Generalization of the Chebyshev inequality for semi(co)normed fuzzy integrals on an abstract fuzzy measure space based on a binary operation is given. Also, Minkowski's and Hölder's inequalities for semi(co)normed fuzzy integrals are studied in a rather general form. The main results of this paper generalize some previous results. Finally, a conclusion is drawn and an open problem for further investigations is given.