Fuzzy graphs in the evaluation and optimization of networks

Referring to some predecessing models the paper introduces the concept of fuzzy vertex graphs. A way is shown for modeling various quantitatively featurable functional capabilities of computer, communication and similar networks. It is shown that functional capability of distributed hierarchical multicomponent systems (networks) can be described by the directed rooted tree model according to the above fuzzy graph idea. The problem of optimizing the overall functional capability with given component (vertex) set is introduced. The fuzzy formulae based on the algebraic connectives which are to be optimized are constructed. In the main part of the paper a series of results are presented concerning some special, however important cases. Also the hypotheses founded on some computer experiments are formulated. Finally, the application of these results and hypotheses are shown by the example of a distributed communication switching system family being in development in Hungary.