Positive Region Reduction Research Articles

New Variable Precision Reduction Algorithm for Decision Tables

Variable precision reduction (VPR) and positive region reduction (PRR) are common definitions in attribute reduction. The compacted decision table is an extension of a decision table. In this paper, we propose another extension, called the weighted decision table. In both types of decision tables, VPR is defined, and the corresponding discernibility matrices for the PRR are proposed. Then, algorithms for obtaining the PRR from the discernibility matrices are presented. In both types of decision tables, the relationship between VPR and PRR is established by comparing the corresponding discernibility matrices. If the precision of the VPR meets the given conditions, then the PRR algorithms can be used to obtain the results after modifying some decision values in the decision tables. An analysis of the modification process of the decision values and the compression process of decision tables is used to propose a new algorithm for VPR in decision tables that ensures credibility. The effectiveness of the proposed algorithm was evaluated by an experimental comparison with existing VPR algorithms.

Three-way reduction for formal decision contexts

Attribute reduction is an important component in rough set theory and formal concept analysis. The three-way concept lattice is a combination of concept lattices and three-way decision theory. We investigate granular reduction, three-way granular reduction, and three-way distribution reduction for general formal decision contexts. We furthermore obtain discernibility matrix-based reduction algorithms for each type of reduction. In particular, we demonstrate that in decision contexts, three-way granular reduction coincides with positive region reduction for decision tables. Furthermore, we evaluate the effectiveness of the three-way granular reduction algorithm using 17 UCI datasets.

Indiscernibility and Discernibility Relations Attribute Reduction with Variable Precision

Attribute reduction is a popular topic in research on rough sets. In the classical model, much progress has been made in the study of the attribute reduction of indiscernibility and discernibility relations. To enhance the fault tolerance of the model, concepts of both indiscernibility and discernibility relations involving uncertain or imprecise information are proposed in this paper. The attribute reductions of the relative β -indiscernibility relation and relative β -discernibility relation and their algorithms are proposed. When the precision satisfies certain conditions, the reduction of two relation concepts can be converted into a positive region reduction. Therefore, the discernibility matrix is used to construct the reductions of the two relation concepts and the positive region. Furthermore, the corresponding algorithm of the relative β -indiscernibility (discernibility) relation reduction can be optimized when the precision is greater than 0.5, and this is used to develop an optimization algorithm that constructs the discernibility matrix more efficiently. Experiments show the feasibility of the two relation reduction algorithms. More importantly, the reduction algorithms of the two relations and the optimization algorithm are compared to demonstrate the feasibility of the optimization algorithm proposed in this paper.

A data fusion method in wireless sensor network based on belief structure

Considering the issue with respect to the high data redundancy and high cost of information collection in wireless sensor nodes, this paper proposes a data fusion method based on belief structure to reduce attribution in multi-granulation rough set. By introducing belief structure, attribute reduction is carried out for multi-granulation rough sets. From the view of granular computing, this paper studies the evidential characteristics of incomplete multi-granulation ordered information systems. On this basis, the positive region reduction, belief reduction and plausibility reduction are put forward in incomplete multi-granulation ordered information system and analyze the consistency in the same level and transitivity in different levels. The positive region reduction and belief reduction are equivalent, and the positive region reduction and belief reduction are unnecessary and sufficient conditional plausibility reduction in the same level, if the cover structure order of different levels are the same the corresponding equivalent positive region reduction. The algorithm proposed in this paper not only performs three reductions, but also reduces the time complexity largely. The above study fuses the node data which reduces the amount of data that needs to be transmitted and effectively improves the information processing efficiency.

Knowledge granularity reduction for decision tables

Attribute reduction is a difficult topic in rough set theory and knowledge granularity reduction is one of the important types of reduction. However, up to now, its reduction algorithm based on a discernibility matrix has not been given. In this paper, we show that knowledge granularity reduction is equivalent to both positive region reduction and X-absolute reduction, and derive its corresponding algorithm based on a discernibility matrix to fill the gap. Particularly, knowledge granularity reduction is the usual positive region reduction for consistent decision tables. Finally, we provide a simple knowledge granularity reduction algorithm for finding a reduct with the help of binary integer programming, and consider six UCI datasets to illustrate our algorithms.

Attribute Reduction in an Incomplete Interval-Valued Decision Information System

An incomplete interval-valued decision information system (IIVDIS) is a significant type of data decision table, which is ubiquitous in real life. Interval value is a form of knowledge representation, and it seems to be an embodiment of the uncertainty of research objects. In this paper, we focus on attribute reduction on the basis of a parameterized tolerance-based rough set model in an IIVDIS. Firstly, we give the similarity degree between information values on each attribute in an IIVDIS by considering incomplete information. Then, we present tolerance relations on the object set of an IIVDIS based on this similarity degree. Next, we define the rough approximations by means of the presented tolerance relation. Based on Kryszkiewicz’s ideal, we introduce $\alpha $ -generalized decision and consider attribute reduction in an IIVDIS by means of this decision. Furthermore, we put forward the notions of $\alpha $ -information entropy, $\alpha $ -conditional information entropy and $\alpha $ -joint information entropy in an IIVDIS. And we prove that $\alpha $ -positive region reduction theorem, $\alpha $ -conditional entropy reduction theorem, $\alpha $ -dependency reduction theorem and $\alpha $ -generalized decision reduction theorem are equivalent to each other. Finally, we propose two attribute reduction methods in an IIVDIS by using entropy measurement and the rough approximations, and design the relevant algorithms. We carry out a series of numerical experiments to verify the effectiveness of the proposed algorithms. The experimental results show that proposed algorithms often choose fewer attributes and improve classification accuracies in most cases.

A common attribute reduction form for information systems

An information system is an important form of knowledge representation, and attribute reduction plays an important role in machine learning, data mining, and intelligent systems. Several techniques are available to solve problems of attribute reduction but a common characterization for them is needed. This paper proposes the concepts of exact reductions and their reduction-invariant matrices. We obtain a unified mathematical model of attribute reduction by exactness for information systems, and show that frequently used methods of attribute reduction for information systems are exact. Specifically, we show that the positive region reduction for a decision table is exact. Our model theoretically unifies frequently used approaches to reduction. We also used a case study using the UCI dataset to verify the effectiveness of our proposed model.

Image steganalysis feature selection based on the improved Fisher criterion.

In order to improve the detection accuracy of hidden message in images, steganalysis features are selected as inputs for steganalysers. However, the existing Fisher criterion ignores the contribution of steganalysis feature components in dispersion to classification, which causes the useful feature components to be deleted, and decreases the detection accuracy of steganalysis features. By analyzing the separability of steganalysis feature components, we introduce the sigmoid function into Fisher's criterion and propose an improved Fisher criterion (I-Fisher criterion), which can make up for the traditional Fisher criterion in separability measurement of steganalysis feature components. To optimize the steganalysis feature and reduce its dimension, we employ the improved Fisher criterion as the heuristic function of the decision rough set α-positive region reduction, and propose the feature selection method based on the improved Fisher. Experimental results show that the proposed method can reduce the dimension and memory of the GFR high-dimensional feature and the CC-PEV lowdimensional feature while maintaining or improving the detection accuracy.

Selection of Rich Model Steganalysis Features Based on Decision Rough Set <inline-formula> <tex-math notation="LaTeX">$\alpha$ </tex-math> </inline-formula>-Positive Region Reduction

Steganography detection based on Rich Model features is a hot research direction in steganalysis. However, rich model features usually result a large computation cost. To reduce the dimension of steganalysis features and improve the efficiency of steganalysis algorithm, differing from previous works that normally proposed new feature extraction algorithm, this paper proposes a general steganalysis feature selection method based on decision rough set $\alpha$ -positive region reduction. First, it is pointed out that decision rough set $\alpha$ -positive region reduction is suitable for steganalysis feature selection. Second, a quantization method of attribute separability is proposed to measure the separability of steganalysis feature components. Third, steganalysis feature components selection algorithm based on decision rough set $\alpha$ -positive region reduction is given; thus, stego images can be detected by the selected feature. The proposed method can significantly reduce the feature dimensions and maintain detection accuracy. Based on the BOSSbase-1.01 image database of 10 000 images, a series of feature selection experiments are carried on two kinds of typical rich model features (35263-D J+SRM feature and 17000-D GFR feature). The results show that even though these two kinds of features are reduced to approximately 8000-D, the detection performance of steganalysis algorithms based on the selected features are also maintained with that of original features, which will remarkably improve the efficiency of feature extraction and stego image detection.

A general reduction method for fuzzy objective relation systems

Fuzzy objective relation systems are an important class of datasets that are generalizations of many types of decision tables. This paper proposes an approach, based on relation systems and fuzzy sets, to reduce data redundancy in fuzzy objective relation systems. We study lower and upper approximation reductions of a relation system for a given fuzzy set. As a generalization of such reductions, we consider lower and upper approximation reductions of fuzzy objective relation systems and give their corresponding reduction algorithms using methods based on the discernibility matrix. We note that the usual positive region reduction for a decision table can be considered a special case of our lower approximation reduction. Finally, we provide two examples from the UCI datasets to verify our theoretical results. These results can help in the decision making analysis of fuzzy objective relation systems.

Positive Region Reduct Based on Relative Discernibility and Acceleration Strategy

Attribute reduction is one of key issues in rough set theory, and positive region reduct is a classical type of reducts. However, a lot of reduction algorithms have more high time expenses when dealing with high-volume and high-dimensional data sets. To overcome this shortcoming, in this paper, a relative discernibility reduction method based on the simplified decision table of the original decision table is researched for obtaining positive region reduct. Moreover, to further improve performance of reduction algorithm, we develop an accelerator for attribute reduction, which reduces the radix sort times of the reduction process to raise algorithm efficiency. By the accelerator, two positive region reduction algorithms, i.e., FARA-RS and BARA-RS, based on the relative discernibility are designed. FARA-RS simultaneously reduce the size of the universe and the number of radix sort to achieve speedup and BARA-RS only reduce the number of radix sort to achieve acceleration. The experimental results show that the proposed reduction algorithms are effective and feasible for high dimensional and large data sets.

Local attribute reductions for decision tables

Attribute reduction is among the most important areas of research in rough sets. This paper investigates the types of local attribute reduction for decision tables. We propose the concepts of lth decision class lower approximation reduction, lth decision class reduction, and lth decision class β-reduction for decision tables, and provide their corresponding reduction algorithms via discernibility matrices. We also establish the relationship between positive-region reduction and the lth decision class β-reduction, and report a case study using the University of California–Irvine dataset to verify the theoretical results.

A unified reduction algorithm based on invariant matrices for decision tables

Attribute reduction is an important issue for decision analysis in databases. Absolute reduction, distributive reduction and positive region reduction are the most common types of attribute reduction discussed in the existing literature. This paper considers these three reduction types from the viewpoint of matrices and proposes the concept of reduction invariant matrices for each type in decision tables. Based on invariant matrices, we establish a unified algorithm for all three reduction types in decision tables. We also study the relationships among the three reduction types. Finally, experiments with UCI data sets are presented to verify the effectiveness of the proposed algorithm.

Attribute Reduction for Generalized Decision Systems*

Attribute reduction of information system is one of the most important applications of rough set theory. This paper focuses on generalized decision system and aims at studying positive region reduction and distribution reduction based on generalized indiscernibility relation. The judgment theorems for attribute reductions and attribute reduction approaches are presented. Our approaches improved the existed discernibility matrix and discernibility conditions. Furthermore, the reduction algorithms based on discernible degree are proposed.

Attribute Reduction in Interval and Set-Valued Decision Information Systems

In many practical situation, some of the attribute values for an object may be interval and set-valued. This paper introduces the interval and set-valued information systems and decision systems. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories: disjunctive (Type 1) and conjunctive (Type 2) systems. In this paper, we mainly focus on semantic interpretation of Type 1. Then, we define a new fuzzy preference relation and construct a fuzzy rough set model for interval and set-valued information systems. Moreover, based on the new fuzzy preference relation, the concepts of the significance measure of condition attributes and the relative significance measure of condition attributes are given in interval and set-valued decision information systems by the introduction of fuzzy positive region and the dependency degree. And on this basis, a heuristic algorithm for calculating fuzzy positive region reduction in interval and set-valued decision information systems is given. Finally, we give an illustrative example to substantiate the theoretical arguments. The results will help us to gain much more insights into the meaning of fuzzy rough set theory. Furthermore, it has provided a new perspective to study the attribute reduction problem in decision systems.

Comparative study of decision performance of decision tables induced by attribute reductions

The given attribute reduction approach decides the decision performance of a reduced decision table, which can give a guidance for selecting one rule-extraction method in practical applications. The objective of this study is to compare the decision performance of positive-region reduction, Shannon entropy reduction and Liang entropy reduction. In this paper, the relationships between positive-region reduction, Shannon entropy reduction and Liang entropy reduction are first investigated. Then, by means of three evaluation indices (certainty measure, consistency measure and support measure), we systemically analyse these change mechanisms for decision performance of a decision table induced by each of these three types of reduction approaches. Finally, by numerical experiments, these change mechanisms of a decision table's decision performance are verified for the above-mentioned three attribute reductions.

Hybrid approaches to attribute reduction based on indiscernibility and discernibility relation

Attribute reduction is one of the key issues in rough set theory. Many heuristic attribute reduction algorithms such as positive-region reduction, information entropy reduction and discernibility matrix reduction have been proposed. However, these methods are usually computationally time-consuming for large data. Moreover, a single attribute significance measure is not good for more attributes with the same greatest value. To overcome these shortcomings, we first introduce a counting sort algorithm with time complexity O(∣ C∣ ∣ U∣) for dealing with redundant and inconsistent data in a decision table and computing positive regions and core attributes (∣ C∣ and ∣ U∣ denote the cardinalities of condition attributes and objects set, respectively). Then, hybrid attribute measures are constructed which reflect the significance of an attribute in positive regions and boundary regions. Finally, hybrid approaches to attribute reduction based on indiscernibility and discernibility relation are proposed with time complexity no more than max( O(∣ C∣ 2∣ U/ C∣), O(∣ C∣∣ U∣)), in which ∣ U/ C∣ denotes the cardinality of the equivalence classes set U/ C. The experimental results show that these proposed hybrid algorithms are effective and feasible for large data.