Transactions on Rough Sets XX

Table of Contents

1. Frontmatter

2. A New Fuzzy-Rough Hybrid Merit to Feature Selection

   Javad Rahimipour Anaraki, Saeed Samet, Wolfgang Banzhaf, Mahdi Eftekhari

   Abstract

   Feature selecting is considered as one of the most important pre-process methods in machine learning, data mining and bioinformatics. By applying pre-process techniques, we can defy the curse of dimensionality by reducing computational and storage costs, facilitate data understanding and visualization, and diminish training and testing times, leading to overall performance improvement, especially when dealing with large datasets. Correlation feature selection method uses a conventional merit to evaluate different feature subsets. In this paper, we propose a new merit by adapting and employing of correlation feature selection in conjunction with fuzzy-rough feature selection, to improve the effectiveness and quality of the conventional methods. It also outperforms the newly introduced gradient boosted feature selection, by selecting more relevant and less redundant features. The two-step experimental results show the applicability and efficiency of our proposed method over some well known and mostly used datasets, as well as newly introduced ones, especially from the UCI collection with various sizes from small to large numbers of features and samples.

3. Greedy Algorithm for the Construction of Approximate Decision Rules for Decision Tables with Many-Valued Decisions

   Mohammad Azad, Mikhail Moshkov, Beata Zielosko

   Abstract

   The paper is devoted to the study of a greedy algorithm for construction of approximate decision rules. This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions. For a given row, we should find a decision from the set attached to this row. We consider bounds on the precision of this algorithm relative to the length of rules. To illustrate proposed approach we study a problem of recognition of labels of points in the plain. This paper contains also results of experiments with modified decision tables from UCI Machine Learning Repository.

4. Algebraic Semantics of Proto-Transitive Rough Sets

   A. Mani

   Abstract

   Rough Sets over generalized transitive relations like proto-transitive ones have been initiated recently by the present author. In a recent paper, approximation of proto-transitive relations by other relations was investigated and the relation with rough approximations was developed towards constructing semantics that can handle fragments of structure. It was also proved that difference of approximations induced by some approximate relations need not induce rough structures. In this research, the structure of rough objects is characterized and a theory of dependence for general rough sets is developed and used to internalize the Nelson-algebra based approximate semantics developed earlier by the present author. This is part of the different semantics of PRAX developed in this paper by her. The theory of rough dependence initiated in earlier papers is extended in the process. This paper is reasonably self-contained and includes proofs and extensions of representation of objects that have not been published earlier.

5. Covering Rough Sets and Formal Topology – A Uniform Approach Through Intensional and Extensional Constructors

   Piero Pagliani

   Abstract

   Approximation operations induced by coverings are reinterpreted through a set of four “constructors” defined by simple logical formulas. The very logical definitions of the constructors make it possible to readily understand the properties of such operators and their meanings.

6. Multiple-Source Approximation Systems, Evolving Information Systems and Corresponding Logics: A Study in Rough Set Theory

   Md. Aquil Khan

   Mathematical logic is used as a tool/language to reason about any kind of data. With the inception of rough set theory (RST), the question of a suitable logic for RST has attracted the attention of many researchers. One of the main contribution of the current article is the development of a logic that can describe aspects of information system such as attribute, attribute-values, as well as the induced concept approximations. Moreover, the current article relates RST to some important issues in artificial intelligence such as multiple-source (agent) knowledge-bases, temporal evolution of knowledge-bases, and information updates. For the multiple-source case, we explored counterparts of standard rough set-theoretic concepts such as concept approximations, definability of concepts, as well as corresponding logics that can express these notions. For the temporal situation, we proposed temporal logics for RST that bring temporal and approximation operators together, to enable reasoning about concept approximations relative to time. An update logic for RST is also introduced that can be used to study flow of information and its effect on concept approximations.

7. Backmatter