Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.Comment: 13 page

Measuring the nearness of layered flow graphs: Application to Content Based Image Retrieval

Preprint version.Rough set based flow graphs represent the flow of information for a given data set where branches of these could be constructed as decision rules. However, in the recent years, the concept of flow graphs has been applied to perceptual systems (also called perceptual flow graphs) where they play a vital role in determining the nearness among disjoint sets of perceptual objects. Perceptual flow graphs were first introduced to represent and reason about sufficiently near visual points in images. In this paper, we have given a practical implementation of flow graphs induced by a perceptual system, defined with respect to digital images, to perform Content-Based Image Retrieval(CBIR). Results are generated using the SIMPLicity dataset, and our results are compared with the near-set based tolerance nearness measure(tNM)."This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) discovery grants 194376 and 418413.