KONEČNÝ Jan. Formal Concept Analysis with Graded Affirmations and Denials. Brno, 2019.
Publication language:english
Original title:Formal Concept Analysis with Graded Affirmations and Denials
Title (cs):Formální konceptuální analýza s potvrzením a popřením ve stupních
Place:Brno, CZ
formal concept analysis, fuzzy set, residuated lattice,
fuzzy Galois connections, concept lattice, affirmation, denial
Formal Concept Analysis (FCA) is a method of analysis of relational data which has proved to be useful in many areas of computer science. In its basic setting FCA is one-valued: it works only with affirmations that objects have attributes. If
a user needs to express a denial of incidence, i.e. that an object does not have an attribute, he can easily achieve it using a logical negation. This is no longer the case for graded settings, where the affirmations and denials of incidences between objects
and attributes are a matter of degrees. Management of graded affirmations is well elaborated in the literature because it represents a direct generalization of a onevalued character of FCA. In contrast, graded denials have received little attention.
This habilitation thesis provides a thoroughly elaborated framework for handling data with graded denials and data with both graded denials and graded affirmations in FCA. A special attention is given to structures behind FCA in a graded setting.

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