(eng): Integral inequalities play important roles in classical probability and measure theory. Universal integrals provide a useful tool in many problems in engineering and non-linear systems where the aggregation of data is required. We discuss several inequalities including Hardy, Berwald, Barnes–Godunova–Levin, Markov and Chebyshev for a monotone measure-based universal integral. Some recent results are obtained as corollaries. Finally, we provide some applications of our results in intelligent decision support systems, estimation and information fusion.