Abstract
In this article we focus on the mathematical development of vulnerability concept and vulnerability index and analyze the dependence of the vulnerability concept definition on that of spreadability [A. El Jai and K. Kassara, “Spreadable distributed systems”, Mathem. and Comp. model., 20, pp. 47--64, 1994; A. Bernoussi and A. El Jai, “New approach of spreadability”, Journal of Mathematical and Computer Modelling 31, pp 93--109, 2000; A. Bernoussi, A. El Jai and A. J. Pritchard, “Spreadability and evolving interfaces”, Inter. J. Syst. Sci., 32, pp. 1217--1232, 2001]. It is found that the mathematical approach of the vulnerability concept is rather attractive and can be applied to many engineering problems. To illustrate this, some examples and applications are considered.