86,820 research outputs found
New neighborhood based rough sets
Neighborhood based rough sets are important generalizations of the classical rough sets of Pawlak, as neighborhood operators generalize equivalence classes. In this article, we introduce nine neighborhood based operators and we study the partial order relations between twenty-two different neighborhood operators obtained from one covering. Seven neighborhood operators result in new rough set approximation operators. We study how these operators are related to the other fifteen neighborhood based approximation operators in terms of partial order relations, as well as to seven non-neighborhood-based rough set approximation operators
NMGRS: Neighborhood-based multigranulation rough sets
AbstractRecently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is based on multiple binary relations on the universe. However, it is worth noticing that the original MGRS can not be used to discover knowledge from information systems with various domains of attributes. In order to extend the theory of MGRS, the objective of this study is to develop a so-called neighborhood-based multigranulation rough set (NMGRS) in the framework of multigranulation rough sets. Furthermore, by using two different approximating strategies, i.e., seeking common reserving difference and seeking common rejecting difference, we first present optimistic and pessimistic 1-type neighborhood-based multigranulation rough sets and optimistic and pessimistic 2-type neighborhood-based multigranulation rough sets, respectively. Through analyzing several important properties of neighborhood-based multigranulation rough sets, we find that the new rough sets degenerate to the original MGRS when the size of neighborhood equals zero. To obtain covering reducts under neighborhood-based multigranulation rough sets, we then propose a new definition of covering reduct to describe the smallest attribute subset that preserves the consistency of the neighborhood decision system, which can be calculated by Chen’s discernibility matrix approach. These results show that the proposed NMGRS largely extends the theory and application of classical MGRS in the context of multiple granulations
Covering rough sets based on neighborhoods: An approach without using neighborhoods
Rough set theory, a mathematical tool to deal with inexact or uncertain
knowledge in information systems, has originally described the indiscernibility
of elements by equivalence relations. Covering rough sets are a natural
extension of classical rough sets by relaxing the partitions arising from
equivalence relations to coverings. Recently, some topological concepts such as
neighborhood have been applied to covering rough sets. In this paper, we
further investigate the covering rough sets based on neighborhoods by
approximation operations. We show that the upper approximation based on
neighborhoods can be defined equivalently without using neighborhoods. To
analyze the coverings themselves, we introduce unary and composition operations
on coverings. A notion of homomorphismis provided to relate two covering
approximation spaces. We also examine the properties of approximations
preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin
Covering matroid
In this paper, we propose a new type of matroids, namely covering matroids,
and investigate the connections with the second type of covering-based rough
sets and some existing special matroids. Firstly, as an extension of
partitions, coverings are more natural combinatorial objects and can sometimes
be more efficient to deal with problems in the real world. Through extending
partitions to coverings, we propose a new type of matroids called covering
matroids and prove them to be an extension of partition matroids. Secondly,
since some researchers have successfully applied partition matroids to
classical rough sets, we study the relationships between covering matroids and
covering-based rough sets which are an extension of classical rough sets.
Thirdly, in matroid theory, there are many special matroids, such as
transversal matroids, partition matroids, 2-circuit matroid and
partition-circuit matroids. The relationships among several special matroids
and covering matroids are studied.Comment: 15 page
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