Nowadays, a rapid progress in information technologies brings the digitalisation into almost every part of our life, with information sources being inter-connected through a variety of online or offline media. The basic idea of the presented paper follows the research report of the British Smith Institute for Industrial Mathematics and System Engineering which states that the design of new products, the delivery of new services, and improvements in operational efficiency in the area of Information Technologies rely in large part on the improvement of collaboration between mathematics and informatics. The problem of the modelling of reality, economical and social processes, is very important in the concept of Information Society. Several methodologies, methods, modelling languages and computer-based tools have been developed. We introduce object-systems as generalizations of graphs as modelling tools in the world of Ambient Intelligence.