For incomplete data with mixed numerical and symbolic attributes, attribute reduction based on neighborhood multi-granulation rough sets (NMRS) is an important method to improve the classification performance. However, most classical attribute reduction methods can only handle finite sets as to produce more attributes and lower classification accuracy. This paper proposes a novel NMRS-based attribute reduction method using Lebesgue and entropy measures in incomplete neighborhood decision systems. First, some concepts of optimistic and pessimistic NMRS models in incomplete neighborhood decision systems are given, respectively. Then, a Lebesgue measure is combined with NMRS to study neighborhood tolerance class-based uncertainty measures. To analyze the uncertainty, noise and redundancy of incomplete neighborhood decision systems in detail, some neighborhood multi-granulation entropy-based uncertainty measures are developed by integrating Lebesgue and entropy measures. Inspired by both algebraic view with information view in NMRS, the pessimistic neighborhood multi-granulation dependency joint entropy is proposed. What is more, the corresponding properties are further deduced and the relationships among these measures are discussed, which can help to investigate the uncertainty of incomplete neighborhood decision systems. Finally, the Fisher linear discriminant method is used to eliminate irrelevant attributes to significantly reduce computational complexity for high-dimensional datasets, and a heuristic attribute reduction algorithm with complexity analysis is designed to improve classification performance of incomplete and mixed datasets. Experimental results under seven UCI datasets and eight gene expression datasets illustrate that the proposed method is effective to select most relevant attributes with higher classification accuracy, as compared with representative algorithms.

Neighborhood multi-granulation rough sets-based attribute reduction using Lebesgue and entropy measures in incomplete neighborhood decision systems

An incremental learning mechanism for object classification based on progressive fuzzy three-way concept

Multi-granulation method for information fusion in multi-source decision information system

The main task of local rough set model is to avoid the interference of complicated calculation and invalid information in the formation of approximation space. In this paper, we first present a local rough set model based on dominance relation to make the local rough set theory applicable to the ordered information system, then two kinds of local multigranulation rough set models in the ordered information system are constructed by extending the single granulation environment to a multigranulation case. Moreover, the updating processes of dynamic objects based on global (classical) and local multigranulation rough sets in the ordered information system are analyzed and compared carefully. It is addressed about how the rough approximation spaces of global multigranulation rough set and local multigranulation rough set change when the object set increase or decrease in an ordered information system. The relevant algorithms for updating approximations with dynamic objects on global and local multigranulation rough sets are provided in ordered information systems. To illustrate the superiority and the effectiveness of the proposed dynamic updating approaches in the ordered information system, experimental evaluation is performed using six datasets coming from the University of California-Irvine repository.

Updating approximations with dynamic objects based on local multigranulation rough sets in ordered information systems

As a generalized extension of Pawlak’s rough set model, the multigranulation decision-theoretic rough set model in ordered information systems utilizes the basic set assignment function to construct probability measure spaces through dominance relations. It is an effective tool to deal with uncertain problems and widely used in practical decision problems. However, when the scale of dataset is large, it takes a lot of time to characterize the approximations of the target concept, as well as complicated calculation processes. In this paper, we develop a novel model called local multigranulation decision-theoretic rough set in an ordered information system to overcome the above-mentioned limitation. Firstly, to reduce the computing time of the information granule independent of the target concept, we only use the characterization of the elements in the target concept to approximate this target concept. Moreover, the corresponding local multigranulation decision-theoretic rough set in an ordered information system is addressed according to the established local model, and the comparisons are made between the proposed local algorithm and the algorithm of original multigranulation decision-theoretic rough set in ordered information systems. Finally, the validity of the local approximation operators is verified through the experimental evaluation using six datasets coming from the University of California-Irvine (UCI) repository.

Local multigranulation decision-theoretic rough set in ordered information systems

With the development of society, data noise and other factors will cause the incompleteness of information systems. Objects may increase or decrease over time in information systems. The classical information system can be extended to the incomplete interval-valued decision information system (IIDIS) that is the researching object of this paper. Incremental learning technique is a significant method for solving approximate sets under dynamic data. This article defines a multi-threshold tolerance relation based on the set pair analysis theory and establishes a rough set model in IIDIS. Then, several methods and algorithms for statically/dynamically solving approximate sets are shown. Finally, comparative experiments from six UCI data sets show both dynamic algorithms take less time than the static algorithm to calculate the approximate sets no matter how object set changes.

Dynamically updating approximations based on multi-threshold tolerance relation in incomplete interval-valued decision information systems

Attribute reduction is an important topic in the research of rough set theory, and it has been widely used in many aspects. Reduction based on an identifiable matrix is a common method, but a lot of space is occupied by repetitive and redundant identifiable attribute sets. Therefore, a new method for attribute reduction is proposed, which compresses and stores the identifiable attribute set by a discernibility information tree. In this paper, the discernibility information tree based on a lower approximation identifiable matrix is constructed in an inconsistent decision information system under dominance relations. Then, combining the lower approximation function with the discernibility information tree, a complete algorithm of lower approximation reduction based on the discernibility information tree is established. Finally, the rationality and correctness of this method are verified by an example.

Lower Approximation Reduction Based on Discernibility Information Tree in Inconsistent Ordered Decision Information Systems

There are two different theory methods that are rough set theory and evidence theory, but these two theories can both handle some incomplete and uncertain information. In this study, these two models are combined in the interval-valued fuzzy ordered information system (IVFOIS). Belief functions and plausibility functions are proposed based on dominance relations in IVFOISs. The belief and plausibility reducts are defined in interval-valued fuzzy ordered decision tables (IVFODTs) and the attribute reduction of IVFODTs based on evidence theory is established. Finally, the authors use an instance to verify the above argument.

Xiaoyan Zhang

Papers

Updating approximations with dynamic objects based on local multigranulation rough sets in ordered information systems

Local multigranulation decision-theoretic rough set in ordered information systems

Dynamically updating approximations based on multi-threshold tolerance relation in incomplete interval-valued decision information systems

Lower Approximation Reduction Based on Discernibility Information Tree in Inconsistent Ordered Decision Information Systems

Attribute reduction in interval-valued fuzzy ordered decision tables via evidence theory