Abstract
We focus on two approaches to formal concept analysis (FCA) of data with fuzzy attributes recently proposed in the literature, namely, on the approach via hedges and the approach via thresholds. Both of the approaches present parameterized ways to FCA of data with fuzzy attributes. Our paper shows basic relationships between the two of the approaches. Furthermore, we show that the approaches can be combined in a natural way, i.e. we present an approach in which one deals with both thresholds and hedges. We argue that while the approach via thresholds is intuitively appealing, it can be considered a special case of the approach via hedges. An important role in this analysis is played by so-called shifts of fuzzy attributes which appeared earlier in the study of factorization of fuzzy concept lattices. In addition to fuzzy concept lattices, we consider the idea of thresholds for the treatment of attribute implications from tables with fuzzy attributes and prove basic results concerning validity and non-redundant bases.
Supported by grant No. 1ET101370417 of GA AV ČR, by grant No. 201/05/0079 of the Czech Science Foundation, and by institutional support, research plan MSM 6198959214.
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Bělohlávek, R., Outrata, J., Vychodil, V. (2006). Thresholds and Shifted Attributes in Formal Concept Analysis of Data with Fuzzy Attributes. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds) Conceptual Structures: Inspiration and Application. ICCS 2006. Lecture Notes in Computer Science(), vol 4068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787181_9
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