Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval (Q2747059)

The theory is based on a continuous t-conorm \(S\) and a left-continuous t-norm \(U\) such that \(U(x, S(y,z))= S(U(x,y), U(x,z)))\) for all \(x,y,z\in [0,1]\) such that \(S(y, z)< 1\) (conditional distributivity). The corresponding \((S,U)\)-integral is constructed with respect to an \(S\)-decomposable measure. The main theorems of the corresponding integration theory are proved and then the relationship of the theory to aggregation operators is discussed.