Narrow Results

We introduce in this paper a new type of extended attribute reduction called M-reducts for an inconsistent decision table, which is defined to preserve the membership degree to a maximum decision class for each object of the table. It is shown that a M-reduct can actually preserve more decision information than it does by definition, including the maximum decision class itself and all deterministic decision information. Compared with other types of extended attribute reductions, the proposed type of attribute reduction is a better trade-off between the knowledge preserving capability and reduction efficiency. Illustrative examples are given and an effective algorithm for computing a M-reduct based on two summation functions of attribute sets is proposed together with its complexity analysis.

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets.

The neighborhood system based rough set is a generalization of Pawlak's rough set model since the former uses the neighborhood system instead of the partition for constructing target approximation. In this paper, the neighborhood system based rough set approach is employed to deal with the incomplete information system. By the coverings induced by the maximal consistent blocks and the support sets of the descriptors, respectively, two neighborhood systems based rough sets are explored. By comparing with the original maximal consistent block and descriptor based rough sets, the neighborhood system based rough sets hold the same lower approximations and the smaller upper approximations. Furthermore, the concept of attribute reduction is introduced into the neighborhood systems and the corresponding rough sets. The judgement theorems and discernibility functions to compute reducts are also presented. Some numerical examples are employed to substantiate the conceptual arguments.

In this paper, we aim to study intuitionistic fuzzy ordered information systems. Firstly, the concept of intuitionistic fuzzy ordered information systems is proposed by introducing an intuitionistic fuzzy relation to ordered information systems. Meanwhile, two approximation operators are defined and a rough set approach is established in intuitionistic fuzzy ordered information systems. Secondly, a ranking approach for all objects is constructed in this system. Thirdly, approximation reduction is addressed in intuitionistic fuzzy ordered decision information system. These results will be helpful for decision-making analysis in intuitionistic fuzzy ordered information systems.

In this paper, a new incremental knowledge acquisition method is proposed based on rough set theory, decision tree and granular computing. In order to effectively process dynamic data, describing the data by rough set theory, computing equivalence classes and calculating positive region with hash algorithm are analyzed respectively at first. Then, attribute reduction, value reduction and the extraction of rule set by hash algorithm are completed efficiently. Finally, for each new additional data, the incremental knowledge acquisition method is proposed and used to update the original rules. Both algorithm analysis and experiments show that for processing the dynamic information systems, compared with the traditional algorithms and the incremental knowledge acquisition algorithms based on granular computing, the time complexity of the proposed algorithm is lower due to the efficiency of hash algorithm and also this algorithm is more effective when it is used to deal with the huge data sets.

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.

Attribute reduction plays an important role in knowledge discovery and data mining. Confronted with data characterized by the interval and missing values in many data analysis tasks, it is interesting to research the attribute reduction for interval-valued data with missing values. Uncertainty measures can supply efficient viewpoints, which help us to disclose the substantive characteristics of such data. Therefore, this paper addresses the attribute reduction problem based on uncertainty measure for interval-valued data with missing values. At first, an uncertainty measure is provided for measuring candidate attributes, and then an efficient attribute reduction algorithm is developed for the interval-valued data with missing values. To improve the efficiency of attribute reduction, the objects that fall within the positive region are deleted from the whole object set in the process of selecting attributes. Finally, experimental results demonstrate that the proposed algorithm can find a subset of attributes in much shorter time than existing attribute reduction algorithms without losing the classification performance.

Attribute reduction is a key data preprocessing technique, and has been widely studied in data mining, machine learning, and granular computing. Minimal test cost attribute reduction is one of important parts researched in cost-sensitive learning. The backtracking algorithm can obtain an optimal reduct, however on only small datasets due to the NP-hardness of the problem. Heuristic algorithms, such as the genetic one and the information gain based one, are employed to deal with this problem. In this paper, we propose the Fast Randomized Algorithm to obtain a satisfactory reduct more efficiently. The focus of the algorithm is a randomization mechanism that deals with attributes addition and deletion. There are two important parameters in the addition stage, namely the selecting probability of attributes and the number of selected attributes per batch. We obtain some appropriate parameter settings through experiments in a variety of datasets. Results show that the optimal settings of two parameters rarely change on different datasets. Our algorithm is more stable and significantly more efficient than existing heuristic ones.

Attribute reduction is proved to be a non-deterministic polynomial problem (NP). Minimal attribute reduction is the main research content in rough set theory. We find that in the traditional rough set attribute reduction algorithm, the rough set attribute reduction based on discrete particle swarm optimization (DPSO) performs well. However, the fitness function of this method has some limitations. When the minimum attribute reduction result is the conditional attribute set itself, the correct result cannot be obtained. For enhancing the accuracy and efficiency of attribute reduction, we propose an attribute reduction algorithm based on DPSO and variable precision rough set (VPRS). The proposed algorithm uses VPRS to process data more accurately. The new fitness function is constructed, and the attribute dependence is used as the function judgment basis. It can be adjusted automatically as the discrete binary particle swarm evolves, ensuring the convergence speed and evolution direction. Experimental results show that compared with traditional method, the proposed algorithm has stronger effectiveness and higher application value.

Attribute reduction of formal context is a crucial reseach issue in formal concept analysis. In this paper, based on the meet-irreducible elements and join-irreducible elements of concept lattice, two kinds of attribute reductions of formal context are proposed, which are called MI-attribute reduction and JI-attribute reduction. Subsequently, we discuss the relationships among them and two existing attribute reductions of formal context, lattice-based attribute reduction and granular reduction. Consequently, we find that the MI-attribute reduction and lattice-based attribute reduction are identical. For JI-attribute reduction, the judgement theorems of JI-consistent attribute sets are obtained. Finally, by using the discernibility attribute sets, a method of computing all JI-attribute reducts of a formal context is presented.

In this research paper, we introduce certain new concepts, including $m$-polar fuzzy formal context, $m$-polar fuzzy concept lattice, discernibility function and discernibility matrix. We discuss interesting applications of $m$-polar fuzzy concept lattice for the detection of women and child trafficking and abduction suspects. We also present certain algorithms for computing $m$-polar fuzzy formal concepts and discernibility function.

Attribute reduction has the ability to identify essential features, reduce feature dimensions, and improve the classification of learning models. The study of attribute reduction methods for ordered decision systems, which are data with preferred order relations, is a popular research topic. In this chapter, a heuristic attribute reduction method based on self-information is proposed by improving the computation of the approximation set. First, by choosing the triangular matrix form, we cleverly optimize the matrix computation process, which facilitates the storage of relations among multiple objects and saves time effectively at the same time. Second, we introduce a more efficient method to compute the approximation set, which further improves the computational efficiency of the algorithm. The adoption of self-information as the uncertainty measure considers both deterministic information and possible categorization information. Finally, the validation practice on multiple datasets fully proves the effectiveness of the algorithm. From the experimental results, the algorithm in this chapter can effectively remove irrelevant or redundant attributes, and at the same time, it is also more efficient compared to other algorithms due to the improved approximation set calculation method.

The system call sequences have already become one of the important data sources in host-based intrusion detection system. There are some merits which are high in accuracy, low in false fault and good in stability and so on by using the system calls analysis to judge the intrusion. This paper puts forward a high-efficient and low-loading abnormal detecting method aiming at sequences. The method is based on rough set and capable of extracting detection rules with the minimum size to form a normal behavior model from the record of sequences generated during the normal execution of process. Compared with other methods, the merits of using the Rough set theory to create the normal model are as follows: it is simple to get the training data; the small rules set is suitable to real-time detection, and the process’ abnormal running state can be detected out effectively. Experiment results show that the efficiency of the method in this paper is obvious higher than other methods.

In this paper, we present an application of rough set methods for rule generation, which includes two steps. Attribute reduction is done first, which reduces the number of unnecessary attributes for the whole decision table. In this process, the relative subdivision distance is proposed as the heuristic information of algorithm REDA. The completeness and the correctness of REDA are also proven from the theoretical analysis. Value reduction is performed afterwards, which reduces the number of redundant attributes for every object. In this process, properties of attribute values of three classes are analyzed and the maximum number of condition attribute values is removed without losing essential information according to their properties. We then can get the optimal decision rules. Experimental results from applying the rough set approach to the set of data samples are given and evaluated to show efficient and effective of our algorithm.

In this paper, we study directed graph combined with the reduction algorithms based on the principle of discernibility matrix. By investigating the discernibility set applied to directed graph, a new function opr( ) is given. The function focuses on the computing of the attribute set gotten from the discernibility matrix, so as to get a optimized set. Hence, we propose a better complete algorithm for attribute reduction based on the function opr( ). Finally we gave the proof of its completeness.

Attribute reduction is a hot topic in rough set theory. Many attribute reduction algorithms have been studied in previous literatures. However, existing algorithms are very time-consuming on massive data. To address this shortcoming, a parallel framework for attribute reduction is proposed. The divide-and-conquer methods for several typical attribute significances are presented. Then the corresponding parallel algorithms on CUDA programing model are developed. The experimental results on UCI datasets show that these proposed parallel algorithms have a good speedup performance.

In order to improve the precision and date processing speed of multi-sensor information fusion, a kind of multi-sensor data fusion process algorithm has been studied in this paper. First, based on rough set theory (RS) to attribute reduction the parameter set, we use the advantages of rough set theory in dealing with large amount of data to eliminate redundant information. Then, the data can be trained and classified by Support Vector Machine (SYM). Experimental results showed that this method can improve the speed and accuracy of multi-sensor fusion system.