Abstract
Considering L being a complete Heyting algebra, this paper mainly proposes a general framework of L-rough approximate operators in which constructive and axiomatic approaches are used. In the constructive approach, upper and lower L-rough approximate operators are introduced and their connections with L-relations are investigated. In the axiomatic approach, various types of set-theoretic L-operators are defined. It is shown that each type of L-rough approximate operators corresponding to special kind of L-relations, including serial, reflexive, symmetric, transitive, mediate, Euclidean and adjoint L-relations as well as their compositions, can be characterized by single axioms.
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Acknowledgements
The authors would like to express their sincere thanks to the Editors and anonymous reviewers for their most valuable comments and suggestions in improving this paper greatly. This work is supported by the Natural Science Foundation of China (Nos. 11701122, 61573127, 61170107) and Beijing Institute of Technology Research Fund Program for Young Scholars (No. 2019CX04111).
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Pang, B., Mi, JS. Using single axioms to characterize L-rough approximate operators with respect to various types of L-relations. Int. J. Mach. Learn. & Cyber. 11, 1061–1082 (2020). https://doi.org/10.1007/s13042-019-01051-z
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DOI: https://doi.org/10.1007/s13042-019-01051-z