99,697 research outputs found
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
Rough matroids based on coverings
The introduction of covering-based rough sets has made a substantial
contribution to the classical rough sets. However, many vital problems in rough
sets, including attribution reduction, are NP-hard and therefore the algorithms
for solving them are usually greedy. Matroid, as a generalization of linear
independence in vector spaces, it has a variety of applications in many fields
such as algorithm design and combinatorial optimization. An excellent
introduction to the topic of rough matroids is due to Zhu and Wang. On the
basis of their work, we study the rough matroids based on coverings in this
paper. First, we investigate some properties of the definable sets with respect
to a covering. Specifically, it is interesting that the set of all definable
sets with respect to a covering, equipped with the binary relation of inclusion
, constructs a lattice. Second, we propose the rough matroids based
on coverings, which are a generalization of the rough matroids based on
relations. Finally, some properties of rough matroids based on coverings are
explored. Moreover, an equivalent formulation of rough matroids based on
coverings is presented. These interesting and important results exhibit many
potential connections between rough sets and matroids.Comment: 15page
Modelling potential movement in constrained travel environments using rough space-time prisms
The widespread adoption of location-aware technologies (LATs) has afforded analysts new opportunities for efficiently collecting trajectory data of moving individuals. These technologies enable measuring trajectories as a finite sample set of time-stamped locations. The uncertainty related to both finite sampling and measurement errors makes it often difficult to reconstruct and represent a trajectory followed by an individual in space-time. Time geography offers an interesting framework to deal with the potential path of an individual in between two sample locations. Although this potential path may be easily delineated for travels along networks, this will be less straightforward for more nonnetwork-constrained environments. Current models, however, have mostly concentrated on network environments on the one hand and do not account for the spatiotemporal uncertainties of input data on the other hand. This article simultaneously addresses both issues by developing a novel methodology to capture potential movement between uncertain space-time points in obstacle-constrained travel environments
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