06041168

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06041168 Yang, Lingyun Xu, Luoshan $L$-definable sets and $L$-rough concept lattices. Fuzzy Syst. Math. 25, No. 2, 131-137 (2011). 2011 National University of Defense Technology, Hunan; China National Publishing Industry Trading Corporation, Beijing ZH residuated lattice $L$-formal context $L$-rough concept lattice $L$-definable set Summary: The notion of $L$-definable sets of an $L$-formal context based on residuated lattices is introduced. Properties of $L$-definable sets are investigated. Relationships of $L$-definable sets and $L$-rough concepts are given. Characterizations of $L$-definable sets and some sufficient and necessary conditions for constant $L$-sets to be $L$-definable sets are obtained. It is proved that the set of $L$-definable sets of an $L$-formal context in the order of $L$-set inclusion is a complete sublattice of the related lattice of the $L$-sets and a complete sublattice of the related $L$-rough concept lattice. A sufficient and necessary condition for the set of $L$-definable sets to be exactly the extension of the related $L$-rough concept lattice is also given.