<p>Attribute reduction of hybrid decision information systems (HDISs) is a significant research area within the field of machine learning. Due to the presence of nominal attributes, it is difficult to accurately measure the distance between objects in HDISs, which often results in poor attribute reduction for these systems. Rough set theory (RST) is a crucial tool for attribute reduction, but it requires computation of upper and lower approximations, which often leads to computational difficulties. In response to the aforementioned issues, this paper proposes a fast attribute reduction algorithm for HDISs based on fuzzy conditional information entropy that utilizes an iterative model and matrix operations. Firstly, a novel measurement of the distance between nominal attribute values is defined using decision attributes. Subsequently, fuzzy conditional information entropy is calculated from the perspective of “the attribute values is fed back to the attribute set” and its properties are provided. Additionally, an iterative attribute reduction model and difference matrix are established, and two new matrix operations are introduced. Finally, an iterative attribute reduction algorithm is provided. The results of experiments and statistical tests on fifteen UCI datasets, including three large datasets, demonstrate that the proposed algorithm is more effective and efficient than nine state-of-the-art algorithms. This paper not only addresses the issue of difficulty in measuring the distance between nominal attribute values but also significantly improves the computational efficiency of attribute reduction algorithms based on RST, making it possible for them to be applied to large datasets.</p>