Considering the multi-source of uncertainty and the complex correlation of uncertain parameters in many engineering practices, the bounded set describing uncertainties is sometimes irregular and lacks a precise mathematical expression. To overcome the limitations of existing methods in handling this issue under incomplete information, this paper proposes a novel uncertainty modeling and analysis strategy based on the rough set theory. Firstly, in terms of limited experimental points, a data-driven partitioning method is introduced to establish an adaptive knowledge base. By means of the equivalence classes in knowledge base, a dual-approximate quantification model composed of upper and lower approximation sets is constructed to describe an arbitrary bounded-but-irregular uncertain set from both internal and external perspectives. In the subsequent uncertainty propagation analysis, a concept of rough approximate accuracy of response prediction is defined by four extreme values to quantitatively characterize the influence of model approximation on system response. Meanwhile, to improve the computational efficiency of extreme-value prediction in engineering application, an adaptive Kriging model combined with rough set theory is developed as the surrogate model of the original time-consuming simulations. Finally, two numerical examples are investigated to substantiate the effectiveness of the proposed method.