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.

Soft set theory is a mathematical tool for dealing with uncertainty. This paper investigates limits of interval type of soft sets (for short, it-soft sets). The concept of it-soft sets is first introduced. Then, limits of it-soft sets are proposed and their properties are obtained. Next, point-wise continuity of it-soft sets and continuous it-soft sets are discussed. Finally, an application for rough sets is given.