Formal Concept Analysis with Graded Affirmations and Denials

Formal Concept Analysis (FCA) is a method of analysis of relational data whichhas proved to be useful in many areas of computer science. In its basic settingFCA 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 anattribute, he can easily achieve it using a logical negation. This is no longer the casefor graded settings, where the affirmations and denials of incidences between objects
and attributes are a matter of degrees. Management of graded affirmations is wellelaborated in the literature because it represents a direct generalization of a onevaluedcharacter of FCA. In contrast, graded denials have received little attention.
This habilitation thesis provides a thoroughly elaborated framework for handlingdata with graded denials and data with both graded denials and graded affirmationsin FCA. A special attention is given to structures behind FCA in a graded setting.