Topological structures induced by L-fuzzifying approximation operators

Document Type : Research Paper


1 School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China

2 School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, PR China

3 Foundational Courses Department, Wuhan Donghu University, Wuhan 430212, PR China


This paper further studies topological structures induced by L-fuzzifying approximation operators, where L denotes a completely distributive De Morgan algebra. Firstly, the Alexandrov topologies induced by L-fuzzy relations are investigated with respect to L-fuzzifying approximation operators. Especially, the relationships among those Alexandrov topologies are discussed. Secondly, pseudo-similarity sets of L-fuzzy relations are proposed based on the Alexandrov topologies induced by upper and lower L-fuzzifying approximation operators. Meanwhile, the properties of pseudo-similarity sets are discussed, where some examples are presented to show the differences between similarity set of fuzzy relations and pseudo-similarity set of L-fuzzy relations.