The absolute additivity and fuzzy additivity of Sugeno integral

In this paper, based on the foundation of the discussion of the Sugeno integral for real functions which was presented by Wu Congxin and Mamadou in 2003, we introduce and consider the concept of the absolute additivity of the Sugeno integral for real functions. We also discuss the fuzzy additivity of the Sugeno, integral for real functions. For these two kinds of additivity, we obtain two necessary and sufficient conditions, a sufficient condition, a necessary condition and several counter examples.