Feature selection is a widely used technique to reduce data processing complexity by eliminating redundant and irrelevant features. A well-designed feature selection approach can address the difficulties associated with high-dimensional data, conserve computational resources, and enhance learning performance. In real-world applications, information systems (IS) commonly exhibit missing data due to uncertainty and incompleteness, which can be converted into a set of possible values. This can be viewed as a distinct type of set-valued information system (SVIS). However, recent research on feature selection in incomplete information systems (IIS) emphasizes the relevance of the granularity structure and the complementary information found in its complements. This paper introduces fuzzy complementary gain ratio model taking inspiration from decision tree theory in data science and machine learning to define uncertainty of IIS. Firstly, we have established a fuzzy similarity relation between two objects, which allows us to derive fuzzy similarity classes within the object set regarding to a subset of conditional features in an IS. In this study, we introduce the concept of complementary information entropy (CIE), based on our fuzzy similarity relation and analyze its properties. Using this information metric, we compute the complementary information gain (CIG), followed by the Complementary information gain ratio (CIGR) to select features. To showcase the effectiveness of the proposed approach, we have developed a practical method and included a step-by-step example to make our approach easy to grasp. Moreover, we perform comparative analyses on real-world datasets and assess our method against three established attribute selection techniques to highlight the superiority of our proposed approach.