Fuzzy item response model: a new approach to generate membership function to score psychological measurement

The aim of this study is to propose an new approach, fuzzy item response model (FIRM), which combines item response theory (IRT) and fuzzy set theory, in the educational or psychological measurement. Applying FIRM to improve the predictive validity of psychological measurement is verified. We set up a detailed procedure for the FIRM and apply it to a valuable empirical study with Beck Depression Inventory-II (Chinese version) administrated on outpatient diagnosed as depression was given. The results showed the correct classification of depression based on FIRM scoring was 80.3% while that of raw score was only 73.2%. That is, via FIRM scoring, 7.9% of the erroneous judgments of depression inferred from self-reported inventory were reduced. It is also suggested that considerable cost concerning prevention and cure of depression might be reduced via FIRM.