ABSTRACT. Irregularity indices are generally used for quantitative characterization of topological structure of non-regular graphs. According to a widely accepted preconception, using a topological invariant (called a graph irregularity index) for that purpose, the results of graph irregularity classification should be consistent with our subjective judgements (intuitive feeling). In the case of structurally strongly similar graphs, it is difficult to select the proper irregularity index by which the irregularity ranking (ordering) of graphs can be performed in a consistent manner to our preliminary expectations. In this work we investigate various possibilities of constructing so-called composite irregularity indices obtained as a function of traditional irregularity indices and test their discriminatory performance. Moreover, it has been demonstrated in examples, that in some cases the subjective evaluation of graph irregularities leads to false conclusions. This phenomenon is called the paradox of quantitative graph irregularity characterization. From our study we have concluded that results of graph irregularity measuring depend not only on the choice of irregularity indices but it is influenced strongly on the preselected set of graphs to be investigated. Similar problems arise for the quantitative evaluation of information content, complexity or branching of molecular graphs.
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With the spread of active styles of living, regular health monitoring and risk estimation of exercises became an essential part of everyday life. In this paper, a fuzzy logic-based hierarchical, classified risk calculation model is introduced, which can be used to assess the risk level of sport activity in realtime. The model considers the current physical status and the preliminary assessed medical conditions of the person, the activity load of the exercise, as well as the environmental conditions. Based on this information, a hierarchical fuzzy decision making system evaluates the risk level and sends warning (to the person to stop the activity) or alerting (to a medical doctor/hospital) or both if necessary. By this, serious health problems/crisis situations can be avoided. The complexity of the model is optimized by the application of the singular value decomposition-based complexity reduction algorithm. In critical situations [when the available (dynamically changing) amount of time, resources, and data become insufficient], the anytime mode of operation helps to cope with the temporal conditions and to find a tradeoff between the computational complexity of the evaluations and the accuracy of the results. The system can be operated real-time at home, thus making more comfortable and safer the active (preventive) life and rehabilitation processes of conscious people.
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