Abstract
Rough set theory is concerned with the lower and upper approximations through a binary relation on the universe. Binary relations play an important role in this theory. This paper investigates similarity of binary relations based on complete Boolean lattices. First, rough approximations based on complete Boolean lattices are proposed through the predecessor neighborhood. Second, L-fuzzy topologies induced by binary relations are researched where L is a complete Boolean lattice. Thirdly, similarity of binary relations is introduced by using L-fuzzy topology and the fact that every binary relation is solely similar to some preorder relation is showed. Finally, as its theoretical expansion, a topological problem “when can the given L-fuzzy topology be coincided with the L-fuzzy topology induced by some binary relation where L is a complete Boolean lattice?” is considered and this problem is answered by introducing L-fuzzy approximating spaces.
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Acknowledgments
The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions which have helped immensely in improving the quality of this paper. This work is supported by the National Natural Science Foundation of China (11461005), the Natural Science Foundation of Guangxi (2014GXNSFAA118001), Guangxi University Science and Technology Research Project (KY2015YB075, KY2015YB081, KY2015YB266), the Science Research Project 2014 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities (KT201427) and Research Project 2014 of Teacher Education (2014JS013).
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Communicated by A. Di Nola.
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Xie, N., Zhang, G. & Li, Z. Similarity of binary relations based on complete Boolean lattices and related results. Soft Comput 21, 1643–1652 (2017). https://doi.org/10.1007/s00500-016-2086-1
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DOI: https://doi.org/10.1007/s00500-016-2086-1