Explicit Descriptions of Associative Sugeno Integrals

Abstract

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n ≥ 1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of Sugeno integrals over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same. © Springer-Verlag Berlin Heidelberg 2010.