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This study presents a system for assessing and managing the risk of natural disasters, particularly under highly uncertain conditions, i.e. where neither the statistical data nor the physical knowledge required for a purely probabilistic risk analysis are sufficient. This insufficient information will afflict the calculated risk probabilities with imprecision which ignoring it might lead to an underestimation of the risk. In this study, fuzzy set theory is employed to complement the probability theory with an additional dimension of uncertainty. This would allow for expressing the likelihood of natural hazards by fuzzy probability. The fuzzy probability is characterized in terms of possibility-probability distributions (PPD), for which a new approach has been developed. It is demonstrated that the approach developed in this thesis can address the deficiencies in both conventional probabilistic approach and an alternative PPD method.

The new methodology is described by breaking down the risk assessment procedure to its components, namely hazard assessment and vulnerability analysis. Essentials of each of these components are identified for the case of seismic hazard. Applying the concept of PPD to seismic hazard analysis generalizes the conventional probabilistic seismic hazard analysis (PSHA) to fuzzy-probabilistic seismic hazard analysis (FPSHA). It has been proven that whenever statistical data are adequate or the background knowledge is credible, the FPSHA results converge to those of PSHA.

Furthermore, uncertainties about the correlation between the parameters of hazard intensity and damage (or loss), i.e. vulnerability relations, have been considered by means of fuzzy relations. It is shown that fuzzy relations are a more viable form of representing uncertainties of the structures, especially when material uncertainties are to be considered. It is also argued that at least in the context of vulnerability of structures, the fuzzy set theory is a better means of representing uncertainty of seismic vulnerability from a subjective point of view. Besides, the flexible structure of the developed system allows for an easy incorporation of other alternative representations of vulnerability. Thus, applying the developed system for risk assessment does not require starting the vulnerability analysis of structures from scratch.

The risk of damage and/or loss is then evaluated by combining the hazard PPD and the fuzzy vulnerability relation. The result is a fuzzy probabilistic risk (of damage or loss), which represented in a more realistic and comprehensive way by means of confidence levels and intervals. This representation is more reliable because of the consideration of uncertainties which are ignored in conventional approaches. Moreover, it provides the decision-maker with a better perception of risk. In order to extend the risk assessment to risk management, a corresponding benefit-cost model has been developed.

In order to provide evidence for the applicability and practicability of the developed methodology, two “real-world” case studies have been analyzed and presented. In the first case study, it is shown that this approach avoids some obvious defects and drawbacks of alternative methods which led to implausible results, contrary to the results obtained from the proposed method. It is also demonstrated how the damage PPD can be interpreted in order to gain a more realistic and informative perception of risk. The second case study demonstrates the other advantage of this system, i.e. its flexibility and ability of incorporating other solutions. The developed methodology is particularly appropriate for implementation onto a webbased risk assessment/management system. The reason is that major computational tasks can be performed off-line and on-line computations are restricted to selection and composition of appropriate fuzzy relations. Moreover, the system can be easily updated and expanded whenever new information is available.