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Due to the high cost of labelling data, a lot of partially hybrid data are existed in many practical applications. Uncertainty measure (UM) can supply new viewpoints for analyzing data. They can help us in disclosing the substantive characteristics of data. Although there are some UMs to evaluate the uncertainty of hybrid data, they cannot be trivially transplanted into partially hybrid data. The existing studies often replace missing labels with pseudo-labels, but pseudo-labels are not real labels. When encountering high label error rates, work will be difficult to sustain. In view of the above situation, this paper studies four UMs for partially hybrid data and proposed semi-supervised attribute reduction algorithms. A decision information system with partially labeled hybrid data (p-HIS) is first divided into two decision information systems: one is the decision information system with labeled hybrid data (l-HIS) and the other is the decision information system with unlabeled hybrid data (u-HIS). Then, four degrees of importance on a attribute subset in a p-HIS are defined based on indistinguishable relation, distinguishable relation, dependence function, information entropy and information amount. We discuss the difference and contact among these UMs. They are the weighted sum of l-HIS and u-HIS determined by the missing rate and can be considered as UMs of a p-HIS. Next, numerical experiments and statistical tests on 12 datasets verify the effectiveness of these UMs. Moreover, an adaptive semi-supervised attribute reduction algorithm of a p-HIS is proposed based on the selected important degrees, which can automatically adapt to various missing rates. Finally, the results of experiments and statistical tests on 12 datasets show the proposed algorithm is statistically better than some stat-of-the-art algorithms according to classification accuracy. [ABSTRACT FROM AUTHOR]

Categorical data is an important class of data in machine learning. Information system based on categorical data is called a categorical information system (CIS), a CIS with missing values is known as an incomplete categorical information system (ICIS) and an ICIS with decision attributes is said to be an incomplete categorical decision information system (ICDIS). Attribute selection is an important subject in rough set theory. This paper investigates attribute reduction in an ICDIS based on fuzzy rough sets. To depict the similarity for incomplete categorical data, fuzzy symmetry relations in an ICDIS are first introduced. Then, some attribute-evaluation functions, such fuzzy positive regions, dependency function and attribute importance functions are given. Next, the fuzzy-rough iterative computation model for an ICDIS is presented, and an attribute reduction algorithm in an ICDIS based on fuzzy rough sets is given. Finally, experiments are carried out as so to evaluate the performance of the proposed algorithm, and Friedman test and Bonferroni-Dunn test in statistics are conducted. The experimental results indicate that the proposed algorithm is more effective than some existing algorithms. [ABSTRACT FROM AUTHOR]

If the samples, features and information values in a real-valued information system are cells, genes and gene expression values, respectively, then for convenience, this system is said to be a single cell gene space. In the era of big data, people are faced with high dimensional gene expression data with redundancy and noise causing its strong uncertainty. D–S evidence theory excels at tackling the problem of uncertainty, and its conditions to be met are weaker than Bayesian probability theory. Therefore, this paper studies the gene selection in a single cell gene space to remove noise and redundancy with D–S evidence theory. The distance between two cells in each gene is first defined. Then, the tolerance relation is established according to the defined distance. In addition, the belief and plausibility functions to grasp the uncertainty of a single cell gene space are introduced on the basis of the tolerance classes. Statistical analysis shows that they can effectively measure the uncertainty of a single cell gene space. Furthermore, several gene selection algorithms in a single cell gene space are presented using the proposed belief and plausibility. Finally, the performance of the proposed algorithm is compared to other algorithms on some published single-cell data sets. Experimental results and statistical tests show that the classification and clustering performance of the presented algorithm not only exceeds the other three state-of-the-art algorithms, but also its gene reduction rate is very high. [ABSTRACT FROM AUTHOR]

A fuzzy relation information system may be viewed as an information system with fuzzy relations. Uncertainty measurement is a critical evaluating tool. This paper investigates uncertainty measurement for a fuzzy relation information system. The concept of information structures in a fuzzy relation information system is first described by using set vectors. Then, dependence between information structures in a fuzzy relation information system is given. Next, the axiom definition of the granularity measurement of the uncertainty for fuzzy relation information systems is proposed by means of its information structures. Based upon this axiom definition, information granulation and rough entropy in a fuzzy relation information system are proposed. Moreover, information entropy, information amount, joint entropy, and condition entropy in a fuzzy relation information system are also considered. To show the feasibility of the proposed measures for uncertainty of a fuzzy relation information system, effectiveness analysis is conducted from the angle of statistics. Finally, characterizations of fuzzy relation information systems under a compatible homomorphism are obtained. These results will be helpful for understanding the essence of uncertainty in a fuzzy relation information system. [ABSTRACT FROM AUTHOR]

A neighborhood information system (NIS) deals with an information system (IS) by means of neighborhoods. Sometimes it has some advantages over an IS. A neighborhood decision information system (NDIS) means a NIS with decision attributes. Single cell RNA (scRNA) data possess the characteristics of high dimensionality, small sample, unbalanced distribution, big noise and high redundancy. It has become an important research topic to select suitable and effective genes. This paper studies feature selection in a NDIS and considers its application for scRNA data classification. We first give the distance between information values on each attribute in a NDIS. Then, we present tolerance relations on the object set of a NDIS based on this distance. Next, we define the rough approximations in a NDIS by means of the presented tolerance relations. Furthermore, we put forward the notions of δ -dependence degree, δ -information entropy, δ -conditional information entropy and δ -joint information entropy in a NDIS. Based on Kryszkiewicz's ideal, we introduce δ -generalized decision and consider feature selection in a consistent NDIS by decision. Finally, we study feature selection in a consistent NDIS by using dependence degree and information entropy, and design the relevant algorithms. The experimental results conducted several scRNA data demonstrate that the designed algorithms possess excellent performance. • We present tolerance relations on the object set of a NDIS. • We define the rough approximations in a NDIS. • We put forward the notions of δ -dependence degree, δ -information entropy, δ -conditional information entropy and δ -joint information entropy in a NDIS. • We introduce δ -generalized decision and consider feature selection in a consistent NDIS by decision. • We propose three feature selection methods in a NDIS by using dependence degree and information entropy and design the relevant algorithms. [ABSTRACT FROM AUTHOR]

Three-way decisions are effective and heuristic methods in information processing, moreover, it provides a trisecting-and-acting framework for complex problem solving. In this paper, combining with the practical application scenario, we propose a novel three-way decisions approach and apply it to medical diagnosis. First, we build an information system which is called a hybrid information system with images by considering the characteristics of the examination items of nephritis, including urinary color, urinary tuberculosis, pH, red blood cell count, urinary irritation, computed tomography, white blood cell count and so on. Second, to describe two objects of the conditional attribute set in a hybrid information system with images, we propose the hybrid distance based on Euclidean distance. Then, the tolerance relation induced by this system is constructed. In addition, considering that missing values exist in a hybrid information system with images, interval-valued numbers are used to obtain the loss function. Given different types of parameters can respond the level of the tolerance relation and the risk preference of decision makers, and the decision rules are shown in tabular forms. Finally, an illustration is showed to verify the feasibility and reasonability of the proposed method. [ABSTRACT FROM AUTHOR]