Strength of connectedness in fuzzy bunch graphs and fuzzy bunch hypergraphs: A new approach

The existing strength of connectedness in fuzzy graph theory is a max–min quantity. According to this definition, thestrength of a path is the membership of its weakest edge, and the connectedness between two vertices is the maximumsuch bottleneck over all paths. That definition is exact for systems in which the weakest edge is the only controllingfactor, but it is too rigid when cumulative route quality matters as well. In this paper we adopt a new notion in whichthe strength of a simple path is a convex combination of its bottleneck and its average edge membership. The newframework defined in this paper for the strength of connectedness is successfully applicable to systems where the classical bottleneck constraint is significant, as well as to systems where the cumulative effects of all edge constraints are more significant than just the bottleneck constraint. Capacity or bandwidth constraints in a network rely only on the weakest (bottleneck) edge, whereas speed, latency, or smoothness constraints have cumulative effects on the entire path from the source to the destination hub in a network. We develop the corresponding theory for fuzzy bunch graphs and fuzzy bunch hypergraphs, that is, grouped fuzzy structures in which vertices are partitioned into bunches and higher-order relations may occur across bunches.

کلیدواژه ها:

Fuzzy graph ، fuzzy bunch graph ، fuzzy bunch hypergraph ، Connectedness ، path strength