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L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems

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Abstract

For a completely distributive De Morgan algebra L, we develop a general framework of L-fuzzy rough sets. Said precisely, we introduce a pair of L-fuzzy approximation operators, called upper and lower L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems. It is shown that the proposed approximation operators are a common extension of the L-fuzzifying approximation operators derived from L-fuzzy relations (INS 2019) and the approximation operators derived from general neighborhood systems (KBS 2014). Furthermore, we investigate the unary, serial, reflexive, transitive and symmetric conditions in general L-fuzzifying neighborhood systems, and then study the associated approximation operators from both a constructive method and an axiomatic method. Particularly, for transitivity (resp., symmetry), we give two interpretations, one is an appropriate generalization of transitivity (resp., symmetry) for L-fuzzy relations, and the other is a suitable extension of transitivity (resp., symmetry) for general neighborhood systems. In addition, for some special L-fuzzifying approximation operators, we use single axiom to characterize them, respectively. At last, the proposed approximation operators are applied in the research of incomplete information system, and a three-way decision model based on them is established. To exhibit the effectiveness of the model, a practical example is presented.

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Acknowledgements

The authors thank the editor and the reviewers for their valuable comments and suggestions. This work is supported by National Natural Science Foundation of China (nos. 11801248, 11961025, 11501278, 11471152) and the KeYan Foundation of Liaocheng University (318011920).

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Correspondence to Bingxue Yao.

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Li, L., Yao, B., Zhan, J. et al. L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems. Int. J. Mach. Learn. & Cyber. 12, 1343–1367 (2021). https://doi.org/10.1007/s13042-020-01237-w

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