Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

Autonomous clustering using rough set theory

This paper proposes a clustering technique that minimises the need for subjective human intervention and is based on elements of rough set theory. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency

Information completeness in Nelson algebras of rough sets induced by quasiorders

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is characterised by a modal operator grasping the notion of "to be classically valid". We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.Comment: 15 page

Rough Set Based Approach for IMT Automatic Estimation

Carotid artery (CA) intima-media thickness (IMT) is commonly deemed as one of the risk marker for cardiovascular diseases. The automatic estimation of the IMT on ultrasound images is based on the correct identification of the lumen-intima (LI) and media-adventitia (MA) interfaces. This task is complicated by noise, vessel morphology and pathology of the carotid artery. In a previous study we applied four non-linear methods for feature selection on a set of variables extracted from ultrasound carotid images. The main aim was to select those parameters containing the highest amount of information useful to classify the image pixels in the carotid regions they belong to. In this study we present a pixel classifier based on the selected features. Once the pixels classification was correctly performed, the IMT was evaluated and compared with two sets of manual-traced profiles. The results showed that the automatic IMTs are not statistically different from the manual one

Class Association Rules Mining based Rough Set Method

This paper investigates the mining of class association rules with rough set approach. In data mining, an association occurs between two set of elements when one element set happen together with another. A class association rule set (CARs) is a subset of association rules with classes specified as their consequences. We present an efficient algorithm for mining the finest class rule set inspired form Apriori algorithm, where the support and confidence are computed based on the elementary set of lower approximation included in the property of rough set theory. Our proposed approach has been shown very effective, where the rough set approach for class association discovery is much simpler than the classic association method.Comment: 10 pages, 2 figure