Abstract
The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct \(F^{\uparrow }\) and \(F^{\downarrow }\)-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces.
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Notes
We omit the reference to L, if it is clear from the content.
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Acknowledgements
This study was supported by the project LQ1602 IT4Innovations excellence in science. Another support was given by the Ministry of Science and Technology, DST, Govt. of India, under Grant No. DST/INSPIRE FELLOWSHIP/2013/502.
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Communicated by F. Di Martino, V. Novákc.
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Perfilieva, I., Singh, A.P. & Tiwari, S.P. On the relationship among F-transform, fuzzy rough set and fuzzy topology. Soft Comput 21, 3513–3523 (2017). https://doi.org/10.1007/s00500-017-2559-x
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DOI: https://doi.org/10.1007/s00500-017-2559-x