Fuzzy Measure Choquet Integral Models and Rough Sets

Abstract

There are close relations between rough set and fuzzy measure theory. The outputs of rough set model and interpretation of fuzzy measure are if-then rules. Therefore, using the outputs of rough set models, fuzzy measures can be identified. That fuzzy measures values are 0 or 1, crisp values. As samples that are included in upper approximation set and are not included in lower approximation set are interpreted as fuzzy decision, fuzzy measure whose values are fuzzy values can be identified. Lastly, when input values are extended to fuzzy values, Choquet integral calculations have superior properties than max-min calculations.