Abstract
This paper studies lattice structure of the family of rough fuzzy sets in a given approximation space. Our result is an extension of standard rough sets. Starting with the definition of rough fuzzy sets, the union, intersection and pseudocomplementation operations are generalized. Then it is proved that the above family with these operations is a distributive lattice. This paper also gives the characterization of borderline region of rough fuzzy sets.
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© 2009 Springer-Verlag Berlin Heidelberg
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Liu, G. (2009). Lattice Structures of Rough Fuzzy Sets. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2009. Lecture Notes in Computer Science(), vol 5908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10646-0_31
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DOI: https://doi.org/10.1007/978-3-642-10646-0_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10645-3
Online ISBN: 978-3-642-10646-0
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