t-Norm Fuzzy Graphs

Abstract

We generalize the definition of a fuzzy graph by replacing minimum in the basic definitions with an arbitrary [Formula: see text]-norm. The reason for this is that some applications are better modeled with a [Formula: see text]-norm other than minimum. We develop a measure on the susceptibility of trafficking in persons for networks by using a [Formula: see text]-norm other than minimum. We also develop a connectivity index for a fuzzy network. In one application, a high connectivity index means a high susceptibility to trafficking. In the other application, we use a method called the eccentricity of an origin country to determine the susceptibility of a network to trafficking in persons. The models rest on the vulnerabilities and the government responses of countries to trafficking.