuzzy pre-uniformities. Conversely, we obtain Alexandrov L-fuzzy pre-uniformities induced by L-lower approximation operators and L-upper approximation operators.

Keywords: Complete residuated lattices, Alexandrov L-fuzzy topologies, L-lower and L-upper approximation operators, Alexandrov L-fuzzy pre-uniformities

DOI: 10.3233/JIFS-161486

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 215-228, 2017