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In this paper, we introduce an algorithm for computing all the shortest reducts in a decision system. The proposed algorithm is based on determining the size of the shortest reducts using a small super-reduct and some new pruning methods. Once the size of the shortest reduct is determined, all other reducts of the same size are found applying the new pruning methods. The results of our experiments using several synthetic and real-world decision systems show that the proposed algorithm is, in most cases, faster than the state of the art algorithms for computing all the shortest reducts reported in the literature. [ABSTRACT FROM AUTHOR]

Attribute reduction is a key aspect of Rough Set Theory. Finding the complete set of reducts is important for solving problems such as the assessment of attribute relevance, multi–objective cost–sensitive attribute reduction and dynamic reduct computation. The main limitation in the application of Rough Set methods is that finding all reducts of a decision system has exponential complexity regarding the number of attributes. Several algorithms have been reported to reduce the cost of reduct computation. Unfortunately, most of these algorithms relay on high cost operations for candidate evaluation. Therefore, in this paper, we propose a new algorithm for computing all reducts of a decision system, based on the pruning properties of gap elimination and attribute contribution , that uses simpler operations for candidate evaluation in order to reduce the runtime. Finally, the proposed algorithm is evaluated and compared with other state of the art algorithms, over synthetic and real decision systems. [ABSTRACT FROM AUTHOR]

Contrast pattern-based classifiers rely on the discriminative power of contrast patterns. For this reason, many quality measures have been proposed to evaluate the quality of a contrast pattern. These measures allow to distinguish among contrast patterns with low and high discriminative ability for classification. In the literature, many comparative studies among quality measures for contrast patterns have been proposed but all of them were performed without taking into account the class imbalance level. However, in many class imbalance problems, those patterns extracted from the minority class have low support, which could negatively affect their discriminative ability. Therefore, in this paper, we present an experimental study of the effect of class imbalance on quality measures for contrast patterns. This study determines which quality measures for contrast patterns are the best for class imbalance problems; both regarding and disregarding the class imbalance level. Also, for the best quality measures we performed a pairwise comparison to determine which other quality measures have statistically similar behavior to them. This will help to simplify future research since it can be used only one quality measure among those with similar performance. [ABSTRACT FROM AUTHOR]

This paper studies the relations between rough set reducts and typical testors from the so-called logical combinatorial approach to pattern recognition. Definitions, comments and observations are formally introduced and supported by illustrative examples. Furthermore, some theorems expressing theoretical relations between reducts and typical testors are enunciated and proved. We also discuss several practical applications of these relations that can mutually enrich the development of research and applications in both areas. Although we focus on the relation between the classical concepts of testor and reduct, our study can be expanded to include other types of testors and reducts. [ABSTRACT FROM AUTHOR]