We consider generated pseudo-operations of the following form: $x\oplus y=g^{(-1)}(g(x)+g(y))$, $x\odot y=g^{(-1)}(g(x)g(y))$, where $g$ is a positive strictly monotone generating function and $g^{(-1)}$ is its pseudoinverse. Using this type of pseudo-operations, the Riemann-Stieltjes type integral is introduced and investigated.