Due to many applications, the Choquet integral as a powerful tool for modeling non-deterministic problems needs to be further extended. Therefore the paper is devoted to a generalization of the Choquet integral. As a basis, the pseudo-integral for bounded integrand is extended to the case for nonnegative integrands at first, and then the generalized Choquet integral is defined. As special cases, pseudo-Choquet Stieltjes integrals, pseudo-fuzzy Stieltjes integrals, g-Choquet integrals, pseudo-(N)fuzzy integrals and pseudo-(S)fuzzy integrals are obtained, and various kinds of properties and convergence theorems are shown, meanwhile Markov, Jensen, Minkowski and Hölder inequalities are proved. In the end, the generalized discrete Choquet integral is discussed. The obtained results for the generalized Choquet integral cover some previous results on different types of nonadditive integrals.

由于应用较多，Choquet 积分作为建模非确定性问题的强大工具需要进一步扩展。因此，本文致力于对 Choquet 积分进行推广。在此基础上，首先将有界被积函数的伪积分推广到非负被积函数的情况，然后定义了广义Choquet积分。作为特殊情况，伪 Choquet Stieltjes 积分、伪模糊 Stieltjes 积分、g-得到了Choquet积分、伪(N)模糊积分和伪(S)模糊积分，并给出了各种性质和收敛定理，同时证明了Markov、Jensen、Minkowski和Hölder不等式。最后讨论了广义离散Choquet积分。广义 Choquet 积分的所得结果涵盖了以前关于不同类型的非加性积分的一些结果。