Abstract
Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering. The main contributions of this paper are threefold. First, any graph is converted to a covering. Two graphs induce the same covering if and only if they are isomorphic. Second, some new concepts are defined in covering-based rough sets to correspond with ones in graph theory. The upper approximation number is essential to describe these concepts. Finally, from a new viewpoint of covering-based rough sets, the general reduct is defined, and its equivalent characterization for the edge cover is presented. These results show the potential for the connection between covering-based rough sets and graphs.
Highlights
Covering is an extensively used form of data representation
From a new viewpoint of covering-based rough sets, the general reduct is defined, and its equivalent characterization for the edge cover is presented. These results show the potential for the connection between covering-based rough sets and graphs
In application, covering-based rough sets have been used in rule learning [22, 23], attribute reduction [24,25,26], feature selection [27, 28], and other fields [29,30,31,32]
Summary
Covering is an extensively used form of data representation. As a generalization of classical rough set theory [1, 2], covering-based rough set theory [3, 4] was proposed to process this type of data. Some graph concepts including vertex covers, independent sets, edge covers, and matchings are equivalently formulated using covering-based rough sets. Vertex covers, edge covers and matchings are equivalently described through the upper approximation number and independent sets with the lower approximation. Due to equivalent characterizations of covering-based rough sets and graphs, these problems can be converted and addressed under the framework of covering-based rough sets. In this way, heuristic reduction algorithms [5,6,7,8] for them may be employed. Two coverings generate the same lower approximation if and only if their reducts are the same
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
