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L-fuzzy rough approximation operators via three new types of L-fuzzy relations

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Abstract

Considering L being a frame with an order-reversing involution, three new types of L-fuzzy relations are introduced, which are called mediate, Euclidean and adjoint L-fuzzy relations, respectively. By means of these L-fuzzy relations, three types of L-fuzzy rough approximation operators are constructed and their connections with those three L-fuzzy relations are examined, respectively. An axiomatic approach is adopted to deal with L-fuzzy rough approximation operators. It is shown that each type of L-fuzzy rough approximation operators corresponding to mediate, Euclidean and adjoint L-fuzzy 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. The first author thanks the National Natural Science Foundation of China (No. 11701122) and Beijing Institute of Technology Research Fund Program for Young Scholars (No. 2019CX04111). The second author thanks the National Natural Science Foundation of China (No. 61573127). The third author thanks the National Natural Science Foundation of China (No. 11871189).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Bin Pang

  2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China

    Ju-Sheng Mi

  3. School of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, China

    Wei Yao

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  1. Bin Pang
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  2. Ju-Sheng Mi
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  3. Wei Yao
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Correspondence to Bin Pang.

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Communicated by A. Di Nola.

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Pang, B., Mi, JS. & Yao, W. L-fuzzy rough approximation operators via three new types of L-fuzzy relations. Soft Comput 23, 11433–11446 (2019). https://doi.org/10.1007/s00500-019-04110-3

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