Variable Precision Rough Set Model Research Articles

An interval rough number variable precision rough sets model and its attribute reduction

The interval rough number rough sets model is the generalization of the classical rough sets. Since the lower approximation condition of interval rough number rough sets model is a full inclusion relation which is too strict to tolerate noisy data, strict conditions increase the possibility of a sample classified into a wrong class. To overcome the above shortcomings, an interval rough number variable precision rough sets model is proposed in this paper, which is combined with interval rough number similarity and the concept of variable precision rough sets. The model introduces the error parameter and can improve the tolerance of noise data. Then the related properties of the model are also proved. Moreover, we construct a maximal positive domain attribute reduction method based on the proposed model, which can process the data type of interval rough number without discretization. Finally, numerical examples are given to verify the rationality of the model.

Generalized fuzzy variable precision rough sets based on bisimulations and the corresponding decision-making.

Recently, the classical rough set has been extended in many ways. However, some of them are based on binary relations which only excavate “one step” information to distinguish objects. The “one step” in the binary relation means that the ordered pair of the starting and end points of the step belongs to the relation. Faced with some complex data sets, the “one step” information may be not feasible. Motivated by the notion of bisimulation in computer science, three types of bisimulation-based generalized fuzzy variable precision rough set (BGFVPRS) models are constructed. Different from many existed rough set models which are based on binary relations, the BGFVPRS models can distinguish objects by excavating the “multi-step” information of underlying relations. The related properties and relationships of BGFVPRS models are investigated. The uncertainty measure of BGFVPRS models and the reduction of fuzzy bisimulations are also discussed. Furthermore, learning from the PROMETHEE II method and combining it with our presented BGFVPRS models, a novel multiple-attribute decision-making method is provided. This method can effectively deal with complex problems including attribute data and relational data. The flexibility and effectiveness of our decision-making method are illustrated by comparative analysis and sensitivity analysis in the Zachary karate club network.

An Accelerating Reduction Approach for Incomplete Decision Table Using Positive Approximation Set.

Due to the explosive growth of data collected by various sensors, it has become a difficult problem determining how to conduct feature selection more efficiently. To address this problem, we offer a fresh insight into rough set theory from the perspective of a positive approximation set. It is found that a granularity domain can be used to characterize the target knowledge, because of its form of a covering with respect to a tolerance relation. On the basis of this fact, a novel heuristic approach ARIPA is proposed to accelerate representative reduction algorithms for incomplete decision table. As a result, ARIPA in classical rough set model and ARIPA-IVPR in variable precision rough set model are realized respectively. Moreover, ARIPA is adopted to improve the computational efficiency of two existing state-of-the-art reduction algorithms. To demonstrate the effectiveness of the improved algorithms, a variety of experiments utilizing four UCI incomplete data sets are conducted. The performances of improved algorithms are compared with those of original ones as well. Numerical experiments justify that our accelerating approach enhances the existing algorithms to accomplish the reduction task more quickly. In some cases, they fulfill attribute reduction even more stably than the original algorithms do.

Grey variable dual precision rough set model and its application

PurposeThe purpose of this paper is to advance a novel grey variable dual precision rough set model for grey concept.Design/methodology/approachTo obtain the approximation of a grey object, the authors first define the concepts of grey rough membership degree and grey degree of approximation on the basic thinking logic of variable precision rough set. Based on grey rough membership degree and grey degree of approximation, the authors proposed a grey variable dual precision rough set model. It uses a clear knowledge concept to approximate a grey concept, and the output result is also a clear concept.FindingsThe result demonstrates that the proposed model may be closer to the actual decision-making situation, can effectively improve the rationality and scientificity of the approximation and reduce the risk of decision-making. It can effectively achieve the whitenization of grey objects. The model can be degenerated to traditional variable precision rough fuzzy set model, variable precision rough set model and classic Pawlak rough set, when some specific conditions are met.Practical implicationsThe method exposed in the paper can be used to solve multi-criteria decision problems with grey decision objects and provide a decision rule. It can also help us better realize knowledge discovery and attribute reduction. It can effectively achieve the whitenization of grey object.Originality/valueThis method proposed in this paper implements a rough approximation of grey decision object and obtains low-risk probabilistic decision rule. It can effectively achieve a certain degree of whitenization of some grey objects.

Attribute reduction based on misclassification cost in variable precision rough set model

Attribute reduction based on misclassification cost in variable precision rough set model

Research on Fuzzy Order Variable Precision Rough Set Over Two Universes and Its Uncertainty Measures

Aiming at the problem that the U × V-type double-domain rough set can’t deal with fuzzy data in the past, this paper firstly established the variable precision rough set model on the basis of U × V-type double-domain rough set,and made an in-depth study on the upper approximation set and the lower approximation set of this model.Then the variable precision rough set model of U × V-type double-domain fuzzy order information system is established by introducing the U × V-type double-domain fuzzy dominance relation, and its related properties are discussed.The uncertainty measures are studied by defining the U × V-type double-domain fuzzy order precision rough set roughness and rough entropy. The conclusions are that as the precision threshold increases, its roughness and roughness entropy decrease gradually. These conclusions are verified by an example, which provides a theoretical basis for further revealing the uncertainty measure law of U × V-type double-domain fuzzy order variable precision rough set.

Non-Deterministic Outlier Detection Method Based on the Variable Precision Rough Set Model

Non-Deterministic Outlier Detection Method Based on the Variable Precision Rough Set Model

A Variable Precision Rough Set Model for Knowledge-assisted Management in Distance Education

To enable the teaching administrator to better obtain effective knowledge from a large amount of information to assist management and improve the efficiency and level of teaching management, a variable precision rough set model for knowledge assisted management of distance education was proposed. First, based on the theory of complete reduction and knowledge extraction, the proposed pedigree ambiguity tree was used as a strategy for obtaining complete reduction. An algorithm for obtaining a complete set of reductions was given. Then, by studying the process of knowledge extraction, a multi-knowledge extraction framework was put forward. The process of data conversion was completely realized. Finally, experimental verification was performed. The results showed that the proposed model overcame the effect of noise data in real data and improved the efficiency of the algorithm. Therefore, the model has high universality.

Application of the Variable Precision Rough Sets Model to Estimate the Outlier Probability of Each Element

In a data mining process, outlier detection aims to use the high marginality of these elements to identify them by measuring their degree of deviation from representative patterns, thereby yielding relevant knowledge. Whereas rough sets (RS) theory has been applied to the field of knowledge discovery in databases (KDD) since its formulation in the 1980s; in recent years, outlier detection has been increasingly regarded as a KDD process with its own usefulness. The application of RS theory as a basis to characterise and detect outliers is a novel approach with great theoretical relevance and practical applicability. However, algorithms whose spatial and temporal complexity allows their application to realistic scenarios involving vast amounts of data and requiring very fast responses are difficult to develop. This study presents a theoretical framework based on a generalisation of RS theory, termed the variable precision rough sets model (VPRS), which allows the establishment of a stochastic approach to solving the problem of assessing whether a given element is an outlier within a specific universe of data. An algorithm derived from quasi-linearisation is developed based on this theoretical framework, thus enabling its application to large volumes of data. The experiments conducted demonstrate the feasibility of the proposed algorithm, whose usefulness is contextualised by comparison to different algorithms analysed in the literature.

VPRS-Based Regional Decision Fusion of CNN and MRF Classifications for Very Fine Resolution Remotely Sensed Images

Recent advances in computer vision and pattern recognition have demonstrated the superiority of deep neural networks using spatial feature representation, such as convolutional neural networks (CNNs), for image classification. However, any classifier, regardless of its model structure (deep or shallow), involves prediction uncertainty when classifying spatially and spectrally complicated very fine spatial resolution (VFSR) imagery. We propose here to characterize the uncertainty distribution of CNN classification and integrate it into a regional decision fusion to increase classification accuracy. Specifically, a variable precision rough set (VPRS) model is proposed to quantify the uncertainty within CNN classifications of VFSR imagery and partition this uncertainty into positive regions (correct classifications) and nonpositive regions (uncertain or incorrect classifications). Those “more correct” areas were trusted by the CNN, whereas the uncertain areas were rectified by a multilayer perceptron (MLP)-based Markov random field (MLP-MRF) classifier to provide crisp and accurate boundary delineation. The proposed MRF-CNN fusion decision strategy exploited the complementary characteristics of the two classifiers based on VPRS uncertainty description and classification integration. The effectiveness of the MRF-CNN method was tested in both urban and rural areas of southern England as well as semantic labeling data sets. The MRF-CNN consistently outperformed the benchmark MLP, support vector machine, MLP-MRF, CNN, and the baseline methods. This paper provides a regional decision fusion framework within which to gain the advantages of model-based CNN, while overcoming the problem of losing effective resolution and uncertain prediction at object boundaries, which is especially pertinent for complex VFSR image classification.

Variable precision rough set model for attribute selection on environment impact dataset

The investigation of environment impact have important role to development of a city. The application of the artificial intelligence in form of computational models can be used to analyze the data. One of them is rough set theory. The utilization of data clustering method, which is a part of rough set theory, could provide a meaningful contribution on the decision making process. The application of this method could come in term of selecting the attribute of environment impact. This paper examine the application of variable precision rough set model for selecting attribute of environment impact. This mean of minimum error classification based approach is applied to a survey dataset by utilizing variable precision of attributes. This paper demonstrates the utilization of variable precision rough set model to select the most important impact of regional development. Based on the experiment, The availability of public open space, social organization and culture, migration and rate of employment are selected as a dominant attributes. It can be contributed on the policy design process, in term of formulating a proper intervention for enhancing the quality of social environment.

Measuring Uncertainty of Probabilistic Rough Set Model From Its Three Regions

The probabilistic rough set model is a generalized rough set model, which was proposed to improve the fault tolerance ability of the classical Pawlak’s rough set model. Compared with the classical Pawlak’s rough set model, the probabilistic rough set model and its several special forms (such as variable precision rough set model, Bayesian rough set model, and decision-theoretic rough set model) divide a domain into three regions by two parameters ( ${\alpha , \beta }$ ), and the objects belong to every region with a certain uncertainty. With the increase of information (attributes), the boundary region of the probabilistic rough set model may become smaller, bigger, or remain unchanged. This paper aims first to study some more complex uncertainty of the probabilistic rough set model. Then the uncertainty of the three regions is defined and analyzed. Besides, the changing regularities of uncertainty of a target concept in the probabilistic rough set model are discovered. Finally, three kinds of incremental information are defined, and their judging theorems are proposed. These results could enrich and improve rough set theory to deal with uncertain information systems.

Dynamic variable precision rough set approach for probabilistic set-valued information systems

Set-valued information systems are important type of data tables in many real applications, where the attribute values are described by sets to characterize uncertain and incomplete information. However, in some real situations, set-values may be depicted by probability distributions, which results in that the traditional tolerance relation based on intersection operation could not reasonably describe the indiscernibility relation of objects. To address this issue, we introduce the concept of probabilistic set-valued information systems (PSvIS), and present the extended variable precision rough set model (VPRS) based on the λ-tolerance relation in terms of Bhattacharyya distance. Considering the features of information systems will evolve over time in a dynamic data environment, it will lead to the change of information granulation and approximation structures. A matrix representation of rough approximation is presented based on two matrix operators and two vector functions in PSvIS. Then incremental mechanisms by the utilization of previously learned approximation results and region relation matrices for updating rough approximations are proposed, and the corresponding algorithms are developed and analyzed. Experimental results show that the proposed algorithms outperform the static algorithms and related incremental algorithms while inserting into or removing from attributes in PSvIS.

Inclusion degree with variable-precision model in analyzing inconsistent decision tables

In this paper, we incorporate the concepts of evidence theory and variable precision rough set model (VP-model) to examine inconsistent decision tables. For the decision classes in a given decision table, we point out the relationship between approximation degree of dependency and the belief functions. We also introduce the notion of weakly discernable decision tables, and show how to obtain the discernibility threshold of a given weakly discernable decision table. We prove that weakly discernibility is a necessary condition of relative consistency in a given decision table.

A variable precision rough set model based on the granularity of tolerance relation

As one of core problems in rough set theory, normally, classification analysis requires that “all” rather than “most”elements in one class are similar to each other. Nevertheless, the situation is just opposite to that in many actual applications. This means users actually just require “most” rather than “all”elements in a class are similar to each other. In the case, to further enhance the robustness and generalization ability of rough set based on tolerance relation, this paper, with concept lattice as theoretical foundation, presents a variable precision rough set model based on the granularity of tolerance relation, in which users can flexibly adjust parameters so as to meet the actual needs. The so-called relation granularity means that the tolerance relation can be decomposed into several strongly connected sub-relations and several weakly connected sub-relations. In essence, classes defined by people usually correspond to strongly connected sub-relations, but classes defined in the paper always correspond to weakly connected sub-relations. In the paper, an algebraic structure can be inferred from an information system, which can organize all hidden covers or partitions in the form of lattice structure. In addition, solutions to the problems are studied, such as reduction, core and dependency. In short, the paper offers a new idea for the expansion of classical rough set models from the perspective of concept lattice.

Grey dominance variable precision rough set model based on grey dominance relationship

Purpose – The purpose of this paper is to construct a novel grey dominance variable precision rough model. Design/methodology/approach – To deal with the problems that the attribute values of the decision-making object are often not exact numbers but interval grey numbers, and the decision-making attributes satisfy a certain preference relationship in the decision-making information because of the complexity and uncertainty of the real world, the authors take advantage of the theoretical thinking of the grey systems, dominance rough set theory and variable precision rough set theory, and construct a novel dominance variable precision rough set model. On the basis of the thinking logic of grey systems, the authors first define the concepts of balance degree, dominance degree and inferior degree, and then the grey dominance relationship based on the comparison of interval grey numbers. Then the authors use the grey dominance relationship to substitute for the indiscernibility relationship of the variable precision rough set so that the grey dominance variable precision rough model is naturally utilized to reduce the system's attributes in order to derive the needed decision rules. At the end, the authors use a decision-making example of the radar target selection to demonstrate the feasibility and effectiveness of the novel model. Findings – The results show that the proposed model possesses certain fault tolerance ability and can well-realize decision rule extraction and knowledge discovery out of a given incomplete information system. Practical implications – The method exposed in the paper can be used to deal with the decision-making problems with the grey information, preference information and noise data. Originality/value – The paper succeeds in realizing both the grey decision-making information with preference information and noise data and the extraction of decision-making rules.

Automatic determination about precision parameter value based on inclusion degree with variable precision rough set model

The rough set theory provides a powerful approach for attributes reduction and data analysis. The variable precision rough set (VPRS) model, an extension of the original rough set approach, tolerates misclassifications of the training data to some degree, which promotes the applications of rough set theory in inconsistent information systems. However, in most existing algorithms of feature reduction based on VPRS, the precision parameter (β) is introduced as prior knowledge, which restricts their applications because it is not clear how to set the β value. By studying β-consistency in the measurement of a decision table and the threshold value of the β-consistent decision table, this paper presents an algorithm for automatic determination of the precision parameter value from a decision table based on VPRS. At the same time, the precision parameter value from our proposed method is compared with the thresholds from the decision-theoretic rough set (DTRS). The influences of the precision parameter are also discussed on attribute reduction, which shows the necessity of the estimated precision parameter from a decision table. The simulation results including VPRS and other classification methods in real data further indicate that different precision parameter values make a great difference on rules and setting a precise parameter near the threshold value of the β-consistent decision table can precisely reflect the decision distribution of the decision table.

Limited and Variable Precision Rough Set Model

In incomplete information system, if the two objects have the same few known attributes and more unknown attributes, both the variable precision rough set model without symmetry and the limited, variable precision rough set model with symmetry can not distinguish them. In order to solve this problem, this paper proposes an improved limited and variable precision rough set model. It uses a more stringent condition to separate the two small probability equivalent objects into the different classes. The study of practical cases shows the model can get accurate and reasonable results.

Novel algorithms of attribute reduction with variable precision rough set model

The variable precision rough set model resists noise in data by introducing a parameter to relax the strict inclusion in approximations of the classical rough set model, and attribute reduction with the variable precision rough set model aims at deleting dispensable condition attributes from a decision system by considering this relaxation. In the variable precision rough set model, the approach of the discernibility matrix is the theoretical foundation of attribute reduction. However, this approach has always heavy computing load, so its effective improvement is clearly of importance in order to find reducts faster. In this paper, we observe that only minimal elements in the discernibility matrix are sufficient to find reducts, and each minimal element is at least determined by one equivalence class pair relative to condition attributes. With this motivation, the relative discernibility relation of a condition attribute is defined to characterize minimal elements in the discernibility matrix, and the algorithm of finding all minimal elements is developed by this characterization. Based on the algorithm of finding all minimal elements, we develop two algorithms to find all reducts and one reduct in variable precision rough sets. Several experiments are performed to demonstrate that our methods proposed in this paper are effective to reduce the computing load.

A set covering based approach to find the reduct of variable precision rough set

Attribute reduction is one of the core problems in Rough Set (RS) theory. In the Variable Precision Rough Set (VPRS) model, attribute reduction faces two difficulties: firstly, in the VPRS model, a reduct anomaly problem may arise and it may cause an inconsistency of positive regions and decision rules after attribute reduction. Secondly, the attribution reduction problem has been proved an NP-hard problem; accordingly, we would need to find a tradeoff between calculating the minimal reduct and reducing computing complexity to avoid the combinatorial explosion problem. We propose a new approach to calculate the reduct in VPRS model. This new method focuses on calculating a β-distribution reduct while avoiding the anomaly problem in the VPRS model. The basic idea of the proposed approach is to convert the reduct problem into a Set Covering Problem (SCP) according to the positive regions in the VPRS model; and consequently, a Set-Covering Heuristic Function (SCHF) algorithm is applied to calculate the reduct after this conversion. This approach keeps the positive regions consistent after the attribute reduction and moreover, based on the SCP, the performance ratio of the proposed method to calculate the minimal reduct ranges between ln(U′)-lnln(U′)+o(1) and (1-o(1))ln(U′) with a computational complexity having an upper bound as o(MN(M+N)2). Finally, we demonstrate the practical application of the VPRS model using real case scenario from China’s electricity power yield to verify the validity of our proposed approach. We then apply statistical evaluation to explain the economic significance of the attributes.