Estimation of fuzzy error matrix accuracy measures under stratified random sampling

A fuzzy error matrix may be used to summarize accuracy assessment information when both the map and reference data are labelled using a soft classification. Accuracy measures analogous to the familiar overall, user's, and producer's accuracies of a hard classification can be derived from a fuzzy error matrix. The formulas for estimating the fuzzy error matrix and accompanying accuracy measures depend on the sampling design used to collect the reference data. We derive these estimation formulas for stratified random sampling, a design commonly implemented in practice. A simulation study is conducted to confirm the validity of the stratified sampling estimators.