T-similarity of fuzzy relations on a complete residuated lattice and its algebraic structures

Article type: Research Article

Authors: Yu, Guangji^{a; *} | Wu, Xiaoyun^a | Xia, Guoen^b

Affiliations: [a] School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R. China | [b] Department of Academic Affairs, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R. China

Correspondence: [*] Corresponding author. Guangji Yu, School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P.R. China. Tel.: +86 07713265661; Fax: +86 07713265661; E-mail: guangjiyu100@126.com.

Abstract: This paper studies T-similarity of L-fuzzy relations and its algebraic structures where L is a complete residuated lattice. L-fuzzy topologies induced by L-fuzzy rough approximation operators are investigated and T-similarity of L-fuzzy relations is first introduced. Next, a characteristic condition for L-fuzzy relations to be T-transitive is established. Finally, algebraic structures on T-similarity of L-fuzzy relations are obtained and an example is given in order to illustrate the practical significance and possible applications of the proposed concepts.

Keywords: Complete residuated lattice, L-fuzzy approximate space, L-fuzzy relation, L-fuzzy topology, T-similarity, algebraic structure

DOI: 10.3233/JIFS-16606

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2641-2653, 2017