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.
The generalized distances of objects in the given formal context:
Is the formal context correctly given?
Is the first given pair of sets a formal concept of the given formal context?
Is the second given pair of sets a formal concept of the given formal context?
The object concept distance of the first type:
The object concept distance of the second type:
The object concept distance of the third type:
The object concept distance of the fourth type:
The application Formal Concept Object Distances is written in Java powered by Wolfram webMathematica 3.1. The application is hosted at the server of the Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology. The results representing its theoretical background were presented by the authors on several scientific conferences as an integral part of their research. In case of interest in more detail, see  or contact the authors. For research and scientific activities the software is available free of charge. In all other cases, please contact RNDr. M. Novák, Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, phone: +420 5 4114 3135. Acknowledgement: FEKT-S-14/2200 "Reprezentace řešení dynamických systémů, numerické algoritmy řešení"