Fuzzy receiver operating characteristic curve: an option to evaluate diagnostic tests

Traditional receiver operating characteristic (ROC) analysis is widely utilized to evaluate diagnostic tests but it is restricted to dichotomous results. The aim of this study is to develop the "fuzzy receiver operating characteristic" methodology combining the fuzzy sets theory and the traditional ROC methodology, and to utilize this new tool to evaluate a diagnostic test. We review traditional ROC analysis in mathematical language that utilizes crisp sets and rewrites it based on fuzzy sets. Fuzzy ROC analysis is used to evaluate a fuzzy-rule-based system (FRBS) developed to predict the pathological stage of a prostate cancer in its ability to discriminate between two states: organ-confined and non-confined. Traditional ROC analysis is insufficient to evaluate this system because the result is given in possibilistic terms. The methodology developed in this work is a generalization of the dichotomous ROC analysis, and appears to better represent the performance of diagnostic tests that include a degree of uncertainty similar to the one presented here.