Finding Fuzzy Sets of Bases and Antibases of Periodic Fuzzy Graph

This paper considers a new graph model—a periodic fuzzy graph. Here, a periodic fuzzy graph means a fuzzy graph in which the fuzziness, as a membership function specified on the edges of the graph, changes in discrete time (horizon). At the same time, discrete time has some cyclicity. Periodic fuzzy graphs can be used as models of complex systems, the elements of which have fuzzy connections that change in discrete time and have the property of periodicity. For example, in problems of scheduling, transport networks, technological processes, etc. The work introduces the concepts of a minimal base and a minimal antibase with a given reachability time, and on their basis - a fuzzy set of bases and a fuzzy set of antibases of a periodic fuzzy graph. An algorithm for their calculation is proposed. Examples of finding minimal bases and minimal antibases of a fuzzy graph are also considered.