Uncertainty Measurement for a Set-Valued Information System: Gaussian Kernel Method

• Main Authors: Jiali He, Pei Wang, Zhaowen Li
• Format: Article
• Language: English
• Published: MDPI AG 2019-02-01
• Series: Symmetry
• Subjects: granular computing; set-valued information system; distance; gaussian kernel; information structure; dependence; uncertainty; measurement
• Online Access: https://www.mdpi.com/2073-8994/11/2/199

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 <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> </mrow> </msub> </semantics> </math> </inline-formula>-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.