Document Type : Research Paper
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, PR China
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.