Traditional Rough Set Theory Research Articles

An Application on an Information System via Nano Ordered Topology

Rough set theory is commonly used to handle uncertainty in various applications. In order to broaden its application scope, the classical rough set model based on equivalence relations, it has been extended to include an additional partial order relation. This partial order relation represents an m-nano flou set, as defined in Section 5, between rough sets and is particularly useful in determining the levels of impact that key factors have on heart failure. The primary objective of the current research is to introduce a novel approximation method based on equivalence relations and partial order relations (ordered approximation spaces), which extends Pawlak's method and investigates related results. The paper establishes the equivalence between our approach and Pawlak's approach under the condition that we have an equivalence relation and a partial order relation that satisfies the criteria required for it to be considered an equality relation. The second objective is to extend the concept of nano topology to include nano ordered topology, which involves nano increasing or decreasing topological spaces. The research indicates that incorporating nano increasing or decreasing topological spaces results in enhanced data analysis accuracy when compared to solely utilizing nano topological spaces. This observation aligns with the discussions in the referenced work by Jayalakshmi. The findings of this research have the potential to significantly impact medical research related to heart failure. Improved methods for handling uncertainty and quantifying the influence of various factors can lead to more accurate and reliable predictions and diagnoses. Ultimately, this work aims to contribute to advancements in heart failure treatment and prevention. By bridging the gap between traditional rough set theory and the nuanced intricacies of heart failure analysis, our research strives to advance our comprehension of this critical medical condition and, in turn, support progress in heart failure treatment and prevention.

Rough set based information theoretic approach for clustering uncertain categorical data

Many real applications such as businesses and health generate large categorical datasets with uncertainty. A fundamental task is to efficiently discover hidden and non-trivial patterns from such large uncertain categorical datasets. Since the exact value of an attribute is often unknown in uncertain categorical datasets, conventional clustering analysis algorithms do not provide a suitable means for dealing with categorical data, uncertainty, and stability. The ability of decision making in the presence of vagueness and uncertainty in data can be handled using Rough Set Theory. Though, recent categorical clustering techniques based on Rough Set Theory help but they suffer from low accuracy, high computational complexity, and generalizability especially on data sets where they sometimes fail or hardly select their best clustering attribute. The main objective of this research is to propose a new information theoretic based Rough Purity Approach (RPA). Another objective of this work is to handle the problems of traditional Rough Set Theory based categorical clustering techniques. Hence, the ultimate goal is to cluster uncertain categorical datasets efficiently in terms of the performance, generalizability and computational complexity. The RPA takes into consideration information-theoretic attribute purity of the categorical-valued information systems. Several extensive experiments are conducted to evaluate the efficiency of RPA using a real Supplier Base Management (SBM) and six benchmark UCI datasets. The proposed RPA is also compared with several recent categorical data clustering techniques. The experimental results show that RPA outperforms the baseline algorithms. The significant percentage improvement with respect to time (66.70%), iterations (83.13%), purity (10.53%), entropy (14%), and accuracy (12.15%) as well as Rough Accuracy of clusters show that RPA is suitable for practical usage. We conclude that as compared to other techniques, the attribute purity of categorical-valued information systems can better cluster the data. Hence, RPA technique can be recommended for large scale clustering in multiple domains and its performance can be enhanced for further research.

Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy

Abstract Traditional rough set theory is mainly used to reduce attributes and extract rules in databases in which attributes are characterised by partitions, which the covering rough set theory, a generalisation of traditional rough set theory, covers. In this article, we posit a method to reduce the attributes of covering decision systems, which are databases incarnated in the form of covers. First, we define different covering decision systems and their attributes’ reductions. Further, we describe the necessity and sufficiency for reductions. Thereafter, we construct a discernible matrix to design algorithms that compute all the reductions of covering decision systems. Finally, the above methods are illustrated using a practical example and the obtained results are contrasted with other results.

Research on Construction of Crude Set Model of Critical Fault Information for Bus Based on CAN-BUS Data

Under the high load, high frequency and high strength operating environment, the frequent occurrence of vehicle fault gradually attracts the attention of the society. The real-time monitoring and data recording function of vehicle-mounted equipment provides data support for vehicle status assessment and fault warning. In this paper, the real-time data collected by CAN-BUS system of Beijing Bus Group are preprocessed and discretized. On the basis of the traditional rough set theory, a new coding method is set up, and the dependency between conditional attributes and decision attributes is set as an adaptive function, which is reduced by genetic algorithm and cellular genetic algorithm respectively. The calculation results show that the key fault information of public transport vehicles is instrumental speed, oil pressure, percentage of torque, timing engine speed, and coolant temperature. By comparing the results of reduction, it is found that the cellular genetic algorithm has higher applicability than the genetic algorithm in terms of algorithm efficiency, stability, and convergence quality. Although the genetic algorithm attribute reduction is slightly better than the cellular genetic algorithm attribute reduction in the rule matching, the cellular genetic algorithm has a better ability to excavate information within the acceptable compatibility range. Finally, the selected key factors will be deployed on the Beijing Bus Group's big data platform and displayed in real time. The conclusion of this paper enriches the theory of bus engine fault warning and establishes an engine failure warning system, which can effectively reduce the failure rate of bus vehicles and reduce the maintenance cost expenditure. It has certain guiding significance for the bus operation work of Beijing Bus Group.

Decision-Making Method based on Mixed Integer Linear Programming and Rough Set: A Case Study of Diesel Engine Quality and Assembly Clearance Data

The purpose of this paper is to establish a decision-making system for assembly clearance parameters and machine quality level by analyzing the data of assembly clearance parameters of diesel engine. Accordingly, we present an extension of the rough set theory based on mixed-integer linear programming (MILP) for rough set-based classification (MILP-FRST). Traditional rough set theory has two shortcomings. First, it is sensitive to noise data, resulting in a low accuracy of decision systems based on rough sets. Second, in the classification problem based on rough sets, the attributes cannot be automatically determined. MILP-FRST has the advantages of MILP in resisting noisy data and has the ability to select attributes flexibly and automatically. In order to prove the validity and advantages of the proposed model, we used the machine quality data and assembly clearance data of 29 diesel engines of a certain type to validate the proposed model. Experiments show that the proposed decision-making method based on MILP-FRST model can accurately determine the quality level of the whole machine according to the assembly clearance parameters.

About a Fuzzy Distance between Two Fuzzy Partitions and Application in Attribute Reduction Problem

Abstract According to traditional rough set theory approach, attribute reduction methods are performed on the decision tables with the discretized value domain, which are decision tables obtained by discretized data methods. In recent years, researches have proposed methods based on fuzzy rough set approach to solve the problem of attribute reduction in decision tables with numerical value domain. In this paper, we proposeafuzzy distance between two partitions and an attribute reduction method in numerical decision tables based on proposed fuzzy distance. Experiments on data sets show that the classification accuracy of proposed method is more efficient than the ones based fuzzy entropy.

An Incomplete Data Filling Approach Based on a New Valued Tolerance Relation

In real life there are many incomplete information system, However, the traditional rough set theory is not sui- table for incomplete information system. A lot of extension of the rough sets theory have been proposed based on this. In these theories, the handling of null value or missing values is the key problem. In this paper a new valued tolerance and a concept of Tolerance Degree Vector are put forward at first; moreover a new incomplete data filling approach which ba- sed on new valued tolerance and tolerance degree vector(for short NVT-TDV) is proposed. Subsequently, two series of experiments have been carried out, one was compared the classification accuracy with other extended rough set model, the other was the data filling accuracy test based on Waikato Environment for Knowledge Analysis platform . The experi- mental results show that it can be adopted as a pre-processing method in data mining.

Research on Granular Computing Approach in Rough Set

Granulation of information appears in many areas, such as machine learning, evidence theory, and data mining. Granular computing is the core research field in granulation of information. It is an effective tool for complex problem, massive data mining and fuzzy information processing. In the basis of principle of granularity, we aim to study the granular decomposing method in granules space based on rough set. Moreover, the criteria conditions for attribution necessity and attribute reduction are proposed. Finally, the corresponding equivalence is proved to traditional rough set theory. It will lay the foundation for attribute reduction under the granular representation in rough set.

Uncertainty Measurement for Covering Rough Sets

Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

Spectral Clustering with Neighborhood Attribute Reduction Based on Information Entropy

Traditional rough set theory is only suitable for dealing with discrete variables and need data preprocessing. Neighborhood rough sets overcome these shortcomings with the ability to directly process numeric data. This paper modifies the attribute reduction method based on neighborhood rough sets, in which the attribute importance is combined with information entropy to select the appropriate attributes. When multiple attributes have the same importance degree, compare the information entropy of these attributes. Put the attribute having the minimal entropy into the reduction set, so that the reduced attribute set is better. Then we introduce this attribute reduction method to improve spectral clustering and propose NRSR-SC algorithm. It can highlight the differences between samples while maintaining the characteristics of data points to make the final clustering results closer to the real data classes. Experiments show that, NRSR-SC algorithm is superior to traditional spectral clustering algorithm and FCM algorithm. Its clustering accuracy is higher, and has strong robustness to the noise in high-dimensional data.

General type-2 fuzzy rough sets based on $$\alpha $$ α -plane Representation theory

Rough sets theory and fuzzy sets theory are mathematical tools to deal with uncertainty, imprecision in data analysis. Traditional rough set theory is restricted to crisp environments. Since theories of fuzzy sets and rough sets are distinct and complementary on dealing with uncertainty, the concept of fuzzy rough sets has been proposed. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle highly uncertainties. Some researchers proposed interval type-2 fuzzy rough sets by combining interval type-2 fuzzy sets and rough sets. However, there are no reports about combining general type-2 fuzzy sets and rough sets. In addition, the $$\alpha $$ ? -plane representation method of general type-2 fuzzy sets has been extensively studied, and can reduce the computational workload. Motivated by the aforementioned accomplishments, in this paper, from the viewpoint of constructive approach, we first present definitions of upper and lower approximation operators of general type-2 fuzzy sets by using $$\alpha $$ ? -plane representation theory and study some basic properties of them. Furthermore, the connections between special general type-2 fuzzy relations and general type-2 fuzzy rough upper and lower approximation operators are also examined. Finally, in axiomatic approach, various classes of general type-2 fuzzy rough approximation operators are characterized by different sets of axioms.

Discretization of Attributes Based on Relative Positive Region of Decision Attribute

Traditional rough set theory can hardly handle the real-life data which contains continuous attribute. In order to solve this problem, a new method for discretization of continuous attributes based on relative positive region of decision attribute is presented. The method which distinguishes from traditional discrete methods firstly gets the relative positive region of decision attribute, and then discrete continuous attributes with the theorem proved in this paper. Finally, the result of an example shows that our method is efficient and feasible.

Diverse reduct subspaces based co-training for partially labeled data

Rough set theory is an effective supervised learning model for labeled data. However, it is often the case that practical problems involve both labeled and unlabeled data, which is outside the realm of traditional rough set theory. In this paper, the problem of attribute reduction for partially labeled data is first studied. With a new definition of discernibility matrix, a Markov blanket based heuristic algorithm is put forward to compute the optimal reduct of partially labeled data. A novel rough co-training model is then proposed, which could capitalize on the unlabeled data to improve the performance of rough classifier learned only from few labeled data. The model employs two diverse reducts of partially labeled data to train its base classifiers on the labeled data, and then makes the base classifiers learn from each other on the unlabeled data iteratively. The classifiers constructed in different reduct subspaces could benefit from their diversity on the unlabeled data and significantly improve the performance of the rough co-training model. Finally, the rough co-training model is theoretically analyzed, and the upper bound on its performance improvement is given. The experimental results show that the proposed model outperforms other representative models in terms of accuracy and even compares favorably with rough classifier trained on all training data labeled.

Covering based approximation – a new type approach

The rough set theory, proposed by Pawlak is termed as basic (traditional) rough set theory and it has been extended in many directions. Covering based rough set is one of the extensions of the basic rough set theory. A covering is a generalisation of notion of partitioned rough set (Pawalk rough set) introduced by W. Zakowski. In this article it is introduced a new type of covering-based rough set in which both lower and upper approximation operators are improved.

An Interval Type-2 Fuzzy Rough Set Model for Attribute Reduction

Rough set theory is a very useful tool for describing and modeling vagueness in ill-defined environments. Traditional rough set theory is restricted to crisp environments. However, nowadays, it has been extended to fuzzy environments, resulting in the development of the so-called fuzzy rough sets. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets, but for the general type-2 fuzzy sets, the computational complexity is severe. On the other hand, set-theoretic and arithmetic computations for the interval type-2 fuzzy sets are very simple. Motivated by the aforementioned accomplishments, in this paper, the concept of fuzzy rough sets is generalized to interval type-2 fuzzy environments. Subsequently, a method of attribute reduction within the interval type-2 fuzzy rough set framework is proposed. Lastly, the properties of the interval type-2 fuzzy rough sets are presented.

Rough Sets and Near Sets in Medical Imaging: A Review

This paper presents a review of the current literature on rough-set- and near-set-based approaches to solving various problems in medical imaging such as medical image segmentation, object extraction, and image classification. Rough set frameworks hybridized with other computational intelligence technologies that include neural networks, particle swarm optimization, support vector machines, and fuzzy sets are also presented. In addition, a brief introduction to near sets and near images with an application to MRI images is given. Near sets offer a generalization of traditional rough set theory and a promising approach to solving the medical image correspondence problem as well as an approach to classifying perceptual objects by means of features in solving medical imaging problems. Other generalizations of rough sets such as neighborhood systems, shadowed sets, and tolerance spaces are also briefly considered in solving a variety of medical imaging problems. Challenges to be addressed and future directions of research are identified and an extensive bibliography is also included.

Approaches to knowledge reduction of covering decision systems based on information theory

In this paper, we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory. Firstly, we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems. Secondly, in inconsistent covering decision systems, the limitary conditional entropy of the covering is proposed and attribute reductions are defined. And finally, by the significance of the covering, some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems. We prove that their computational complexity are polynomial. Numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets. In addition, in traditional rough set theory, MIBARK-algorithm [G.Y. Wang, H. Hu, D. Yang, Decision table reduction based on conditional information entropy, Chinese J. Comput., 25 (2002) 1–8] cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems. Here, we solve this problem in inconsistent covering decision systems.

Approximations and reducts with covering generalized rough sets

The covering generalized rough sets are an improvement of traditional rough set model to deal with more complex practical problems which the traditional one cannot handle. It is well known that any generalization of traditional rough set theory should first have practical applied background and two important theoretical issues must be addressed. The first one is to present reasonable definitions of set approximations, and the second one is to develop reasonable algorithms for attributes reduct. The existing covering generalized rough sets, however, mainly pay attention to constructing approximation operators. The ideas of constructing lower approximations are similar but the ideas of constructing upper approximations are different and they all seem to be unreasonable. Furthermore, less effort has been put on the discussion of the applied background and the attributes reduct of covering generalized rough sets. In this paper we concentrate our discussion on the above two issues. We first discuss the applied background of covering generalized rough sets by proposing three kinds of datasets which the traditional rough sets cannot handle and improve the definition of upper approximation for covering generalized rough sets to make it more reasonable than the existing ones. Then we study the attributes reduct with covering generalized rough sets and present an algorithm by using discernibility matrix to compute all the attributes reducts with covering generalized rough sets. With these discussions we can set up a basic foundation of the covering generalized rough set theory and broaden its applications.

Learning fuzzy rules from fuzzy samples based on rough set technique

Although the traditional rough set theory has been a powerful mathematical tool for modeling incompleteness and vagueness, its performance in dealing with initial fuzzy data is usually poor. This paper makes an attempt to improve its performance by extending the traditional rough set approach to the fuzzy environment. The extension is twofold. One is knowledge representation and the other is knowledge reduction. First, we provide new definitions of fuzzy lower and upper approximations by considering the similarity between the two objects. Second, we extend a number of underlying concepts of knowledge reduction (such as the reduct and core) to the fuzzy environment and use these extensions to propose a heuristic algorithm to learn fuzzy rules from initial fuzzy data. Finally, we provide some numerical experiments to demonstrate the feasibility of the proposed algorithm. One of the main contributions of this paper is that the fundamental relationship between the reducts and core of rough sets is still pertinent after the proposed extension.

A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets

Traditional rough set theory is mainly used to extract rules from and reduce attributes in databases in which attributes are characterized by partitions, while the covering rough set theory, a generalization of traditional rough set theory, does the same yet characterizes attributes by covers. In this paper, we propose a way to reduce the attributes of covering decision systems, which are databases characterized by covers. First, we define consistent and inconsistent covering decision systems and their attribute reductions. Then, we state the sufficient and the necessary conditions for reduction. Finally, we use a discernibility matrix to design algorithms that compute all the reducts of consistent and inconsistent covering decision systems. Numerical tests on four public data sets show that the proposed attribute reductions of covering decision systems accomplish better classification performance than those of traditional rough sets.