Due to the high cost of labelling data, a lot of partially hybrid data are existed in many practical applications. Uncertainty measure (UM) can supply new viewpoints for analyzing data. They can help us in disclosing the substantive characteristics of data. Although there are some UMs to evaluate the uncertainty of hybrid data, they cannot be trivially transplanted into partially hybrid data. The existing studies often replace missing labels with pseudo-labels, but pseudo-labels are not real labels. When encountering high label error rates, work will be difficult to sustain. In view of the above situation, this paper studies four UMs for partially hybrid data and proposed semi-supervised attribute reduction algorithms. A decision information system with partially labeled hybrid data (p-HIS) is first divided into two decision information systems: one is the decision information system with labeled hybrid data (l-HIS) and the other is the decision information system with unlabeled hybrid data (u-HIS). Then, four degrees of importance on a attribute subset in a p-HIS are defined based on indistinguishable relation, distinguishable relation, dependence function, information entropy and information amount. We discuss the difference and contact among these UMs. They are the weighted sum of l-HIS and u-HIS determined by the missing rate and can be considered as UMs of a p-HIS. Next, numerical experiments and statistical tests on 12 datasets verify the effectiveness of these UMs. Moreover, an adaptive semi-supervised attribute reduction algorithm of a p-HIS is proposed based on the selected important degrees, which can automatically adapt to various missing rates. Finally, the results of experiments and statistical tests on 12 datasets show the proposed algorithm is statistically better than some stat-of-the-art algorithms according to classification accuracy.

A set-valued information system (SIS) is the generalization of a single-valued information system. This article explores uncertainty measurement for a SIS by using Gaussian kernel. The fuzzy $T_{cos}$ -equivalence relation lead by a SIS is first obtained by using Gaussian kernel. Then, information structures in this SIS are described by set vectors. Next, dependence between information structures is presented and properties of information structures are investigated. Lastly, uncertainty measures of a SIS are presented by using its information structures. Moreover, effectiveness analysis is done to assess the feasibility of our presented measures. The consequence of this article will help us understand the intrinsic properties of uncertainty in a SIS.