Discernibility Matrix Research Articles

Partial reduction algorithms for fuzzy relation systems

Relationships among elements of sets appear in many contexts and can be represented using fuzzy relations. A fuzzy relation system is an extensive information system. Attribute reduction is widely used to discover knowledge hidden in databases. Many approaches to reduction based on the rough set theory have been proposed in recent years to deal with information systems, and partial reductions have been proposed in relation to decision systems to extract partial decision rules. This paper considers an approach to fuzzy relation systems based on significant partial attribute reduction by means of discernibility matrices. We propose the concept of X-lower and -upper approximation reductions, and develop their corresponding reduction algorithms. These methods of reduction unify results that have been reported in the literature. We provide examples from the UCI datasets to verify our algorithms.

A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System

The basic idea underneath the generalized intuitionistic fuzzy soft set is very constructive in decision making, since it considers how to exploit an extra intuitionistic fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is redefined and clarified by F. Feng. In this paper, we introduced a method to solve decision making problems using an adjustable weighted soft discernibility matrix in a generalized intuitionistic fuzzy soft set. We define the threshold functions like mid-threshold, top-bottom-threshold, bottom-bottom-threshold, top-top-threshold, med-threshold function and their level soft sets of the generalized intuitionistic fuzzy soft set. After, we proposed two algorithms based on threshold functions, a weighted soft discernibility matrix and a generalized intuitionistic fuzzy soft set and also to show the supremacy of the given methods we illustrate a descriptive example using a weighted soft discernibility matrix in the generalized intuitionistic fuzzy soft set. Results indicate that the proposed method is more effective and generalized over all existing methods of the fuzzy soft set.

Heuristic Approaches to Attribute Reduction for Generalized Decision Preservation

Attribute reduction is a challenging problem in rough set theory, which has been applied in many research fields, including knowledge representation, machine learning, and artificial intelligence. The main objective of attribute reduction is to obtain a minimal attribute subset that can retain the same classification or discernibility properties as the original information system. Recently, many attribute reduction algorithms, such as positive region preservation, generalized decision preservation, and distribution preservation, have been proposed. The existing attribute reduction algorithms for generalized decision preservation are mainly based on the discernibility matrix and are, thus, computationally very expensive and hard to use in large-scale and high-dimensional data sets. To overcome this problem, we introduce the similarity degree for generalized decision preservation. On this basis, the inner and outer significance measures are proposed. By using heuristic strategies, we develop two quick reduction algorithms for generalized decision preservation. Finally, theoretical and experimental results show that the proposed heuristic reduction algorithms are effective and efficient.

Reduction foundation with multigranulation rough sets using discernibility

When multiple granulated knowledge in multigranulation spaces are involved in decision making, protocol principles are adopted to arrive at the final consensus. Multigranulation rough set theory utilizes a voting principle to combine the decision options derived from individual granulated knowledge. Note that those knowledge may provide different degrees of support to the final results, some are key, some are of less importance and some are even of no use. Selecting valuable knowledge and reducing worthless one are thus necessary for data processing, which can alleviate the storage occupancy and facilitate the logical and statistical analysis. However, the basic reduction foundation of multigranulation spaces has been rarely touched by researchers, which brings in many difficulties in algorithmic and real applications. This work aims to disclose the principles of multiple knowledge reduction in multigranulation spaces from the viewpoint of discernibility. First, the notions of knowledge reduction of multigranulation spaces are defined based on multigranulation rough set theory. Second, a decision function mapping each object into the decision options of its neighborhood granule is introduced. Third, several pairs of discernibility matrices and discernibility functions are successively developed using the decision function. We claim that the valuable and worthless knowledge in multigranulation spaces can be explicitly chose and eliminated respectively by using the proposed discernibility matrices and discernibility functions. That is to say, these discernibility tools provide a precise criterion for the knowledge reduction of multigranulation spaces. As a theoretical extension, a multigranulation information entropy is proposed and an approximate algorithm is constructed to compute a suboptimal reduct of a multigranulation space based on this entropy. In the end, numerical experiments are performed on public data sets to verify the effectiveness of the proposed reduction methods. This study can get us a grasp of the foundational principle of knowledge reduction and may bring a new insight for the designation of substantial reduction algorithms of multigranulation knowledge.

Knowledge Reduction Model of Crowd Evacuation Stability Based on Rough Set Theory

To reduce the redundant knowledge discovered from the evolution of crowd evacuation in case of emergencies, this paper aims at knowledge reduction model of crowd evacuation stability evolution. First, the evolutionary mechanism of evacuation stability state is analysed from the perspective of knowledge engineering, and the characteristics of evacuation scenario elements such as physical properties of crowd, structure of evacuation scenario and psychological behaviour of evacuees are analysed and extracted by using self-organizing mapping network algorithm; Secondly, the evolutionary characteristics of evacuation scenario elements and evacuation stability state are discretized and mapped to conditional attributes and decision attributes in rough set universe respectively. Thereby a knowledge representation method of evacuation stability evolution mechanism based on rough set decision information table is constructed. Then, the improved attribute reduction algorithm based on discernibility matrix is used to reduce the knowledge of decision information table processed by self-organizing network algorithm. Finally, a knowledge reduction model of crowd evacuation stability based on rough sets is proposed. It is validated effective to achieve the decision-making of crowd stability, and which provides theoretical basis and methodological support for scientific guidance of emergency evacuation.

A Dynamic Multi-Reduction Algorithm for Brain Functional Connection Pathways Analysis

Revealing brain functional connection pathways is of great significance in understanding the cognitive mechanism of the brain. In this paper, we present a novel rough set based dynamic multi-reduction algorithm (DMRA) to analyze brain functional connection pathways. First, a binary discernibility matrix is introduced to obtain a reduction, and a reduction equivalence theorem is proposed and proved to verify the feasibility of reduction algorithm. Based on this idea, we propose a dynamic single-reduction algorithm (DSRA) to obtain a seed reduction, in which two dynamical acceleration mechanisms are presented to reduce the size of the binary discernibility matrix dynamically. Then, the dynamic multi-reduction algorithm is proposed, and multi-reductions can be obtained by replacing the non-core attributes in seed reduction. Comparative performance experiments were carried out on the UCI datasets to illustrate the superiority of DMRA in execution time and classification accuracy. A memory cognitive experiment was designed and three brain functional connection pathways were successfully obtained from brain functional Magnetic Resonance Imaging (fMRI) by employing the proposed DMRA. The theoretical and empirical results both illustrate the potentials of DMRA for brain functional connection pathways analysis.

An Improved Attribute Reeducation Algorithm Based on Mutual Information for Non-Care Information System

For an information system the attribute reduction is one key to choose some important indexes, but the core attribute is the foundation for the present heuristic attribute reduction algorithms of rough set theory based on discernibility matrix and mutual information theory. When we apply these algorithms on the non-core information system, there will be the following problems, such as too much calculation problem, excessive reduction, or insufficient reduction. According to the characteristics of non-core information system, we propose one new heuristic attribute reduction algorithm based on mutual information, in which the evaluation of attribute important degree depends on the increment of mutual information and information entropy. And the attribute with the largest attribute important degree is selected for the initial core attribute, by which the problem that the random selection attribute cause the computational complexity is solved. By the proposed algorithm we cannot only improve the efficiency of attribute reduction, but decrease the number of attribute reduction. Both the theoretic analysis and the simulation experiments verify that the proposed algorithm is validity

A novel machine learning based feature selection for motor imagery EEG signal classification in Internet of medical things environment

Abstract In Internet of Medical Things (IoMT) environment, feature selection is an efficient way of identifying the most discriminant health-related features from the original feature-set. Feature selection not only finds the best informative features, but also helps in reducing the overall dimensions of the given dataset. In this paper, the actual feature-set is obtained from Brain Computer Interface (BCI) Competition-II Dataset-III motor-imagery electroencephalogram (EEG) signal using the Adaptive Auto-regressive (AAR) feature extraction technique. Based on the order (number of AR coefficients) of the AAR algorithm, two variants of datasets have been generated: 12 ( o r d e r = 6 per electrode) and 24 ( o r d e r = 12 per electrode) AAR features datasets. Here, a new fuzzified version of discernibility matrix has been proposed to determine a subset of features, which provides the best classification accuracy. In order to find the best feature subset, various types of dissimilarity measures have been used and compared with one another in our proposed fuzzy discernibility matrix (FDM) based feature selection technique. We have implemented the proposed algorithm on the given datasets using both the holdout technique as well as the 10-fold cross-validation in our study. The performances of the selected feature-subsets are evaluated based on accuracies using the Support Vector Machine (SVM) and Ensemble variants of classifiers. The empirical results obtained from our experiments in this paper is competitive in terms of accuracy and outperformed the other popular t-test, Kullback–Leibler Divergence (KLD), Bhattacharyya distance and Gini index based feature selection techniques. Our proposed FDM based feature selection algorithm using holdout technique provides 80% and 78.57% accuracies for the 12 and 24 features AAR datasets respectively. The results obtained in the holdout technique with only 50% of the best discriminant features are even better than the performances obtained while using the original feature-sets (without using any feature selection technique). Again, it gives 78.57% and 75.57% mean-accuracies from 5 × 10-fold cross-validations using only 6and 12 most discriminant AAR features from the actual 12 & 24 features-sets respectively.

The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context.

Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the theory of concept lattice. Moreover, this paper studies, in detail, the algorithms and case study of data analysis in the intuitionistic fuzzy generalized consistent decision formal context. The potential value of the method to deal with information discussed in this paper, especially the value of forecasting and decision-making, is expected in future.

A novel algorithm for the vertex cover problem based on minimal elements of discernibility matrix

Minimal vertex cover problem (MVCP) is a famous important NP-hard problem in graph theory. It has been reported that MVCP is equivalent to finding reducts of information systems in rough sets theory. This relationship motivates our idea to deal with MVCP in terms of approaches to discernibility matrix in rough set. First we point out that only minimal elements in the discernibility matrix are useful for MVCP, and we present a novel algorithm based on minimal elements for MVCP. Then we make experimental comparisons to demonstrate the effectiveness of this new algorithm on big graphs.

Compressed binary discernibility matrix based incremental attribute reduction algorithm for group dynamic data

The datasets in real-world applications often vary dynamically over time. Moreover, datasets often expand by introducing a group of data in many cases rather than a single object one by one. The traditional incremental attribute reduction approaches for a single dynamic object may not be applied to such cases. Focusing on this issue, a compressed binary discernibility matrix is introduced and an incremental attribute reduction algorithm for group dynamic data is developed. The single dynamic object and the group dynamic objects are both considered in this algorithm. According to the dynamic data is a single object or a group of objects, different branches can be chosen to update the compressed binary discernibility matrix. Thereafter, the incremental reduction result can be obtained based on the updated compressed binary discernibility matrix. The validity of this algorithm is demonstrated by simulation and experimental analysis.

Minimal Element Selection in the Discernibility Matrix for Attribute Reduction

Discernibility matrix is a beautiful theoretical result to get reducts in the rough set, but the existing algorithms based on discernibility matrix share the same problem of heavy computing load and large store space, since there are numerous redundancy elements in discernibility matrix and these algorithms employ all elements to find reducts. We introduce a new method to compute attribute significance. A novel approach is proposed, called minimal element selection tree, which utilizes many strategies to eliminate redundancy elements in discernibility matrix. This paper presents two methods to find out a minimal reduct for a given decision table based this tree structure. The experimental results with UCI data show that the proposed approaches are effective and efficient than the benchmark methods.

Large Data Generalized Dynamic Fault Feature Extraction Algorithm Based on Intuitionistic Fuzzy-Rough Set Discernibility Matrix

Large Data Generalized Dynamic Fault Feature Extraction Algorithm Based on Intuitionistic Fuzzy-Rough Set Discernibility Matrix

A Quick Algorithm for Binary Discernibility Matrix Simplification using Deterministic Finite Automata

The binary discernibility matrix, originally introduced by Felix and Ushio, is a binary matrix representation for storing discernible attributes that can distinguish different objects in decision systems. It is an effective approach for feature selection, knowledge representation and uncertainty reasoning. An original binary discernibility matrix usually contains redundant objects and attributes. These redundant objects and attributes may deteriorate the performance of feature selection and knowledge acquisition. To overcome this shortcoming, row relations and column relations in a binary discernibility matrix are defined in this paper. To compare the relationships of different rows (columns) quickly, we construct deterministic finite automata for a binary discernibility matrix. On this basis, a quick algorithm for binary discernibility matrix simplification using deterministic finite automata (BDMSDFA) is proposed. We make a comparison of BDMR (an algorithm of binary discernibility matrix reduction), IBDMR (an improved algorithm of binary discernibility matrix reduction) and BDMSDFA. Finally, theoretical analyses and experimental results indicate that the algorithm of BDMSDFA is effective and efficient.

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.

A fast attribute reduction method for large formal decision contexts

Attribute reduction in formal decision contexts is an important issue in formal concept analysis, which can help us to discover the knowledge hidden in formal decision contexts. However, most reduction methods in formal decision contexts are very time-consuming due to two main problems. The first is that one needs to construct a discernibility matrix after generating all the formal concepts of formal decision contexts. This is not an easy task because it requires much more storage space and computation time. Another problem is that most reduction methods are based on the Boolean reasoning and the computational complexity of which is exponential in the worst case. To overcome these problems, we propose a new attribute reduction method for formal decision contexts in this paper. A more simplified discernibility matrix which does not need to generate all the formal concepts is first constructed. It shows that the storage space and computation time are far less than the original method. Furthermore, different from the Boolean reasoning method, an approximation algorithm for obtaining a minimum reduct in formal decision contexts based on graph theory is designed. Finally, experiments are carried out to verify the effectiveness of the proposed method. The results, on 22 large data sets, demonstrate that the proposed method not only produces smaller subset of attributes but also has better performance in both storage space and speed.

Cost-sensitive approximate attribute reduction with three-way decisions

In the research spectrum of rough set, the task of attribute reduction is obtaining a minimal attribute subset that preserves certain properties of the original data. Cost-sensitive attribute reduction aims at minimizing various types of costs. Approximate attribute reduction allows decision makers to leverage the advantages of knowledge discovery and their own preferences. This paper proposes the cost-sensitive approximate attribute reduction problem under both qualitative and quantitative criteria. The qualitative criterion refers to the indiscernibility, while the quantitative criterion refers to the approximate parameter ε and the cost. We present a framework based on three-way decisions and discernibility matrix to handle this new problem. First, a quality function for attribute subsets is designed with the interpretation of a hierarchical granular structure. Second, a fitness function is designed for cost performance index by investigating attribute significance. Third, three-way decision theory is applied to partition the attributes into three groups based on the fitness function and a threshold pair (α,β). Finally, deletion-based and addition-based cost-sensitive approximate reduction algorithms are designed under this framework. Experimental results indicate that our algorithms outperform the state-of-the-art methods.

Attributes set reduction in multigranulation approximation space of a multi-source decision information system

The multiple granular structures in multigranulation approximation space can be integrated by different approximation operators. These operators are induced by multigranulation rough set or others. In this paper, numerical algorithms of attributes set reduction are developed by using evidence theory or minimal elements of discernibility matrix, respectively. Firstly, a pair of multi-source rough approximation operators and their corresponding multigranulation rough approximation operators are defined based on a bijective and new transitional domain. Then, we propose attributes set reduction with respect to multi-source rough approximation. It is based on the relationship between multi-source rough approximations and evidence theory. Therefore, a heuristic algorithm of attributes set reduction for multi-source lower rough approximation is given. Secondly, we define a multigranulation variable precision rough set (MVRS) by considering weight of each attributes set relative to all of attributes sets. Finally, we investigate attributes set reduction with MVRS by combing the minimal elements of discernibility matrix and distribution discernibility function. There are some illustrative examples to elaborate the operation mechanism of above conclusions.

Accelerating incremental attribute reduction algorithm by compacting a decision table

The evolution of object sets over time is ubiquitous in dynamic data. To acquire reducts for this type of data, researchers have proposed many incremental attribute reduction algorithms based on discernibility matrices. Although all reducts of an updated decision table can be obtained using these algorithms, their high computation time is a critical issue. To address this issue, we first construct three new types of discernibility matrices by compacting a decision table to eliminate redundant entries in the discernibility matrices of the original decision table. We then demonstrate that the set of reducts obtained from the compacted decision table are the same as those acquired from the original decision table. Extensive experiments have demonstrated that an incremental attribute reduction algorithm based on a compacted decision table can significantly accelerate attribute reduction for dynamic data with changing object sets while the acquired reducts are identical to those obtained using existing algorithms.

On attribute reduction in concept lattices: Experimental evaluation shows discernibility matrix based methods inefficient

In recent years, discernibility matrix based methods of attribute reduction in concept lattices (DM-methods) enjoyed an increase in attention and were applied in many extensions of formal concept analysis. In our previous paper, we pointed out that there exists an older method (CR-method) with theoretically lesser time complexity and we proposed a wrapping procedure to use the CR-method in any extension where the DM-methods are used. Now we evaluate the methods experimentally. Results of the evaluation assert our previous theoretical findings that the CR-method is strictly superior as it outperforms the DM-methods by several order of magnitude. To emphasize the poor performance of the DM-methods we introduce a new naïve and deliberately slow algorithm called SIMPEL. Subsequently, we show that even its performance is not so bad in comparison with the DM-methods. Our conclusions are that it is inefficient to use the DM-methods for attribute reduction in concept lattices and that the CR-method should be used instead in practice.