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The decision tree is one of the most important and representative classification algorithms in the field of machine learning, and it is an important technique for solving data mining classification tasks. In this paper, a decision tree classification algorithm based on granular matrices is proposed on the basis of granular computing theory. Firstly, the bit-multiplication and bit-sum operations of granular matrices are defined. The logical operations between granules are replaced by simple multiplication and addition operations, which reduces the operation time. Secondly, the similarity between granules is defined, the similarity metric matrix of the granular space is constructed, the classification actions are extracted from the similarity metric matrix, and the classification accuracy is defined by weighting the classification actions with the probability distribution of the granular space. Finally, the classification accuracy of the conditional attribute is used to select the splitting attributes of the decision tree as the nodes to form forks in the tree, and the similarity between granules is used to judge whether the data types in the sub-datasets are consistent to form the leaf nodes. The feasibility of the algorithm is demonstrated by means of case studies. The results of tests conducted on six UCI public datasets show that the algorithm has higher classification accuracy and better classification performance than the ID3 and C4.5. [ABSTRACT FROM AUTHOR]

Uncertainty measures are instrumental in describing the classification abilities in information systems, and uncertain information has been measured and processed with granular computing theory. While the fuzzy set-valued information system is a generalization of fuzzy information systems, the relationship between the information granulation and the uncertainty in fuzzy set-valued information systems remains to be studied. This paper probes into uncertainty measures in fuzzy set-valued information systems based on the fuzzy β -neighborhood and the idea of granulation. Specifically, the fuzzy β -neighborhood similarity relation that reflects the similarity between two objects is defined in terms of the nearness degree. We propose the concepts of information granules and granular structures induced by fuzzy β -neighborhood similarity relations, based on which we introduce the granularity measures and rough approximation measures of granular structures in fuzzy set-valued information systems. Given the situation of decision information systems, we propose the granularity-based rough approximation measures by combining granularity measures with rough approximation measures. Experiment results and effectiveness analysis show that the measures we proposed are reasonable and feasible. [ABSTRACT FROM AUTHOR]

Binary information table, multi-valued information table and set-valued information table are three kinds of information systems often encountered in information processing. For any information system, we can often induce different information granular structures, and then construct the corresponding rough set models. Generally speaking, for the same information system, three models of Pawlak rough set, covering rough set and multi-granulation rough set can be induced according to different rules. These three kinds of rough set models are effective tools for data mining and information processing. This paper studies the relationship among Pawlak rough set, covering rough set and multi-granularity rough set induced in binary information table, multi-valued information table and set-valued information table, and obtains many important conclusions. The research content of this paper effectively connects the theories, methods and applications of Pawlak rough set, covering rough set and multi-granularity rough set, which not only enriches the rough set theory, but also expands the application prospect of rough set. [ABSTRACT FROM AUTHOR]

An approximation space is one basic concept in rough set theory. This paper investigates measures of uncertainty for an approximation space from granular computing viewpoint. Granular structures of an approximation spaces are first described by means of set vectors. Then, relationships between granular structures of an approximation spaces are studied from the two aspects of dependence and separation. Next, properties of granular structures of an approximation space are given. Furthermore, as an application for granular structures of an approximation spaces, measuring uncertainty of approximation spaces is investigated. Finally, one example is employed to illustrate features of the proposed measures for uncertainty of approximation spaces. These results will be helpful for understanding the essence of uncertainty for an approximation space. [ABSTRACT FROM AUTHOR]

Abstract Granular computing is an emerging field of study in which the complexity of problem solving is reduced through granulation. Researchers have proposed various granularity measures of partitions to quantify the effects of granulation with respect to simplification. However, two important issues still remain and require careful investigation. The first issue is that a partition is only a simple two-level granular structure, which may not be sufficient for the full scope of granular computing. The second issue is a clarification of the differences between granularity and complexity. Although they are related to each other, they represent different things. To address the two issues, this paper makes three contributions. First, we extend the partition granulation scheme into multilevel granular structures based on progressive partitioning. Second, we propose a complexity measure of a partition that incorporates both the block-level interactions (interactions within a block) and the partition-level interactions (interactions between blocks of the partition). Third, we generalize the complexity measure to multilevel granular structures generated from a progressive partitioning process. [ABSTRACT FROM AUTHOR]

An approximation space is one basic concept in rough set theory. This paper investigates measures of uncertainty for an approximation space from granular computing viewpoint. Granular structures of an approximation spaces are first described by means of set vectors. Then, relationships between granular structures of an approximation spaces are studied from the two aspects of dependence and separation. Next, properties of granular structures of an approximation space are given. Furthermore, as an application for granular structures of an approximation spaces, measuring uncertainty of approximation spaces is investigated. Finally, one example is employed to illustrate features of the proposed measures for uncertainty of approximation spaces. These results will be helpful for understanding the essence of uncertainty for an approximation space. [ABSTRACT FROM AUTHOR]

A fundamental notion of granular computing is a multilevel granular structure in which different levels are characterized by different degrees of abstraction and details. By making use of a granular structure, we propose a unified model of sequential three-way decisions and multilevel incremental processing for complex problem solving. At a particular level, a set of objects is divided into positive, negative, and boundary regions. A yes/no decision is made for objects in the positive/negative region when available information is sufficient to warrant such a decision. We defer a definite decision for objects in the boundary region to the next level where more detailed information is given. In this way, we have an effective and efficient sequential three-way decisions strategy to achieve a faster decision process with a less overall decision cost. We consider, at each level, seven situations resulting from combinations of three regions. We introduce the cost of decision process for granularity transformation and processing. We also examine the decrease of objects and the change of thresholds when the attributes are added to an information system. In order to dynamically update a sequence of three regions, we suggest multilevel incremental mechanisms and algorithms. Finally, we report experimental results on datasets from UCI to show the performance of proposed models and algorithms. [ABSTRACT FROM AUTHOR]

Highlights: [•] We present a granular view on ontology that: the ontology is granular. [•] The ontology is a granular approximation of the conceptualization. [•] The conceptual relation granules are ordered tuples. [•] We also present a granular ontology design approach. [ABSTRACT FROM AUTHOR]