Abstract
A set-valued information system (SIS) is the generalization of a single-valued informationsystem. This article explores uncertainty measurement for a SIS by using Gaussian kernel. The fuzzyTcos-equivalence relation lead by a SIS is first obtained by using Gaussian kernel. Then, informationstructures in this SIS are described by set vectors. Next, dependence between information structuresis presented and properties of information structures are investigated. Lastly, uncertainty measuresof a SIS are presented by using its information structures. Moreover, effectiveness analysis is doneto assess the feasibility of our presented measures. The consequence of this article will help usunderstand the intrinsic properties of uncertainty in a SIS.
Highlights
The collection of all these information granules constitutes an information structure by means of set vector in the given information system (IS) induced by this attribute subset
set-valued information system (SIS); Qian et al [47,48] presented the axiomatic definition of information granulation in a knowledge base and examined information granularity of a fuzzy relation by using its fuzzy granular structure; Xu et al [49] considered knowledge granulation in ordered information systems; Dai et al [50] studied the uncertainty of incomplete interval-valued information systems based on α-weak similarity; Xie et al [51] put forward new uncertainty measurement for an interval-valued information system; Zhang et al [52] measured the uncertainty of a fully fuzzy information system
Why do we investigate uncertainty measurement for a SIS? This is because a SIS itself has uncertainty
Summary
Granular computing (GrC) as a fundamental issue in knowledge representation and data mining was presented by Zadeh [1,2,3,4]. Each attribute subset can determine an equivalence relation which partitions the object set into some disjoint classes. The collection of all these information granules constitutes an information structure by means of set vector in the given IS induced by this attribute subset. Yao et al [9] presented a granularity measure on the viewpoint of granulation; Wierman [29] provided measures of uncertainty and granularity in RST; Bianucci et al [41,42] explored entropy and co-entropy approaches for uncertainty measurements of coverings; Yao [25] studied several types of information-theoretical measures for attribute importance in RST; Beaubouef et al [43] proposed a method for measuring the uncertainty of rough sets. Liang et al [44,45] investigated information granulation in complete information systems; Dai et al [46] researched entropy and granularity measures for SISs; Qian et al [47,48] presented the axiomatic definition of information granulation in a knowledge base and examined information granularity of a fuzzy relation by using its fuzzy granular structure; Xu et al [49] considered knowledge granulation in ordered information systems; Dai et al [50] studied the uncertainty of incomplete interval-valued information systems based on α-weak similarity; Xie et al [51] put forward new uncertainty measurement for an interval-valued information system; Zhang et al [52] measured the uncertainty of a fully fuzzy information system
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