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Risk from an act of terrorism is a combination of the likelihood of an attack, the likelihood of success of the attack, and the consequences of the attack. The considerable epistemic uncertainty in each of these three factors can be addressed using the belief/plausibility measure of uncertainty from the Dempster/Shafer theory of evidence. The adversary determines the likelihood of the attack. The success of the attack and the consequences of the attack are determined by the security system and mitigation measures put in place by the defender. This report documents a process for evaluating risk of terrorist acts using an adversary/ defender model with belief/plausibility as the measure of uncertainty. Also, the adversary model is a linguistic model that applies belief/plausibility to fuzzy sets used in an approximate reasoning rule base. 4 AcknowledgementsThe use of a linguistic rule base for modeling the adversary is based on concepts from the Logic Evolved Decision (LED) methodology developed at Los Alamos National Laboratory (LANL) by Terry Bott and Steve Eisenhawer, extended in this work to include belief/plausibility as the measure of uncertainty. The numerical model for the defender benefited from the work and suggestions of Jon Helton at Arizona State University.The evaluation of belief/plausibility for fuzzy sets is based on the development of Ronald Yager at Iona College.Scott Ferson of Applied Biomathematics provided suggestions and helpful reference material during the formulation of the concepts. The RAMAS RiskCalc software (version 4.0) developed by Ferson, et al., was used to check test case results of the BeliefConvolution code written by the author.

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LinguisticBelief is a Java computer code that evaluates combinations of linguistic variables using an approximate reasoning rule base. Each variable is comprised of fuzzy sets, and a rule base describes the reasoning on combinations of variables' fuzzy sets. Uncertainty is considered and propagated through the rule base using the belief/plausibility measure. The mathematics of fuzzy sets, approximate reasoning, and belief/ plausibility are complex. Without an automated tool, this complexity precludes their application to all but the simplest of problems. LinguisticBelief automates the use of these techniques, allowing complex problems to be evaluated easily. LinguisticBelief can be used free of charge on any Windows XP machine. This report documents the use and structure of the LinguisticBelief code, and the deployment package for installation client machines.

Terrorist acts are intentional and therefore differ significantly from "dumb" random acts that are the subject of most risk analyses. There is significant epistemic (state of knowledge) uncertainty associated with such intentional acts, especially for the likelihood of specific attack scenarios. Also, many of the variables of concern are not numeric and should be treated as purely linguistic (words).Epistemic uncertainty can be addressed using the belief/ plausibility measure of uncertainty, an extension of the traditional probability measure of uncertainty. Fuzzy sets can be used to segregate a variable into purely linguistic values. Linguistic variables can be combined using an approximate reasoning rule base to map combinations of fuzzy sets of the constituent variables to fuzzy sets of the resultant variable.We have implemented the mathematics of fuzzy sets, approximate reasoning, and belief/plausibility into Java software tools. The PoolEvidence© software tool combines evidence (pools) from different experts. The LinguisticBelief© software tool evaluates the risk associated with scenarios of concern using the pooled evidence as input.The tools are not limited to the evaluation of terrorist risk; they are useful for evaluating any decision involving significant epistemic uncertainty and linguistic variables. Sandia National Laboratories' analysts have applied the tools to: risk of terrorist acts, security of nuclear materials, cyber security, prediction of movements of plumes of hazardous materials, and issues with nuclear weapons. This paper focuses on evaluating the risk of acts of terrorism.