A Methodology to Estimate Input-Output Inoperability Model Parameters

  • Roberto Setola
  • Stefano De Porcellinis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5141)


Input-output Inoperability Model (IIM) is a simple tool able to emphasize cascade effects induced in a complex infrastructure scenario by dependencies phenomena. One of the most challenging tasks for its use is the estimation of the model parameters. In the literature they are generally evaluated on the base of the amount of mutual economical exchanges. In this paper we illustrate a methodology to evaluate IIM parameters on the base of behavioural characteristics of the different infrastructures during a crisis. The approach exploits data collected via experts’ interviews handling also information about failure duration, estimation confidence and expert reliability. The methodology has been applied, as case study, to analyse Italian situation.


Input-output Inoperability Model (IIM) Interdependencies Critical Infrastructures Impact Analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amin, M.: Modelling and Control of Complex Interactive Networks. IEEE Control Syst. Mag., 22–27 (2002)Google Scholar
  2. 2.
    Bologna, S., Setola, R.: The Need to Improve Local Self-Awareness in CIP/CIIP. In: Proc. First IEEE International Workshop on Critical Infrastructure Protection (IWCIP 2005), Darmstadt, Germany, November 3–4, 2005, pp. 84–89 (2005)Google Scholar
  3. 3.
    Dubois, D., Prade, H.: Possibility Theory: an Approach to Computerized Processing of Uncertainty. Plenum Publishing Corporation, New York (1998)Google Scholar
  4. 4.
    Giacchetti, R.E., Young, R.E.: A Parametric Representation of Fuzzy Numbers and their Arithmetic Operators. Fuzzy Sets and Systems 91, 185–202 (1997)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Haimes, Y.Y., Horowitz, B.M., Lambert, J.H., Santos, J., Lian, C., Crowther, K.: Inoperability Input-Output Model for Interdependent Infrastructure Sector II: Case Studies. Journal of Infrastructure Systems, 80–92 (2005)Google Scholar
  6. 6.
    Haimes, Y.Y., Horowitz, B.M., Lambert, J.H., Santos, J.R., Lian, C., Crowther, K.G.: Inoperability Input-Output Model for Interdependent Infrastructure Sector I: Theory and Methodology. Journal of Infrastructure Systems, 67–79 (2005)Google Scholar
  7. 7.
    Haimes, Y.Y., Jiang, P.: Leontief-based Model of Risk in Complex Interconnected Infrastructures. Journal of Infrastructure Systems, 1–12 (2001)Google Scholar
  8. 8.
    Irion, A.: Fuzzy Rules and Fuzzy Functions: a Combination of Logic and Arithmetic Operations for Fuzzy Numbers. Fuzzy Sets and Systems 99, 49–56 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Leontief, W.W.: Che Structure of the American Economy, pp. 1919–1939. Oxford.Univ. Press, Oxford (1951)Google Scholar
  10. 10.
    Rosato, V., Tiriticco, F., Issacharoff, L., Meloni, S., De Porcellinis, S., Setola, R.: Modelling interdependent infrastructures using interacting dynamical networks. Int. J. Critical Infrastructures (IJCI) (to be published)Google Scholar
  11. 11.
    Ross, T.J.: Fuzzy Logic With Engineering Applications, ch. 12. J. Wiley and Sons Ltd, Chichester (2004)zbMATHGoogle Scholar
  12. 12.
    Satos, J.R.: Inoperability input-output modeling of disruptions to interdependent economic systems. Journal of Statistic Physics 9, 20–34 (2006)Google Scholar
  13. 13.
    Setola, R.: Availability of Healthcare services in a network-based scenario. Int. J. Networking and Virtual Organization (IJNVO) 4, 130–144 (2007)CrossRefGoogle Scholar
  14. 14.
    Setola, R.: Analysis of Interdependencies among Italian Economic Sectors via Input-Output Interoperability Model. In: Critical Infrastructure Protection: Issues and Solutions. LNCS, pp. 311–321. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roberto Setola
    • 1
  • Stefano De Porcellinis
    • 1
  1. 1.Università CAMPUS Bio-Medico, Complex Systems & Security Lab. 

Personalised recommendations