Author
Guilong Liu
Bio: Guilong Liu is an academic researcher from Beijing Language and Culture University. The author has contributed to research in topics: Rough set & Dominance-based rough set approach. The author has an hindex of 14, co-authored 49 publications receiving 1204 citations.
Papers published on a yearly basis
Papers
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TL;DR: The structures of the lower and upper approximations based on arbitrary binary relations in the generalized rough sets are presented and an algorithm to compute atoms for these two Boolean algebras is presented.
229 citations
TL;DR: This paper compares the covering-based rough sets defined by Zhu with ones defined by Xu and Zhang, and further explores the properties and structures of these types of rough set models.
176 citations
TL;DR: From the viewpoint of the constructive approach, the basic properties of generalized rough sets over fuzzy lattices are obtained and the matrix representation of the lower and upper approximations is given.
135 citations
TL;DR: For two universal sets U and V, the concept of solitary set is defined for any binary relation from U to V and the further properties that are interesting and valuable in the theory of rough sets are studied.
Abstract: For two universal sets U and V, we define the concept of solitary set for any binary relation from U to V. Through the solitary sets, we study the further properties that are interesting and valuable in the theory of rough sets. As an application of crisp rough set models in two universal sets, we find solutions of the simultaneous Boolean equations by means of rough set methods. We also study the connection between rough set theory and Dempster-Shafer theory of evidence. In particular, we extend some results to arbitrary binary relations on two universal sets, not just serial binary relations. We consider the similar problems in fuzzy environment and give an example of application of fuzzy rough sets in multiple criteria decision making in the case of clothes.
132 citations
Journal Article•
TL;DR: A new matrix view of the theory of rough sets is proposed, which starts with a binary relation and redefines a pair of lower and upper approximation operators using the matrix representation.
Abstract: The theory of rough sets deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called, respectively, the lower and the upper approximation. There are at least two methods for the development of this theory, the constructive and the axiomatic approaches. The rough set axiomatic system is the foundation of rough sets theory. This paper proposes a new matrix view of the theory of rough sets, we start with a binary relation and we redefine a pair of lower and upper approximation operators using the matrix representation. Different classes of rough set algebras are obtained from different types of binary relations. Various classes of rough set algebras are characterized by different sets of axioms. Axioms of upper approximation operations guarantee the existence of certain types of binary relations (or matrices) producing the same operators. The upper approximation of the Pawlak rough sets, rough fuzzy sets and rough sets of vectors over an arbitrary fuzzy lattice are characterized by the same independent axiomatic system.
98 citations
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TL;DR: It is shown that Pawlak's rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set.
494 citations
TL;DR: A framework for the study of covering based rough set approximations is proposed and three equivalent formulations of the classical rough sets are examined by using equivalence relations, partitions, and @s-algebras.
440 citations
TL;DR: The equivalency between this type of covering-based rough sets and a type of binary relation based rough sets is established and axiomatic systems for this type-of-covering lower and upper approximation operations are presented.
427 citations
TL;DR: This paper studies arbitrary binary relation based generalized rough sets, in which a binary relation can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied.
416 citations