Intuitionistic Fuzzy Real Time Multigraphs for Communication Networks: A Theoretical Model

Many problems of computer science, communication network, transportation systems, etc. can not be modeled into graphs, but into multigraphs only, and then can be easily solved. Nowadays, the networks are expanding very fast in huge volumes in terms of their nodes and links/arcs. For a given alive network, in many situations, its complete topology may not be always available to the communication systems at a given point of time because of the reason that few or many of its links/arcs may be temporarily disable owing to damage or external attack or blockage upon them, and of course they are under repair at that point of time. Besides that, in most of the cases the cost parameters corresponding to its links are not crisp numbers, rather intuitionistic fuzzy numbers (or fuzzy numbers). Thus at any real time instant, the complete multigraph is not available but a submutigraph of it is available to the system for executing its communication or packets transfer. There is no mathematical model available in the existing literature to represent such type of real time network. In this paper the authors propose a mathematical model for such types of multigraphs be called by ‘Real Time Multigraphs’ (RT-multigraphs) in which all real time information (being updated every q quantum of time) are incorporated so that the communication/transportation system can be made very efficiently with optimal results. It is a theoretical work, a kind of intuitionistic fuzzy mathematical model being the most generalized form of the crisp multigraphs.