Fuzzy signal detection theory: Basic postulates and formulas for analyzinghuman and machine performance

Signal detection theory (SDT) assumes a division of objective truths or "st ates of the world" into the nonoverlapping categories of signal and noise. The definition of a signal in many real settings, however, varies with cont ext and over time. In the terminology of fuzzy logic, a real-world signal h as a value that falls in a range between unequivocal presence and unequivoc al absence. The definition of a response can also be nonbinary, Accordingly the methods of fuzzy logic can be combined with SDT, yielding fuzzy SDT. W e describe the basic postulates of fuzzy SDT and provide formulas for fuzzy analysis of detection performance, based on four steps: (a) selection of m apping functions for signal and response; (b) use of mixed-implication func tions to assign degrees of membership in hits, false alarms, misses, and co rrect rejections: (c) computation of fuzzy hit, false alarm, miss, and corr ect rejection rates; and (d) computation of fuzzy sensitivity and bias meas ures. Fuzzy SDT can considerably extend the range and utility of SDT by han dling the contextual and temporal variability of most real-world signals. A ctual or potential applications of fuzzy SDT include evaluation of the perf ormance of human, machine, and human-machine detectors in real systems.