Abstract
A grey information system (GIS) is a new kind of IS. Uncertainty measurement (UM) can provide a new perspective for data analysis and help to reveal the essential features of data. This article studies UM for a GIS. The main work of this paper includes: first, the similarity degree between two information values of each attribute in a GIS is constructed. And then, the tolerance relation induced by a given subsystem is acquired by the similarity degree. After that, the information structure of this subsystem is brought forward. Additionally, measures of uncertainty for a GIS are explored. Moreover, the optimal selection of information structures based on the proposed uncertainty measures is studied and the application of these measures is displayed. Finally, to verify the validity of these measures, statistical effectiveness analysis is carried out. These results will help us understand the intrinsic properties of uncertainty in a GIS.
Highlights
Why do we study measures of uncertainty for a grey information system (GIS)? This is because a GIS has uncertainty and has wide application foreground, the tools for dealing with the uncertainty of a GIS are special and important, and the impact of Uncertainty measurement (UM) for a GIS is significant
The tolerance relation in a GIS has been presented on the basis of similarity degree
The concept of information structure in a GIS has been introduced based on tolerance relation, and properties of these information structures have been discussed
Summary
He presents the connection between information and uncertainty He proposes several uncertain clustering methods, i.e. fuzzy clustering, possibilistic clustering, shadowed clustering, rough sets-based clustering, intuitionistic fuzzy clustering, evidential clustering, credibilistic clustering, type-2 fuzzy clustering, neutrosophic clustering, hesitant fuzzy clustering, interval-based fuzzy clustering, and picture fuzzy clustering for measuring uncertainty. They introduce some uncertainty measures such as neighborhood entropy, conditional neighborhood entropy, neighborhood mutual information and neighborhood conditional mutual information in order to evaluate the relevance between genes and related decision in neighborhood rough set They investigate some important properties and propositions of these measures, and establish the relationships among these measures. Due to the particularity of GISs, we use rough set theory and grey system theory to deal with GISs. The main work of this paper includes: first, we construct the similarity degree between two information values in a given subsystem of a GIS.
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