Tolerance Rough Set Model Research Articles

Incremental updating fuzzy tolerance rough set approach in intuitionistic fuzzy information systems with fuzzy decision

As information technology develops rapidly and data is constantly updated, efficient mining knowledge from dynamic intuitionistic fuzzy information systems with fuzzy decision (IFFD) is a significant topic. In the dynamic data environment, the corresponding IFFD is always changing with time when object sets of datasets may evolve in time. Fuzzy tolerance rough set (FTRS), as one of extended rough set models, has a strong capacity for the expression of information and better representation of uncertainty. Therefore, it is very effective and necessary to use FTRS to acquire valuable knowledge from dynamic IFFD. In this paper, we investigate the dynamic fuzzy tolerance rough set approach for IFFD. Firstly, a new fuzzy tolerance similarity is defined to describe fuzzy tolerance relation between objects in the IFFD. Second, we construct a fuzzy tolerance rough set model in the IFFD, discuss some properties, and propose the corresponding static algorithm. Subsequently, incremental approaches which update fuzzy tolerance rough approximations with the insertion and deletion of objects in the IFFD are investigated and the corresponding dynamic algorithms are also designed. Finally, the feasibility of the FTRS model and the effectiveness and efficiency of the dynamic algorithm in dynamic environments are validated through a series of comparative experiments on nine datasets.

Matrix-based approaches for updating three-way regions in incomplete information systems with the variation of attributes

As a commonly used framework for uncertainty reasoning, tolerance rough set has achieved remarkable success in handling incomplete information systems with missing values. Three-way regions generated from tolerance rough set model play an increasingly crucial role in decision making and intelligent data analysis. Nevertheless, the dynamic change of attributes often exists in incomplete information systems. With this dynamic characteristic, three-way regions must be effectively updated for potential decision-making processes. Therefore, we develop incremental algorithms for maintenance of three-way regions in incomplete information systems when adding or deleting attributes, accelerating the calculation by making use of prior information. First, we put forward an effective matrix-based approach to calculate three-way regions in incomplete data. With the dynamic change of attributes, we further investigate the updating strategies of related matrices for constructing three-way regions. Accordingly, matrix-based algorithms for incrementally updating three-way regions are developed and discussed while the attributes vary over time. In addition, the complexity comparisons of non-incremental and incremental algorithms are illustrated. Finally, empirical experiments are performed to reveal the efficiency of the incremental algorithms compared with matrix-based non-incremental and related incremental algorithms.

Filter-Wrapper Incremental Algorithms for Finding Reduct in Incomplete Decision Systems When Adding and Deleting an Attribute Set

The tolerance rough set model is an effective tool to solve attribute reduction problem directly on incomplete decision systems without pre-processing missing values. In practical applications, incomplete decision systems are often changed and updated, especially in the case of adding or removing attributes. To solve the problem of finding reduct on dynamic incomplete decision systems, researchers have proposed many incremental algorithms to decrease execution time. However, the proposed incremental algorithms are mainly based on filter approach in which classification accuracy was calculated after the reduct has been obtained. As the results, these filter algorithms do not get the best result in term of the number of attributes in reduct and classification accuracy. This paper proposes two distance based filter-wrapper incremental algorithms: the algorithm IFWA_AA in case of adding attributes and the algorithm IFWA_DA in case of deleting attributes. Experimental results show that proposed filter-wrapper incremental algorithm IFWA_AA decreases significantly the number of attributes in reduct and improves classification accuracy compared to filter incremental algorithms such as UARA, IDRA.

Sentence Similarity Calculation Based on Probabilistic Tolerance Rough Sets

Sentence similarity calculation is one of the important foundations of natural language processing. The existing sentence similarity calculation measurements are based on either shallow semantics with the limitation of inadequately capturing latent semantics information or deep learning algorithms with the limitation of supervision. In this paper, we improve the traditional tolerance rough set model, with the advantages of lower time complexity and becoming incremental compared to the traditional one. And then we propose a sentence similarity computation model from the perspective of uncertainty of text data based on the probabilistic tolerance rough set model. It has the ability of mining latent semantics information and is unsupervised. Experiments on SICK2014 task and STSbenchmark dataset to calculate sentence similarity identify a significant and efficient performance of our model.

Local Generalized Multigranulation Variable Precision Tolerance Rough Sets and its Attribute Reduction

In the era of big data, as for an important granular computing model, rough set model is an important tool for us to deal with data. As a kind of extension of classical rough sets, multigranulation rough sets have two forms, including optimistic and pessimistic cases. However, these two models have their shortcomings, one is too loose, and the other is too strict. To overcome the above shortcomings, based on the concept of local multigranulation tolerance rough sets in set-valued information systems, the local generalized multigranulation variable precision tolerance rough sets model by introducing characteristic function is established. Then the related properties are studied and proved. In addition, we define the concepts of lower approximate quality, inner and outer importance of attribute according to different granularity structures in set-valued decision information systems because different granularity structures have different effectives on the decision classes. Finally, the local attribute reduction algorithm and the global attribute reduction algorithm of local generalized multigranulation variable precision tolerance rough sets in set-valued decision information systems are given, and the effectiveness of the algorithms is proved by using UCI data sets.

About a Distance Measure and Application for Finding Reduct in Incomplete Decision Tables

Tolerance rough set model is an effective tool to reduce attributes in incomplete decision tables. Over 40 years, several attribute reduction methods have been proposed to improve the efficiency of execution time and the number of attributes of the reduct. However, they are classical filter algorithms, in which the classification accuracy of decision tables is computed after obtaining the reducts. Therefore, the obtained reducts of these algorithms are not optimal in terms of reduct cardinality and classification accuracy. In this paper, we propose a filter-wrapper algorithm to find a reduct in incomplete decision tables. We then use this measure to determine the importance of the property and select the attribute based on the calculated importance (filter phase). In the next step, we find the reduct with the highest classification accuracy by iterating over elements of the set containing the sequence of attributes selected in the first step (wrapper phase). To verify the effectiveness of the method, we conduct experiments on 6 famous UCI data sets. Experimental results show that the proposed method increase classification accuracy as well as reduce the cardinality of reduct compared to Algorithm 1 [12].

A DISTANCE BASED INCREMENTAL FILTER-WRAPPER ALGORITHM FOR FINDING REDUCT IN INCOMPLETE DECISION TABLES

Tolerance rough set model is an effective tool for attribute reduction in incomplete decision tables. In recent years, some incremental algorithms have been proposed to find reduct of dynamic incomplete decision tables in order to reduce computation time. However, they are classical filter algorithms, in which the classification accuracy of decision tables is computed after obtaining reduct. Therefore, the obtained reducts of these algorithms are not optimal on cardinality of reduct and classification accuracy. In this paper, we propose the incremental filter-wrapper algorithm IDS_IFW_AO to find one reduct of an incomplete desision table in case of adding multiple objects. The experimental results on some sample datasets show that the proposed filter-wrapper algorithm IDS_IFW_AO is more effective than the filter algorithm IARM-I [17] on classification accuracy and cardinality of reduct

An Improved Limited Tolerance Rough Set Model

An Improved Limited Tolerance Rough Set Model

An Improved Limited Tolerance Rough Set Model

An Improved Limited Tolerance Rough Set Model

Probabilistic Tolerance Rough Set Model and Its Decision Risk Optimization

Probabilistic Tolerance Rough Set Model and Its Decision Risk Optimization

Hybrid Tolerance Rough Set

Breast cancer is the most common malignant tumor found among young and middle aged women. Feature Selection is a process of selecting most enlightening features from the data set which preserves the original significance of the features following reduction. The traditional rough set method cannot be directly applied to deafening data. This is usually addressed by employing a discretization method, which can result in information loss. This paper proposes an approach based on the tolerance rough set model, which has the flair to deal with real-valued data whilst simultaneously retaining dataset semantics. In this paper, a novel supervised feature selection in mammogram images, using Tolerance Rough Set - PSO based Quick Reduct (STRSPSO-QR) and Tolerance Rough Set - PSO based Relative Reduct (STRSPSO-RR), is proposed. The results obtained using the proposed methods show an increase in the diagnostic accuracy.

Rough set approach to incomplete numerical data

Rough set theory has been applied successfully in many fields. However, classical rough set model can only deal with complete and symbolic data sets. Some researchers have proposed extended rough set models to handle incomplete data while others proposed extensions of classical rough set models to deal with numerical data. However, there exist many data which contain numerical attributes and missing values simultaneously. We propose, in this paper, an extended rough set model, i.e. tolerance-fuzzy rough set model to deal with this type of data characterized with numerical attributes and missing values, that is, incomplete numerical data. Discernibility matrices and discernibility functions for incomplete numerical information systems and incomplete numerical decision systems are defined to compute reducts or relative reducts. Meanwhile, the relationship between the proposed tolerance-fuzzy rough set model and the tolerance rough set model is also examined. It is shown that the tolerance-fuzzy rough set model is an extension of the tolerance rough set model. Finally, uncertainty measurement is also investigated. It is suggested that the proposed tolerance-fuzzy rough set model provide an optional approach to incomplete numerical data.

Multi-granulation rough sets based on tolerance relations

The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues, the classical rough set model was extended to multi-granulation rough set model (MGRS). This paper extends the single-granulation tolerance rough set model (SGTRS) to two types of multi-granulation tolerance rough set models (MGTRS). Some important properties of the two types of MGTRS are investigated. From the properties, it can be found that rough set model based on a single tolerance relation is a special instance of MGTRS. Moreover, the relationship and difference among SGTRS, the first type of MGTRS and the second type of MGTRS are discussed. Furthermore, several important measures are presented in two types of MGTRS, such as rough measure and quality of approximation. Several examples are considered to illustrate the two types of multi-granulation tolerance rough set models. The results from this research are both theoretically and practically meaningful for data reduction.

A Similarity Rough Set Model for Document Representation and Document Clustering

Document clustering is a textmining technique for unsupervised document organization. It helps the users browse and navigate large sets of documents. Ho et al. proposed a Tolerance Rough Set Model (TRSM) [1] for improving the vector space model that represents documents by vectors of terms and applied it to document clustering. In this paper we analyze their model to propose a new model for efficient clustering of documents. We introduce Similarity Rough Set Model (SRSM) as another model for presenting documents in document clustering. The model is evaluated by experiments on test collections. The experiment results show that the SRSM document clusteringmethod outperforms the one with TRSM and the results of SRSM are less affected by the value of parameter than TRSM.

On-line Hot Topic Recommendation Using Tolerance Rough Set Based Topic Clustering

In this paper we present our research of online hot topic detection and label extraction method for our hot topic recommendation system. Using a new topical feature selection method, the feature space is compressed suitable for an online system. The tolerance rough set model is used to enriching the small set of topical feature words to a topical approximation space. According to the distance defined on the topical approximation space, the web pages are clustered into groups which will be merged with document overlap. The topic labels are extracted based on the approximation topical space enriched with the useful but high frequency topical words dropped by the clustering process. The experiments show that our method could generate more information abundant classes and more topical class labels, alleviate the topical drift caused by the non-topical and noise words.

Attribute reduction and optimal decision rules acquisition for continuous valued information systems

For continuous valued information systems, the attribute values of objects for the same attribute represent not only their ordinal relationship but also their relative distances. Therefore, the classical rough set model is not suitable for deducing attribute reductions and optimal decision rules for continuous valued information systems. Though some discretization methods are proposed to transform the continuous valued information systems into discrete ones, but those methods are too categorical and may lead to loss of information in some cases. To solve such information loss problem, we propose a tolerance rough set model in this paper. With a given level, the proposed model can divide a universe into some maximal tolerance classes. Also two types of lower and upper approximations are defined accordingly. Then the reductions of the maximal tolerance class and optimal decision rules based on the proposed attribute descriptors are defined, and the approximate discernibility function for the maximal tolerance class is constructed and used to compute all the corresponding optimal decision rules via using Boolean reasoning techniques. Finally, the general reductions and consistent reductions for continuous valued information systems are discussed.

Exploring the boundary region of tolerance rough sets for feature selection

Of all of the challenges which face the effective application of computational intelligence technologies for pattern recognition, dataset dimensionality is undoubtedly one of the primary impediments. In order for pattern classifiers to be efficient, a dimensionality reduction stage is usually performed prior to classification. Much use has been made of rough set theory for this purpose as it is completely data-driven and no other information is required; most other methods require some additional knowledge. However, traditional rough set-based methods in the literature are restricted to the requirement that all data must be discrete. It is therefore not possible to consider real-valued or noisy data. This is usually addressed by employing a discretisation method, which can result in information loss. This paper proposes a new approach based on the tolerance rough set model, which has the ability to deal with real-valued data whilst simultaneously retaining dataset semantics. More significantly, this paper describes the underlying mechanism for this new approach to utilise the information contained within the boundary region or region of uncertainty. The use of this information can result in the discovery of more compact feature subsets and improved classification accuracy. These results are supported by an experimental evaluation which compares the proposed approach with a number of existing feature selection techniques.

Cluster-based Information Retrieval with Tolerance Rough Set Model

The objectives of this paper are twofold. First is to introduce a model for representing documents with semantics relatedness using rough sets but with tolerance relations instead of equivalence relations (TRSM). Second is to introduce two document hierarchical and nonhierarchical clustering algorithms based on this model and TRSM cluster-based information retrieval using these two algorithms. The experimental results show that TRSM offers an alterative approach to text clustering and information retrieval.

Nonhierarchical document clustering based on a tolerance rough set model

Document clustering, the grouping of documents into several clusters, has been recognized as a means for improving efficiency and effectiveness of information retrieval and text mining. With the growing importance of electronic media for storing and exchanging large textual databases, document clustering becomes more significant. Hierarchical document clustering methods, having a dominant role in document clustering, seem inadequate for large document databases as the time and space requirements are typically of order O(N3) and O(N2), where N is the number of index terms in a database. In addition, when each document is characterized by only several terms or keywords, clustering algorithms often produce poor results as most similarity measures yield many zero values. In this article we introduce a nonhierarchical document clustering algorithm based on a proposed tolerance rough set model (TRSM). This algorithm contributes two considerable features: (1) it can be applied to large document databases, as the time and space requirements are of order O(NlogN) and O(N), respectively; and (2) it can be well adapted to documents characterized by a few terms due to the TRSM's ability of semantic calculation. The algorithm has been evaluated and validated by experiments on test collections. © 2002 John Wiley & Sons, Inc.