We aim to construct a formal theory of affordances seen as ternary relations. Beginning with a characterization of affordances proposed by James J. Gibson, and utilizing the tools provided by Zdzisław Pawlak's information systems and rough sets, we construct a mathematically precise definition of both crisp and rough affordances. Then, we analyze modal and approximation operators that enable reasoning about affordances in both scenarios.

Confusion matrices and their associated statistics are a well established tool in machine learning to evaluate the accuracy of a classifier. In the present study, we define a rough confusion matrix based on a very general classifier, and derive various statistics from it which are related to common rough set estimators. In other words, we perform a rough set–like analysis on a confusion matrix, which is the converse of the usual procedure; in particular, we consider upper approximations. A suitable index for measuring the tightness of the upper bound uses a ratio of odds. Odds ratios offer a symmetric interpretation of lower and upper precision, and remove the bias in the upper approximation. We investigate rough odds ratios of the parameters obtained from the confusion matrix; to guard against undue random influences, we also approximate their standard errors.

We explore the usage of the modal possibility operator (and its dual necessity operator) in qualitative data analysis, and show that it-quite literally-complements the derivation operator of formal concept analysis; we also propose a new generalization of the rough set approximation operators. As an example for the applicability of the concepts we investigate the Morse data set which has been frequently studied in multidimensional scaling procedures.

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.

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.

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.