Abstract
A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space. A rough fuzzy set algebra is a fuzzy set algebra with added dual pair of rough fuzzy approximation operators. In this paper, structures of rough fuzzy set algebras are studied. It is proved that if a system \(({\cal F}(U), \cap, \cup, \sim, L, H)\) is a (a serial, a reflexive, a symmetric, a transitive, an Euclidean, a Pawlak, respectively) rough fuzzy set algebra then the derived system \(({\cal F}(U), \cap, \cup, \sim, LL, HH)\) is a (a serial, a reflexive, a symmetric, a transitive, an Euclidean, a Pawlak, respectively) rough fuzzy set algebra. Properties of rough fuzzy approximation operators in different types of rough fuzzy set algebras are also examined.
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Wu, WZ., Xu, YH. (2006). On Rough Fuzzy Set Algebras. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2006. Lecture Notes in Computer Science(), vol 4223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881599_29
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DOI: https://doi.org/10.1007/11881599_29
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