By Bernhard Ganter, Sergei Obiedkov

ISBN-10: 3662492903

ISBN-13: 9783662492901

ISBN-10: 3662492911

ISBN-13: 9783662492918

This is the 1st textbook on characteristic exploration, its idea, its algorithms forapplications, and a few of its many attainable generalizations. characteristic explorationis necessary for buying established wisdom via an interactive strategy, byasking queries to a professional. Generalizations that deal with incomplete, defective, orimprecise facts are mentioned, however the concentration lies on wisdom extraction from areliable info source.The technique relies on Formal notion research, a mathematical conception ofconcepts and suggestion hierarchies, and makes use of its expressive diagrams. The presentationis self-contained. It presents an advent to Formal thought Analysiswith emphasis on its skill to derive algebraic buildings from qualitative data,which will be represented in significant and distinctive graphics.

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The path between v and w belongs to every subtree containing v and w and therefore to each of the selected subtrees. Consequently, it is also contained in their intersection. Thus, S is the vertex set of a subtree. 1. Definition and examples 41 • Take any algebraic structure, for example, a group, and take the set of its subalgebras (subgroups). This is a closure system, because the intersection of arbitrary subgroups is again a subgroup, and, more generally, the intersection of subalgebras is a subalgebra.

For every concept extent A in the list compute the corresponding intent A to obtain a list of all formal concepts (A, A ) of (G, M, I). 2 An example We illustrate the method by means of an example from elementary geometry. The objects of our example are seven triangles. 14. 4. 14: A formal context of triangles and their attributes. The pictures of the triangles have different scales 24 Chapter 1. Concept lattices 1. Write the attribute extents to a list. No. e1 e2 e3 e4 e5 := := := := := extent {T4 } {T1 , T2 , T4 , T6 } {T3 , T4 , T6 } {T1 , T5 } {T2 , T7 } found as {a} {b} {c} {d} {e} 2.

A stronger operation is reduction, which refers to omitting attributes that are equivalent to combinations of other attributes (and dually for objects). For defining reduction, it is convenient to work with a clarified context. 7 When {m} = S , an object g has the attribute m if and only if it has all the attributes from S. If we delete the column m from our cross-table, no essential information is lost because we can reconstruct this column from the data contained in other columns (those of S).

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