On the exisitence of derivatives for fuzzy Integral

Abstract

The Graf’s condition and the chain condition are known for the conditions of two fuzzy measures for the existence of derivative for Choquet integral. They are complicated and are not useful for considering the application. In this paper, we propose a condition as a theorem, that is easy to understand and calculate in the discrete case. We present an application of the theorem to the possibility measure ｓ. Moreover we present a condition for Sugeno integral.