A signal improvement to signal detection analysis: fuzzy SDT on the ROCs

Fuzzy Signal Detection Theory (FSDT) combines traditional Signal Detection Theory (SDT) with Fuzzy Set Theory to generalize signal detection analysis beyond the traditional categorical decision-making model. This advance upon SDT promises to improve measurement of performance in domains in which stimuli do not fall into discrete, mutually exclusive categories; a situation which characterizes many detection problems in real-world operational contexts. FSDT allows for events to simultaneously be in more than one state category (e.g., both signal and nonsignal). The present study derived FSDT Receiver Operating Characteristic (ROC) functions to test whether application of FSDT meets the Gaussian and equal variance assumptions of traditional SDT and, therefore, whether the standard representation of the SDT decision space can be extended to the broader case of FSDT. Results supported the contention that FSDT does meet these traditional SDT assumptions, and further, that it yields higher sensitivity scores than traditional SDT when the category membership of events is ambiguous. ROC analyses indicate that use of traditional SDT formulas with fuzzy hit and false alarm rates is thus justified. The implications of this advance to both theoretical and practical domains are adumbrated.