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Information system is a database that shows relationships between objects and attributes. A real-valued information system is an information system whose information values are real numbers. A real-valued information system with decision attributes is referred to as a real-valued decision information system. If objects, conditional attributes and information values in a real-valued decision information system are cells, genes and gene expression values, respectively, then this information system is said to be a gene decision space. In a gene decision space, people are faced with gene expression data. If gene expression data in a gene decision space changes to single cell RNA-seq data, then this space is referred to as a single cell gene decision space. This paper explores gene selection in a single cell gene decision space in terms of Gaussian kernel. In the first place, the distance between two cells in each subspace of a single cell gene decision space is constructed. Next, the fuzzy T cos -equivalence relation on the cell set is obtained in terms of Gaussian kernel. After that, measures of uncertainty for a single cell gene decision space are investigated. Lastly, gene selection algorithms in a single cell gene decision space are presented in terms of the proposed information entropy and information granularity. The presented algorithms are testified in several publicly open single cell RNA-seq data sets. Experimental results reveal that the presented algorithms can select appropriate genes related to classification, and significantly improve classification performances. [ABSTRACT FROM AUTHOR]

Due to limitations in data acquisition, data in real life often contains a wealth of uncertain information. Uncertainty measurement (UM) constructed within the framework of rough set theory (RST) is an important tool for processing uncertain information. Some basic UMs in RST such as classification precision, rough membership degree, dependence degree, and attribute importance cannot accurately measure the uncertainty of a hybrid information system (HIS). For example, dependence degree only considers the information provided by the lower approximation of the decision and ignores the upper approximation, which may lead to some information loss. In addition to these basic UMs, some extended entropy-based UMs such as rough entropy, information entropy and conditional entropy are also frequently used to measure the uncertainty of a HIS. However, these three UMs also have their own drawbacks. For instance, rough entropy is sensitive to the distribution of hybrid data. When the distribution of hybrid data is uneven, the calculation results of rough entropy may be greatly affected, leading to a decrease in measurement accuracy. This paper proposes four new UMs in a HIS and provides an application in attribute reduction. First of all, a distance function is defined to deal with each type of attribute in a HIS and construct a tolerance relation. On this basis, four UMs are listed to measure the uncertainty of a HIS. Next, the strength and weakness of the proposed UMs are verified by statistical analysis. Subsequently, the UM with the best performance is selected to design an attribute reduction algorithm. Finally, the designed algorithm is compared with other five attribute reduction algorithms to show its superior performance. [ABSTRACT FROM AUTHOR]

A fuzzy set-valued information system (FSVIS) refers to an information system (IS) whose information values are fuzzy sets. This article investigates information structures (ISts) in a FSVIS based on granular computing (GrC). First, FSVISs and homomorphism between them are introduced. Next, ISts in a FSVIS are described. The dependence and information distance between ISts are discussed, and characterizations of ISts in a FSVIS are acquired. Additionally, as an application of ISts in a FSVIS, the entropy measure of uncertainty for a FSVIS is discussed, and on the basis of this uncertainty measure, the optimal selection of ISts is investigated. The obtained consequence will be conducive to establishing a framework for GrC in a FSVIS. Last, the difference between this paper and the references for ISts in this paper is compared and discussed. [ABSTRACT FROM AUTHOR]