The authors give an axiomatic definition of a certain binary operation on \([0, +\infty]\) (called a pseudo-addition) and then characterize it by showing that the operation is always of the form \[ (x, y)\mapsto g^{- 1}(g(x)+ g(y))\quad (x, y\in [0, +\infty]), \] where \(g\) is a continuous and strictly increasing function of \([0, +\infty]\) onto itself. A corresponding pseudo-multiplication on \([0, +\infty]\) [in the sense of M. Sugeno and T. Murofushi, J. Math. Anal. Appl. 122, 197-222 (1987; Zbl 0611.28010)] is characterized in a similar fashion and some conditions that guarantee its commutativity are discussed. The authors intend to apply these results to fuzzy measure theory.