Signal detection theory (SDT) has proven to be a robust and useful statistical model for analyzing human performance in detection and decision making tasks. As with many models extensions have been proposed in order capture and represent the real world to a greater degree. Multidimensional Signal Detection Theory (MSDT) has had success in describing and modeling complex signals, signals that are comprised by more than one identifiable component dimension. Fuzzy Signal Detection Theory (FSDT) has had success in modeling and measuring human performance in cases where there exist ambiguity in the signal or response dimension characteristics, through the application of fuzzy set theory to the definition of the performance outcome categories. Multidimensional Fuzzy Signal Detection Theory (MFSDT) was developed to accommodate simultaneously both the multidimensionality of a signal and the fuzzification of outcome categories in order to integrate the two extensions. A series of three studies were performed to develop and test the theory. One study's purpose was to develop and derive multidimensional mapping functions, the aspect of MFSDT where MSDT and FSDT were integrated. Two receiver operating characteristic (ROC) studies were performed, one simulated and one empirical. The results from both ROC analysis indicated that for perceptually separable and perceptually integral complex stimuli that MFDST is a viable methodological approach to analyzing performance of signal detection tasks where there are complex signals with ambiguous signal characteristics.

Signal detection theory (SDT) provides a theoretical framework for describing performance on decision making tasks, and fuzzy signal detection theory (FSDT) extends this description to include tasks in which there are levels of uncertainty regarding the categorization of stimulus events. Specifically, FSDT can be used to quantify the degree to which an event is 'signal-like', i.e., the degree to which a stimulus event can be characterized by both signal and non-signal properties. For instance, an improvised explosive device (IED) poses little threat when missing key elements of its assembly (a stimulus of low, but not zero, signal strength) whereas the threat is greater when all elements necessary to ignite the device are present (a stimulus of high signal strength). This research develops a link between key individual cognitive (i.e., spatial orientation and visualization) and personality (i.e., extroversion, conscientiousness, and neuroticism) differences among observers to performance on a fuzzy signal detection task, in which the items to be detected (IEDs) are presented in various states of assembly. That is, this research relates individual difference measures to task performance, uses FSDT in target detection, and provides application of the theory to vigilance tasks. In two experiments, participants viewed pictures of IEDs, not all of which are assembled or include key components, and categorize them using a fuzzy rating scale (no threat, low threat potential, moderate threat potential, or definite threat). In both experiments, there were significant interactions between the stimulus threat level category and the variability of images within each category. The results of the first experiment indicated that spatial and mechanical ability were stronger predictors of performance when the signal was ambiguous than when individuals viewed stimuli in which the signal was fully absent or fully present (and, thus, less ambiguous). The second study showed that the length of time a stimulus is viewed is greatest when the signal strength is low and there is ambiguity regarding the threat level of the stimulus. In addition, response times were substantially longer in study 2 than in study 1, although patterns of performance accuracy, as measured by the sensitivity index d', were similar across the two experiments. Together, the experiments indicate that individuals take longer to evaluate a potential threat as less critical, than to identify either an absence of threat or a high degree of threat and that spatial and mechanical ability assist decision making when the threat level is unclear. These results can be used to increase the efficiency of employees working in threat-detection positions, such as luggage screeners, provides an exemplar of use of FSDT, and contributes to the understanding of human decision making.