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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]

In the era of explosive data growth, data sources and volumes are rapidly increasing. A multi-source data refers to information from multi-sources. However, not every source of information is equally important; some sources are more important and some are essentially worthless. Therefore, it is very meaningful to study how to select the most valuable sources and to efficiently fuse information. Multi-source incomplete interval-valued data (MSIIV-data) is an important kind of multi-source data. This paper proposes a novel method to information fusion in MSIIV-data via conditional information entropy (CIE) and considers its application to attribute reduction based on mutual information entropy. First, the distance between two information values for each incomplete interval-valued data is defined, the neighborhood classes with a tunable parameter are obtained, and the neighborhood granularity structure is established. Then, a source selection method is given via CIE, which is used to fuse MSIIV-data into single-source incomplete interval-valued data (SSIIV-data). Based on the minimization of CIE, this method allows worthy and reliable information sources to be chosen. Moreover, an attribute reduction algorithm (denoted as MMQPSO) for the fused SSIIV-data is proposed by means of combining mutual information entropy and QPSO-algorithm. Finally, experiments are done to validate the effectiveness of the proposed algorithms. The results of experiment and statistical test on 12 datasets show that the proposed algorithms have certain feasibility and advancement than 6 other advanced algorithms. [ABSTRACT FROM AUTHOR]

Categorical data is a significant kind of data in machine learning.Generally, rough set theory (RS -theory) deals with categorical data in the following way.First, an equivalence relation based on the equality of attribute values of categorical data is established.Then, information granules (I -granules) based on equivalence classes are obtained.Finally, information structures (I -structures) consisting of I -granules are formed.However, an equivalence relation is too strict, and there are some limitations in the I -structure of a categorical information system (CIS) that may result in filtering out potentially useful information.This paper investigates fuzzy information structures (FI -structures) and new uncertainty measurements for categorical data from the perspective that "the equality of attribute values is fed back to the attribute set".First, a fuzzy symmetry relation based on the number of attributes with equal attribute values is established. Then, fuzzy information granules (FI -granules) based on the fuzzy symmetry relation are obtained. Next, FI -structures consisting of FI -granules are formed.Finally, some concepts related to FI -structures in a CIS are given.The set vector is used to denote FI -structures, and the inclusion degree is used to study the dependence between FI -structures.In addition, four new uncertainty measurements based on FI -structures in a CIS are proposed, including fuzzy information granulation ( G f ), fuzzy information entropy ( H f ), fuzzy rough entropy ( E r f ) and fuzzy information amount ( E f ).Moreover, numerical experiments and statistical tests to evaluate the performance of the proposed new measurements are carried out.The results of the paired t -test show that the performance of the four new measurements based on FI -structures is better than that of the corresponding four measurements based on I -structures.Finally, attribute reduction algorithms based on G f and H f are presented, and clustering analysis is conducted on the reduced CIS. The experimental results show that the proposed algorithms are effective and perform well on attribute reduction according to three evaluation indicators of clustering performance. [ABSTRACT FROM AUTHOR]