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The paper presents a method for evaluation of questionnaires supported by formal concept analysis. Formal concept analysis provides an expert with a structured view on the data contained in the questionnaires. The method results from experiments with IPAQ (International Physical Activity Questionnaire). The structured view on the data provided by the method suggests various hypotheses which can later be tested. In addition, the structured view on data itself proved to be sufficiently informative to the expert. In addition to the method, the paper presents experiments with evaluation of IPAQ.

Formal concept analysis is a method of exploratory data analysis that aims at the extraction of natural clusters from object-attribute data tables. The clusters, called formal concepts, are naturally interpreted as human-perceived concepts in a traditional sense and can be partially ordered by a subconcept-superconcept hierarchy. The hierarchical structure of formal concepts (so-called concept lattice) represents a structured information obtained automatically from the input data table. The present paper focuses on the analysis of input data with a predefined hierarchy on attributes thus extending the basic approach of formal concept analysis. The motivation of the present approach derives from the fact that very often, people (consciously or unconsciously) attach various importance to attributes which is then reflected in the conceptual classification based on these attributes. We define the notion of a formal concept respecting the attribute hierarchy. Formal concepts which do not respect the hierarchy ...

In formal concept analysis of data with fuzzy attributes, both the extent and the intent of a formal (fuzzy) concept may be fuzzy sets. In this paper we focus on so-called crisply generated formal concepts. A concept $\langle{A,B}\rangle \in \mathcal{B}(X, Y, I)$ is crisply generated if A = D↓ (and so B = D↓↑) for some crisp (i.e., ordinary) set D ⊆ Y of attributes (generator). Considering only crisply generated concepts has two practical consequences. First, the number of crisply generated formal concepts is considerably less than the number of all formal fuzzy concepts. Second, since crisply generated concepts may be identified with a (ordinary, not fuzzy) set of attributes (the largest generator), they might be considered “the important ones” among all formal fuzzy concepts. We present basic properties of the set of all crisply generated concepts, an algorithm for listing all crisply generated concepts, a version of the main theorem of concept lattices for crisply generated concepts, and show that crisply generated concepts are just the fixed points of pairs of mappings resembling Galois connections. Furthermore, we show connections to other papers on formal concept analysis of data with fuzzy attributes. Also, we present examples demonstrating the reduction of the number of formal concepts and the speed-up of our algorithm (compared to listing of all formal concepts and testing whether a concept is crisply generated).