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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 c o s -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. [ABSTRACT FROM AUTHOR]

Soft set theory is a mathematical tool for handling uncertainty. This paper investigates the limits of the interval type of soft sets ( i t -soft sets). The notion of i t -soft sets is first introduced. Then, the limits of i t -soft sets are proposed and their properties obtained. Next, point-wise continuity of i t -soft sets and continuous i t -soft sets is discussed. Finally, an application for rough sets is given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new covering-based set in which the lower and the upper approximation operations are defined by neighborhood systems. We systematically discuss this new type of covering-based set in two steps. First, we study the basic properties of this covering-based set, such as normality, contraction, and monotone properties. Second, we discuss the relationship between the new type of covering-based set and the other ten proposed sets. [ABSTRACT FROM AUTHOR]