by   Martin Kovár, Marie Klimešová, Štěpán Křehlík

Formal concept of a formal context is a notion introduced by B. Ganter and R. Wille at the end of the 70's. Both, formal context and formal concept, are two key notions of Formal Concept Analysis. They are used in theoretical computer scince for especially in connection with data representation, organization and analysis. The generalized distance of two formal concepts is an important characteristic of their mutual similarity. This can be used for classification of various objects and structures in mathematics and information sciences. As examples there can be mentioned databases, information systems, dynamical systems, topological structures, causal structures and others.

Our experimental application Formal Concept Object Distances checks first if the formal context and its two formal concepts are correctly given by the input. If so it calculates the four modifications of the generalized distance between the two given concepts. The calcullation is based on the properties of the framework associated with the formal context on the set of its objects. The notion of a generalized distance is inspired by the notion of partial metrics due to S. Matthews. A source of inspiration of this application is also the joint research of the first author with his former student, A. Chernikava during her doctoral study. The coauthors, M. Klimešová and Š. Křeklík are the current doctoral students of the Department of Mathematics.