Abstract
So far the core of all considerations was the partial order and its visualization by a Hasse diagram. On the one hand, the system of lines allowed us to identify comparabilities and on the other hand, it also revealed the status of objects relative to the others. In some cases, the Hasse diagram had a structure so that it was possible to explain as to why a certain relative position was obtained for an object. The concept of antagonistic indicators helped in clarifying the reasons for certain positions. The Hasse diagram is a graph focusing on the objects and their mutual relations. It will be extremely helpful, if we can construct a directed graph, where at the same time the constellation of the relevant attribute values responsible for the position of the object is exhibited. As we have seen in Chapters 6 and 7, we may perform ordinal modeling by focusing on object-related or attribute-related manipulations. In the theory of “formal concept analysis,” mutual relationship of the position of an object with the values of its attributes inducing its position is depicted into one single diagram (Davey and Priestley, 1990; Ganter and Wille, 1986; Wolff, 1993; Gugisch, 2001; Carpineto and Romano, 1994; Annoni and Bruggemann, 2008, 2009; Bartel and Nofz, 1997; Bartel, 1997; Kerber, 2006).
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Notes
- 1.
An object has a property or not. Although we can describe the presence or the absence of a property by a binary attribute, we are using the concept “property” for the sake of the simplicity of the text.
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Brüggemann, R., Patil, G.P. (2011). Formal Concept Analysis. In: Ranking and Prioritization for Multi-indicator Systems. Environmental and Ecological Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8477-7_8
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