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1
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A rough set-based knowledge discovery process

100%
Zhong N., Skowron A.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
603-619
EN
The knowledge discovery from real-life databases is a multi-phase process consisting of numerous steps, including attribute selection, discretization of real-valued attributes, and rule induction. In the paper, we discuss a rule discovery process that is based on rough set theory. The core of the process is a soft hybrid induction system called the Generalized Distribution Table and Rough Set System (GDT-RS) for discovering classification rules from databases with uncertain and incomplete data. The system is based on a combination of Generalization Distribution Table (GDT) and the Rough Set methodologies. In the preprocessing, two modules, i.e. Rough Sets with Heuristics (RSH) and Rough Sets with Boolean Reasoning (RSBR), are used for attribute selection and discretization of real-valued attributes, respectively. We use a slope-collapse database as an example showing how rules can be discovered from a large, real-life database.
2
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Rough membership functions: a tool for reasoning with uncertainty

100%
Pawlak Z., Skowron A.
Banach Center Publications
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1993
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tom 28
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nr 1
135-150
EN
A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.
3
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Rough modeling - a bottom-up approach to model construction

100%
Loken T., Komorowski J.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
|
nr 3
675-690
EN
Traditional data mining methods based on rough set theory focus on extracting models which are good at classifying unseen obj-ects. If one wants to uncover new knowledge from the data, the model must have a high descriptive quality-it must describe the data set in a clear and concise manner, without sacrificing classification performance. Rough modeling, introduced by Kowalczyk (1998), is an approach which aims at providing models with good predictive emphand descriptive qualities, in addition to being computationally simple enough to handle large data sets. As rough models are flexible in nature and simple to generate, it is possible to generate a large number of models and search through them for the best model. Initial experiments confirm that the drop in performance of rough models compared to models induced using traditional rough set methods is slight at worst, and the gain in descriptive quality is very large.
4
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Topological Interpretation of Rough Sets

100%
Grabowski A.
Formalized Mathematics
|
2014
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tom 22
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nr 1
89-97
EN
Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in [14]) and about fourteen sets of Kuratowski [17] (encoded with the help of Mizar adjectives and clusters’ registrations in [1]) in terms of rough approximations. The upper bounds which were 14 and 7 in the original paper of Kuratowski, in our case are six and three, respectively. It turns out that within the classification given by Isomichi, 1st class subsets are precisely crisp sets, 2nd class subsets are proper rough sets, and there are no 3rd class subsets in topological spaces generated by approximations. Also the important results about these spaces is that they are extremally disconnected [15], hence lattices of their domains are Boolean. Furthermore, we develop the theory of abstract spaces equipped with maps possessing characteristic properties of rough approximations which enables us to freely use the notions from the theory of rough sets and topological spaces formalized in the Mizar Mathematical Library [10].
5
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Rough sets methods in feature reduction and classification

100%
Świniarski R. W.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
565-582
EN
The paper presents an application of rough sets and statistical methods to feature reduction and pattern recognition. The presented description of rough sets theory emphasizes the role of rough sets reducts in feature selection and data reduction in pattern recognition. The overview of methods of feature selection emphasizes feature selection criteria, including rough set-based methods. The paper also contains a description of the algorithm for feature selection and reduction based on the rough sets method proposed jointly with Principal Component Analysis. Finally, the paper presents numerical results of face recognition experiments using the learning vector quantization neural network, with feature selection based on the proposed principal components analysis and rough sets methods.
6
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Concept approximations based on rough sets and similarity measures

100%
Saquer J., Deogun J. S.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
655-674
EN
The formal concept analysis gives a mathematical definition of a formal concept. However, in many real-life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts (Saquer and Deogun, 2000a). The process of finding formal concepts that best describe non-definable concepts is called the concept approximation. In this paper, we present two different approaches to the concept approximation. The first approach is based on rough set theory while the other is based on a similarity measure. We present algorithms for the two approaches.
7
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Minimal decision rules based on the apriori algorithm

88%
Fernández M. C., Menasalvas E., Marbán Ó., Peña J. M., Millán S.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
691-704
EN
Based on rough set theory many algorithms for rules extraction from data have been proposed. Decision rules can be obtained directly from a database. Some condition values may be unnecessary in a decision rule produced directly from the database. Such values can then be eliminated to create a more comprehensible (minimal) rule. Most of the algorithms that have been proposed to calculate minimal rules are based on rough set theory or machine learning. In our approach, in a post-processing stage, we apply the Apriori algorithm to reduce the decision rules obtained through rough sets. The set of dependencies thus obtained will help us discover irrelevant attribute values.
8
Content available remote

Knowledge vagueness and logic

88%
Wybraniec-Skardowska U.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
719-737
EN
The aim of the paper is to outline an idea of solving the problem of the vagueness of concepts. The starting point is a definition of the concept of vague knowledge. One of the primary goals is a formal justification of the classical viewpoint on the controversy about the truth and object reference of expressions including vague terms. It is proved that grasping the vagueness in the language aspect is possible through the extension of classical logic to the logic of sentences which may contain vague terms. The theoretical framework of the conception refers to the theory of Pawlak's rough sets and is connected with Zadeh's fuzzy set theory as well as bag (or multiset) theory. In the considerations formal logic means and the concept system of set theory have been used. The paper can be regarded as an outline of the logical theory of vague concepts.
9
Content available remote

On classification with missing data using rough-neuro-fuzzy systems

88%
Nowicki R.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 1
55-67
EN
The paper presents a new approach to fuzzy classification in the case of missing data. Rough-fuzzy sets are incorporated into logical type neuro-fuzzy structures and a rough-neuro-fuzzy classifier is derived. Theorems which allow determining the structure of the rough-neuro-fuzzy classifier are given. Several experiments illustrating the performance of the roughneuro-fuzzy classifier working in the case of missing features are described.
10
Content available remote

Relative sets and rough sets

75%
Mousavi A., Jabedar-Maralani P.
International Journal of Applied Mathematics and Computer Science
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2001
|
tom 11
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nr 3
637-653
EN
In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.
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