Lattice Structures of Rough Fuzzy Sets

Authors:
Guilong Liu
Affiliations:
School of Information Science, Beijing Language and Culture University, Beijing, China 100083
Venue:
RSFDGrC '09 Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
Year:
2009

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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.