Matroidal approaches to rough sets via closure operators

AbstractThis paper studies rough sets from the operator-oriented view by matroidal approaches. We firstly investigate some kinds of closure operators and conclude that the Pawlak upper approximation operator is just a topological and matroidal closure operator. Then we characterize the Pawlak upper approximation operator in terms of the closure operator in Pawlak matroids, which are first defined in this paper, and are generalized to fundamental matroids when partitions are generalized to coverings. A new covering-based rough set model is then proposed based on fundamental matroids and properties of this model are studied. Lastly, we refer to the abstract approximation space, whose original definition is modified to get a one-to-one correspondence between closure systems (operators) and concrete models of abstract approximation spaces. We finally examine the relations of four kinds of abstract approximation spaces, which correspond exactly to the relations of closure systems

A comparison of two types of rough sets induced by coverings

Rough set theory is an important technique in knowledge discovery in databases. In covering-based rough sets, many types of rough set models were established in recent years. In this paper, we compare the covering-based rough sets defined by Zhu with ones defined by Xu and Zhang. We further explore the properties and structures of these types of rough set models. We also consider the reduction of coverings. Finally, the axiomatic systems for the lower and upper approximations defined by Xu and Zhang are constructed

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Rough sets, their extensions and applications

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Despite its recency, the theory and its extensions have been widely applied to many problems, including decision analysis, data-mining, intelligent control and pattern recognition. This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets. It also shows the diversity of successful applications these theories have entailed, ranging from financial and business, through biological and medicine, to physical, art, and meteorological