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Similarity of binary relations based on L-fuzzy topologies

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Abstract

Binary relations play an important role in rough set theory. This paper investigates the similarity of binary relations based on L-fuzzy topologies, where L is a boolean algebra. First, rough approximations based on a boolean algebra are proposed through successor neighborhoods on binary relations. Next, L-fuzzy topologies induced by binary relations are investigated. Finally, similarity of binary relations is introduced by using the L-fuzzy topologies and the fact that every binary relation is solely similar to some preorder relation is proved. It is worth mentioning that similarity of binary relations are both originated in the L-fuzzy topology and independent of the L-fuzzy topology.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of this paper. This work is supported by the NSF of China (11261005, 11161029, 11461002, 11461005), the NSF of Guangxi (2012GXNSFDA276040, 2014GXNSFAA118001), the NSF for Young Scholar of Guangxi (2013GXNSFBA019020), Guangxi Province Universities and Colleges Excellence Scholar and Innovation Team Funded Scheme, Key Discipline of Quantitative Economics in Guangxi University of Finance and Economics (2014YBKT07) and Quantitative Economics Key Laboratory Program of Guangxi University of Finance and Economics (2014SYS01).

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Correspondence to Bin Qin.

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All authors declare that there is no conflict of interest regarding the publication of this manuscript.

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Communicated by A. Di Nola.

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Qin, B., Zeng, F. & Yan, K. Similarity of binary relations based on L-fuzzy topologies. Soft Comput 20, 3497–3504 (2016). https://doi.org/10.1007/s00500-015-1968-y

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  • DOI: https://doi.org/10.1007/s00500-015-1968-y

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