Gabriele Oliva, Stefano Panzieri and Roberto Setola, "Fuzzy Dynamic Input-Output Inoperability Model," International Journal on Critical Infrastructure Protection, 2011. (doi:10.1016/j.ijcip.2011.09.003) [Sciencedirect]
This paper describes an extension of the input–output inoperability model (IIM) that accommodates uncertain and vague data. In the resulting “fuzzy version” of the dynamic IIM model (FD-IIM), the level of inoperability of each infrastructure and the Leontief coefficients are specified using fuzzy variables that express expert knowledge about infrastructure interdependences. An important result is that, under certain conditions, solution convergence for the fuzzy model can be inferred based on the stability properties of the “crisp” (non-fuzzy) version of the system of interest. A case study involving the Italian critical infrastructure is used to demonstrate the feasibility and utility of the approach.