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Ordered data widely exists in practical problems. Dominance-based Rough Set Approach (DRSA) is an effective mathematical tool to obtain approximations of concepts and discovery knowledge from ordered data. In this paper, we focus on the dynamic DRSA for the multi-dimensional variation of an ordered information system, and propose a novel incremental simplified algorithm which can efficiently update approximations of DRSA when objects and attributes increase simultaneously. Most of existing algorithms can efficiently deal with the single-dimensional variation of an information system. However, multi-dimensional variations often occur in real dynamic data. That is, the object set, the attribute set or attribute values of an information system often vary simultaneously. Although we can directly use the definitions of approximations, or integrate some single-dimensional incremental algorithms to cope with multi-dimensional variations, this always results in complex algorithm architectures and a large amount of inefficient computation. In our works, by simplifying traditional definitions of DRSA and employing the incremental learning strategy, we develop an algorithm to neglect unnecessary parameters and avoid much redundant computation. Then, we present two different storage schemes for our proposed algorithm to solve the problem of memory consumption. Finally, a series of experiments are conducted to evaluate its efficiency. Experimental results clearly show that for the two-dimensional variation of objects and attributes in an ordered information system, our proposed algorithm is much faster not only than the non-incremental algorithm based on traditional definitions, but also than the integration of two single-dimensional incremental algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Swapped Networks (SNs) are a family of two-level interconnection networks, suitable for constructing large parallel and distributed systems. In this paper, the Minimum Dominating Set (MDS) problem and the Minimum Connected Dominating Set (MCDS) problem in SNs are investigated based on the connectivity rule of SNs. We prove the two problems in SNs are -hard, and present two efficient algorithms for building dominating sets and connected dominating sets in SNs. The proposed algorithms use as input a given (connected) dominating set of the factor network, and yield a good approximation of an MDS or MCDS for the SN provided that the input is a good approximation of an MDS or MCDS for the factor network. We also derive several non-trivial bounds on the (connected) domination parameters of SNs. We believe this work is of theoretical interest in graph theory since SNs form a family of graphs. It may also motivate further research on dominating problems in SNs with their potential applications. [Copyright &y& Elsevier]

Abstract: The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak’s rough set model to a multi-granulation rough set model (MGRS), where the set approximations are defined by using multi equivalence relations on the universe. A number of important properties of MGRS are obtained. It is shown that some of the properties of Pawlak’s rough set theory are special instances of those of MGRS. Moreover, several important measures, such as accuracy measure , quality of approximation and precision of approximation , are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski–Steinhaus metric and the inclusion degree measure. A concept of approximation reduct is introduced to describe the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in MGRS as well. Finally, we discuss how to extract decision rules using MGRS. Unlike the decision rules (“AND” rules) from Pawlak’s rough set model, the form of decision rules in MGRS is “OR”. Several pivotal algorithms are also designed, which are helpful for applying this theory to practical issues. The multi-granulation rough set model provides an effective approach for problem solving in the context of multi granulations. [Copyright &y& Elsevier]