Günther Gediga

Uncertainly measures of rough set prediction

Abstract The main statistics used in rough set data analysis, the approximation quality, is of limited value when there is a choice of competing models for predicting a decision variable. In keeping within the rough set philosophy of non-invasive data analysis, we present three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle. Our main procedure is based on the principle of indifference combined with the maximum entropy principle, thus keeping external model assumptions to a minimum. The applicability of the proposed method is demonstrated by a comparison of its error rates with results of C4.5, using 14 published data sets.

Approximation Operators in Qualitative Data Analysis

A large part of qualitative data analysis is concerned with approximations of sets on the basis of relational information. In this paper, we present various forms of set approximations via the unifying concept of modal–style operators. Two examples indicate the usefulness of the approach.

The IsoMetrics usability inventory: An operationalization of ISO 9241-10 supporting summative and formative evaluation of software systems

Aiming at a user-oriented approach in software evaluation on the basis of ISO 9241 Part 10, we present a questionnaire (IsoMetrics) which collects usability data for summative and formative evaluation, and document its construction. The summative version of IsoMetrics shows a high reliability of its subscales and gathers valid information about differences in the usability of different software systems. Moreover, we show that the formative version of IsoMetrics is a powerful tool for supporting the identification of software weaknesses. Finally, we propose a procedure to categorize and prioritize weak points, which subsequently can be used as basic input to usability reviews.

Statistical evaluation of rough set dependency analysis

Rough set data analysis (RSDA) has recently become a frequently studied symbolic method in data mining. Among other things, it is being used for the extraction of rules from databases; it is, however, not clear from within the methods of rough set analysis, whether the extracted rules are valid.In this paper, we suggest to enhance RSDA by two simple statistical procedures, both based on randomization techniques, to evaluate the validity of prediction based on the approximation quality of attributes of rough set dependency analysis. The first procedure tests the casualness of a prediction to ensure that the prediction is not based on only a few (casual) observations. The second procedure tests the conditional casualness of an attribute within a prediction rule.The procedures are applied to three data sets, originally published in the context of rough set analysis. We argue that several claims of these analyses need to be modified because of lacking validity, and that other possibly significant results were overlooked.

Maximum Consistency of Incomplete Datavia Non-Invasive Imputation

We present an algorithm to impute missingvalues from given dataalone, and analyse its performance. Theproposed procedure is based onnon-numeric rule based data analysis, and aimsto maximise consistency of imputation from known values. Incontrast to the prevailingstatistical imputation algorithms, it does notmake representationalassumptions or presupposes other modelconstraints. Therefore, it is suitablefor a wide variety of data – sets, and can beused as a pre-processing step beforeresorting to harder numerical methods.

Algebraic Aspects Of Attribute Dependencies In Information Systems

We exhibit some new connections between structure of an information system and its corresponding semilattice of equivalence relations. In particular, we investigate dependency properties and introduce a partial ordering of information systems over a fixed object set U which reflects the sub-semilattice relation on the set of all equivalence relations on U.

Simple data filtering in rough set systems

Abstract In symbolic data analysis, high granularity of information may lead to rules based on a few cases only for which there is no evidence that they are not due to random choice, and thus have a doubtful validity. We suggest a simple way to improve the statistical strength of rules obtained by rough set data analysis by identifying attribute values and investigating the resulting information system. This enables the researcher to reduce the granularity within attributes without assuming external structural information such as probability distributions or fuzzy membership functions.

Classificatory filtering in decision systems

Abstract Classificatory data filtering is concerned with reducing data in size while preserving classification information. Duntsch and Gediga [I. Duntsch, G. Gediga, International Journal of Approximate Reasoning 18 (1998) 93–106] presented a first approach to this problem. Their technique collects values of a single feature into a single value. In this paper we present a novel approach to classificatory filtering, which can be regarded as a generalisation of the approach in the above mentioned paper. This approach is aimed at collecting values of a set of features into a single value. We look at the problem abstractly in the context of lattices. We focus on hypergranules (arrays of sets) in a problem domain, and it turns out the collection of all hypergranules can be made into a lattice. Our solution (namely, LM algorithm) is formulated to find a set of maximal elements for each class, which covers all elements in a given dataset and is consistent with the dataset. This is done through the lattice sum operation. In terms of decision systems, LM collects attributes values while preserving classification structure. To use the filtered data for classification, we present and justify two measures ( C 0 and C 1 ) for the relationship between two hypergranules. Based on the measures, we propose an algorithm (C2) for classification. Both algorithms are evaluated using real world datasets and are compared with C4.5. The result is analysed using statistical test methods and it turns out that there is no statistical difference between the two. Regression analysis shows that the reduction ratio is a strong indicator of prediction success.

Roughian : Rough information analysis

Rough set data analysis (RSDA), introduced by Pawlak, has become a much researched method of knowledge discovery with over 1200 publications to date. One feature which distinguishes RSDA from other data analysis methods is that, in its original form, it gathers all its information from the given data, and does not make external model assumptions as all statistical and most machine learning methods (including decision tree procedures) do. The price which needs to be paid for the parsimony of this approach, however, is that some statistical backup is required, for example, to deal with random influences to which the observed data may be subjected. In supplementing RSDA by such meta‐procedures care has to be taken that the same non‐invasive principles are applied. In a sequence of papers and conference contributions, we have developed the components of a non‐invasive method of data analysis, which is based on the RSDA principle, but is not restricted to “classical” RSDA applications. In this article, we present for the first time in a unified way the foundation and tools of such rough information analysis. © 2001 John Wiley & Sons, Inc.

Relational attribute systems

We introduce a relational operationalization of data which generalizes, among others, the deterministic information systems of Pawlak (1982), the indeterministic systems of Lipski (1976) and Or?owska and Pawlak (1987), and the context relations of Wille (1982); it can also be used for fuzzy data modelling. Using an example from the area of psychometrics, we show how our operationalization can lead to an improved understanding of agreements and disagreements by experts in classification tasks. Copyright 2001 Academic Press.“Das Merkwurdigste an einem Loch ist der Rand”.?(Tucholsky, 1975)