Showing papers on "Rough set published in 2007"

Decision-theoretic rough set models

Abstract: Decision-theoretic rough set models are a probabilistic extension of the algebraic rough set model. The required parameters for defining probabilistic lower and upper approximations are calculated based on more familiar notions of costs (risks) through the well-known Bayesian decision procedure. We review and revisit the decision-theoretic models and present new results. It is shown that we need to consider additional issues in probabilistic rough set models.

On Three Types of Covering-Based Rough Sets

Abstract: Rough set theory is a useful tool for data mining. It is based on equivalence relations and has been extended to covering-based generalized rough set. This paper studies three kinds of covering generalized rough sets for dealing with the vagueness and granularity in information systems. First, we examine the properties of approximation operations generated by a covering in comparison with those of the Pawlak's rough sets. Then, we propose concepts and conditions for two coverings to generate an identical lower approximation operation and an identical upper approximation operation. After the discussion on the interdependency of covering lower and upper approximation operations, we address the axiomization issue of covering lower and upper approximation operations. In addition, we study the relationships between the covering lower approximation and the interior operator and also the relationships between the covering upper approximation and the closure operator. Finally, this paper explores the relationships among these three types of covering rough sets.

Fuzzy-Rough Sets Assisted Attribute Selection

Abstract: Attribute selection (AS) refers to the problem of selecting those input attributes or features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition and signal processing. Unlike other dimensionality reduction methods, attribute selectors preserve the original meaning of the attributes after reduction. This has found application in tasks that involve datasets containing huge numbers of attributes (in the order of tens of thousands) which, for some learning algorithms, might be impossible to process further. Recent examples include text processing and web content classification. AS techniques have also been applied to small and medium-sized datasets in order to locate the most informative attributes for later use. One of the many successful applications of rough set theory has been to this area. The rough set ideology of using only the supplied data and no other information has many benefits in AS, where most other methods require supplementary knowledge. However, the main limitation of rough set-based attribute selection in the literature is the restrictive requirement that all data is discrete. In classical rough set theory, it is not possible to consider real-valued or noisy data. This paper investigates a novel approach based on fuzzy-rough sets, fuzzy rough feature selection (FRFS), that addresses these problems and retains dataset semantics. FRFS is applied to two challenging domains where a feature reducing step is important; namely, web content classification and complex systems monitoring. The utility of this approach is demonstrated and is compared empirically with several dimensionality reducers. In the experimental studies, FRFS is shown to equal or improve classification accuracy when compared to the results from unreduced data. Classifiers that use a lower dimensional set of attributes which are retained by fuzzy-rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method. In addition, it is shown that FRFS is more powerful than the other AS techniques in the comparative study

A rough sets based characteristic relation approach for dynamic attribute generalization in data mining

Abstract: Any attribute set in an information system may be evolving in time when new information arrives. Approximations of a concept by rough set theory need updating for data mining or other related tasks. For incremental updating approximations of a concept, methods using the tolerance relation and similarity relation have been previously studied in literature. The characteristic relation-based rough sets approach provides more informative results than the tolerance-and-similarity relation based approach. In this paper, an attribute generalization and its relation to feature selection and feature extraction are firstly discussed. Then, a new approach for incrementally updating approximations of a concept is presented under the characteristic relation-based rough sets. Finally, the approach of direct computation of rough set approximations and the proposed approach of dynamic maintenance of rough set approximations are employed for performance comparison. An extensive experimental evaluation on a large soybean database from MLC shows that the proposed approach effectively handles a dynamic attribute generalization in data mining.

Rough Set Based Generalized Fuzzy $C$ -Means Algorithm and Quantitative Indices

Abstract: A generalized hybrid unsupervised learning algorithm, which is termed as rough-fuzzy possibilistic C-means (RFPCM), is proposed in this paper. It comprises a judicious integration of the principles of rough and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of overlapping partitions. It incorporates both probabilistic and possibilistic memberships simultaneously to avoid the problems of noise sensitivity of fuzzy C-means and the coincident clusters of PCM. The concept of crisp lower bound and fuzzy boundary of a class, which is introduced in the RFPCM, enables efficient selection of cluster prototypes. The algorithm is generalized in the sense that all existing variants of C-means algorithms can be derived from the proposed algorithm as a special case. Several quantitative indices are introduced based on rough sets for the evaluation of performance of the proposed C-means algorithm. The effectiveness of the algorithm, along with a comparison with other algorithms, has been demonstrated both qualitatively and quantitatively on a set of real-life data sets.

Near Sets. Special Theory about Nearness of Objects

Abstract: The problem considered in this paper is how to approximate sets of objects that are qualitatively but not necessarily spatially near each other. The term qualitatively near is used here to mean closeness of descriptions or distinctive characteristics of objects. The solution to this problem is inspired by the work of Zdzislaw Pawlak during the early 1980s on the classification of objects by means of their attributes. This article introduces a special theory of the nearness of objects that are either static (do not change) or dynamic (change over time). The basic approach is to consider a link relation, which is defined relative to measurements associated with features shared by objects independent of their spatial relations. One of the outcomes of this work is the introduction of new forms of approximations of objects and sets of objects. The nearness of objects can be approximated using rough set methods. The proposed approach to approximation of objects is a straightforward extension of the rough set approach to approximating objects, where approximation can be considered in the context of information granules (neighborhoods). In addition, the usual rough set approach to concept approximation has been enriched by an increase in the number of granules (neighborhoods) associated with the classification of a concept as near to its approximation. A byproduct of the proposed approximation method is what we call a near set. It should also be observed that what is presented in this paper is considered a special (not a general) theory about nearness of objects. The contribution of this article is an approach to nearness as a vague concept which can be approximated from the state of objects and domain knowledge.

Rough Sets and Intelligent Systems Paradigms

Abstract: Second International Conference, RSEISP 2014, Held as Part of JRS 2014, Granada and Madrid, Spain, July 9-13, 2014. Proceedings

RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets

Abstract: A hybrid unsupervised learning algorithm, termed as rough-fuzzy c-means, is proposed in this paper. It comprises a judicious integration of the principles of rough sets and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of overlapping partitions. The concept of crisp lower bound and fuzzy boundary of a class, introduced in rough-fuzzy c-means, enables efficient selection of cluster prototypes. Several quantitative indices are introduced based on rough sets for evaluating the performance of the proposed c-means algorithm. The effectiveness of the algorithm, along with a comparison with other algorithms, has been demonstrated on a set of real life data sets.

Evolutionary Rough Feature Selection in Gene Expression Data

Abstract: An evolutionary rough feature selection algorithm is used for classifying microarray gene expression patterns. Since the data typically consist of a large number of redundant features, an initial redundancy reduction of the attributes is done to enable faster convergence. Rough set theory is employed to generate reducts, which represent the minimal sets of nonredundant features capable of discerning between all objects, in a multiobjective framework. The effectiveness of the algorithm is demonstrated on three cancer datasets.

On covering rough sets

Abstract: This paper is devoted to the discussion of extended covering rough set models. Based on the notion of neighborhood, five pairs of dual covering approximation operators were defined with their properties being discussed. The relationships among these operators were investigated. The main results are conditions with which these covering approximation operators are identical.

Lattice theory for rough sets

Abstract: This work focuses on lattice-theoretical foundations of rough set theory. It consist of the following sections: 1: Introduction 2: Basic Notions and Notation, 3: Orders and Lattices, 4: Distributive, Boolean, and Stone Lattices, 5: Closure Systems and Topologies, 6: Fixpoints and Closure Operators on Ordered Sets, 7: Galois Connections and Their Fixpoints, 8: Information Systems, 9: Rough Set Approximations, and 10: Lattices of Rough Sets. At the end of each section, brief bibliographic remarks are presented.

Reduction method for concept lattices based on rough set theory and its application

Abstract: Rough set theory and formal concept analysis are two complementary mathematical tools for data analysis. In this paper, we study the reduction of the concept lattices based on rough set theory and propose two kinds of reduction methods for the above concept lattices. First, we present the sufficient and necessary conditions for justifying whether an attribute and an object are dispensable or indispensable in the above concept lattices. Based on the above justifying conditions, we propose a kind of multi-step attribute reduction method and object reduction method for the concept lattices, respectively. Then, on the basis of the defined discernibility functions of the concept lattices, we propose a kind of single-step reduction method for the concept lattices. Additionally, the relations between the attribute reduction of the concept lattices in FCA and the attribute reduction of the information system in rough set theory are discussed in detail. At last, we apply the above multi-step attribute reduction method for the concept lattices based on rough set theory to the reduction of the redundant premises of the multiple rules used in the job shop scheduling problem. The numerical computational results show that the reduction method for the concept lattices is effective in the reduction of the multiple rules.

Fuzzy Rough Sets: The Forgotten Step

Abstract: Traditional rough set theory uses equivalence relations to compute lower and upper approximations of sets. The corresponding equivalence classes either coincide or are disjoint. This behaviour is lost when moving on to a fuzzy T-equivalence relation. However, none of the existing studies on fuzzy rough set theory tries to exploit the fact that an element can belong to some degree to several "soft similarity classes" at the same time. In this paper we show that taking this truly fuzzy characteristic into account may lead to new and interesting definitions of lower and upper approximations. We explore two of them in detail and we investigate under which conditions they differ from the commonly used definitions. Finally we show the possible practical relevance of the newly introduced approximations for query refinement

Rough Set Theory

Abstract: In this article, basic concepts and different areas of research in rough set theory are presented. Keywords: indiscernibility; approximation space; concept approximation; rough set; rough mereology

Rough Set Theory in analyzing the attributes of combination values for the insurance market

Abstract: Based on Rough Set Theory, this research addresses the effect of attributes/features on the combination values of decisions that insurance companies make to satisfy customers’ needs. Attributes impact on combination values by yielding sets with fewer objects (such as one or two objects), which increases both the lower and upper approximations. It also increases the decision rules, and degrades the precision of decisions. Our approach redefines the value set of attributes through expert knowledge by reducing the independent data set and reclassifying it. This approach is based on an empirical study. The results demonstrate that the redefined combination values of attributes can contribute to the precision of decisions in insurance marketing. Following an empirical analysis, we use a hit test that incorporates 50 validated sample data into the decision rule so that the hit rate reaches 100%. The results of the empirical study indicate that the generated decision rules can cover all new data. Consequently, we believe that the effects of attributes on combination values can be fully applied in research into insurance marketing.