Terrorist attacks launched by extremist groups or individuals have caused catastrophic consequences worldwide. Terrorism risk assessment therefore plays a crucial role in national and international security. Fuzzy reasoning based terrorism risk assessment systems offer a significant potential of providing decision support in combating terrorism, where highly complex situations may be involved. Nevertheless, little has been done in developing and applying an integrated hierarchical bidirectional (forward/backward) fuzzy rule interpolation mechanism that is tailored to suit decision support for terrorism risk assessment. This paper presents such an integrated approach that is capable of dealing with dynamic and insufficient information in the risk assessing process. In particular, the hierarchical system implementing the proposed techniques can predict the likelihood of terrorism attacks on different segments of focused attention. The results of an experimental investigation of this implemented system are represented, demonstrating the potential and efficacy of the proposed approach.
Top1. Introduction
Terrorism and especially suicide terrorist campaigns are now being focused on more and more by governments, the media and general public. It is imperative to have a comprehensive security risk management program including effective risk assessment and appropriate decision support. Terrorism risk assessment (TRA) therefore plays a crucial role in national and international security. In order to predict terrorist behaviors from a given set of evidence (including hypothesized), it is often necessary for investigators to reconstruct the possible scenarios that may have taken place. The difficulty of such constructed assessments lies with the inherent complexity and uncertainty of the underlying problem domain, which may be too challenging to directly comprehend (Ezell et al., 2010). Fuzzy reasoning-based systems (Darby, 2006), (Inyaem et al., 2010) can be beneficial in dealing with the shortage of knowledge or information, especially when concepts such as the “likelihood” of terrorist attacks become expressions involving uncertain qualitative values.
In the literature, a number of fuzzy reasoning-based TRA systems have been developed in an effort to assist the task of combating terrorism, including (Akgun et al., 2010), (Bowles et al., 1995), (Darby, 2006), (Inyaem et al., 2010), (Shen et al., 2006). A fuzzy decision-making support system may generate plausible scenarios so that investigators can analyze them hypothetically as well as objectively (Shen et al., 2006). Fuzzy inference systems have also been used to classify terrorism events (Inyaem et al., 2010), (Jiang et al., 2016). In addition, a fuzzy belief/plausibility measure has been proposed (Darby, 2006) to capture the uncertainty of evaluating the risks of intentional terrorist acts, and a fuzzy ontology construction methodology regarding terrorism events is proposed in (Inyaem et al., 2010). Approaches that evaluate the terrorist scenarios using approximate reasoning have also been implemented in terms of linguistic beliefs (Bowles et al., 1995).
The use of the aforementioned fuzzy reasoning-based TRA systems has revealed two major challenges: high-dimensionality (Wang, 2014), and sparse rule base problems (John Garrick et al., 2004). To model a fuzzy system with K variables and M fuzzy sets in each dimension, the number of necessary rules 
that are required to fully cover a given domain is
(1)The amount of data required to generate such a rule base increases exponentially with the number of input variables. This problem of rules explosion (often referred to the “curse of dimensionality” in machine learning (Fan, 2015), (Song et al., 1993), reduces the transparency and interpretability of the resultant fuzzy systems, whilst increasing significant computational complexity. Thus, it is essential to reduce either 
or 
, or both. A hierarchical fuzzy system (HFS) (Raju et al., 1991), (Anitha et al., 2010) is often effective in reducing 
. It consists of a number of hierarchically connected, low dimensional fuzzy sub-systems, so that the number of rules in the system may appropriately increase only linearly with the number of input variables.