Estimating Terrorist Risk with Possibility Theory

This report summarizes techniques that use possibility theory to estimate the risk of terrorist acts. These techniques were developed under the sponsorship of the Department of Homeland Security (DHS) as part of the National Infrastructure Simulation Analysis Center (NISAC) project. The techniques have been used to estimate the risk of various terrorist scenarios to support NISAC analyses during 2004. The techniques are based on the Logic Evolved Decision (LED) methodology developed over the past few years by Terry Bott and Steve Eisenhawer at LANL. [LED] The LED methodology involves the use of fuzzy sets, possibility theory, and approximate reasoning. LED captures the uncertainty due to vagueness and imprecision that is inherent in the fidelity of the information available for terrorist acts; probability theory cannot capture these uncertainties. This report does not address the philosophy supporting the development of nonprobabilistic approaches, and it does not discuss possibility theory in detail. The references provide a detailed discussion of these subjects. [Shafer] [Klir and Yuan] [Dubois and Prade] Suffice to say that these approaches were developed to address types of uncertainty that cannot be addressed by a probability measure. An earlier report discussed in detail the problems with using a probability measure to evaluate terrorist risk. [Darby Methodology]. Two related techniques are discussed in this report: (1) a numerical technique, and (2) a linguistic technique. The numerical technique uses traditional possibility theory applied to crisp sets, while the linguistic technique applies possibility theory to fuzzy sets. Both of these techniques as applied to terrorist risk for NISAC applications are implemented in software called PossibleRisk. The techniques implemented in PossibleRisk were developed specifically for use in estimating terrorist risk for the NISAC program. The LEDTools code can be used to perform the same linguistic evaluation as performed in PossibleRisk. [LEDTools] LEDTools is a general purpose linguistic evaluation tool and allows user defined universes of discourse and approximate reasoning rules, whereas PossibleRisk uses predefined universes of discourse (risk, attack, success, loss, and consequence) and rules. Also LEDTools has the capability to model a large number of threat scenarios with a graph and to integrate the scenarios (paths from the graph) into the linguistic evaluation. Example uses of PossibleRisk and LEDTools for the possibilistic evaluation of terrorist risk are provided in this report.