Classical Rough Set Research Articles

A decision support system for diagnosis of hepatitis disease using an integrated rough set and fish swarm algorithm

AbstractHealthcare data analysis is a primary concern. It leads to multiple levels of knowledge extraction for decision support systems because of the presence of uncertainties. Therefore, this paper integrates the rough set and artificial fish swarm optimization to develop a decision support system that handles uncertainties present in an information system. In the initial stage, the artificial fish swarm—the rough set procedure is implemented in finding vital features. Further, in the second phase, the rough set uses these vital features to develop a decision support system. The above model is analyzed over hepatitis B disease. The proposed model attains an accuracy of 92.4%. Further, the proposed model is compared with the classical rough set, decision tree, and artificial fish swarm‐decision tree model. The accuracy obtained is 88.9%, 83.3%, and 90.8%, respectively. The proposed model has a greater accuracy of 3.5% than the rough set model and has a greater accuracy of 9.1% than the decision tree model. Simultaneously, the proposed model has 1.6% greater accuracy than the artificial fish swarm‐decision tree model. Therefore, it is believed that the projected decision support system may be used to prevent and detect hepatitis B diseases.

General assembly framework for online streaming feature selection via Rough Set models

We may not know the entire feature space in advance for real-world applications, and features can exist in a stream mode, called streaming features. Online streaming feature selection aims to select optimal streaming features on the fly and can be summarized into three main components: irrelevant feature discarding, relevant feature selecting, and redundant feature removing. Therefore, the core issue of the streaming feature selection framework is the calculation of the relationship between features. This paper applies Rough Set models to discover the feature relationships for the most crucial advantages: they do not require any domain knowledge and can measure the selected features as integral. After the formal definitions of feature relevance, irrelevance, and redundancy from the Rough Set perspective, we analyze and abstract the feature relationship calculation from three levels: Rough Set model, positive region, and consistency calculation. Then we design a novel general assembly Rough Set based Streaming Feature Selection Framework, named RS-SFSF, which could assemble new algorithms for different problems step by step. Researchers in different areas can quickly build the algorithms they need based on our new framework. To demonstrate the effectiveness of RS-SFSF, we derived four new algorithms based on RS-SFSF by using the classical Rough Set model, neighborhood Rough Set model, and fuzzy Rough Set model, respectively. Extensive experiments conducted on twelve real-world datasets indicate the efficiency of our new framework.

Local knowledge distance for rough approximation measure in multi-granularity spaces

As the significant expansion of classical rough sets, local rough sets(LRS) is an effective model for processing large-scale datasets with finite labels. However, the process of establishing a category of monotonic uncertainty measure with strong distinguishing ability for LRS remains ambiguous. To construct this model, both the monotonicity of local lower approximation set and the local structure of granularity should be considered. First, the monotonicity of local rough approximation measure(LRAM) is established by the local lower and upper approximation sets. Subsequently, the local knowledge distance(LKD) is proposed to measure the uncertainty derived from the disparities between local upper and lower approximation sets. The more rational uncertainty measure associated LRAM with LKD is designed as a feature selection algorithm. Eventually, the experiments reflect the feasibility of the developed uncertainty measure.

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.

The cost-sensitive approximation of neighborhood rough sets and granular layer selection

Neighborhood rough sets (NRS) are the extended model of the classical rough sets. The NRS describe the target concept by upper and lower neighborhood approximation boundaries. However, the method of approximately describing the uncertain target concept with existed neighborhood information granules is not given. To solve this problem, the cost-sensitive approximation model of the NRS is proposed in this paper, and its related properties are analyzed. To obtain the optimal approximation granular layer, the cost-sensitive progressive mechanism is proposed by considering user requirements. The case study shows that the reasonable granular layer and its approximation can be obtained under certain constraints, which is suitable for cost-sensitive application scenarios. The experimental results show that the advantage of the proposed approximation model, moreover, the decision cost of the NRS approximation model will monotonically decrease with granularity being finer.

Automatic Classification of Basic Nursing Teaching Resources Based on the Fusion of Multiple Neural Networks

Automatic classification is one of the hot topics in the field of information retrieval and natural language processing, but it still faces many problems to be solved. The classic automated classification approach has a sluggish classification speed and poor processing accuracy for resources with a large quantity of data. Based on this, an automated classification approach based on the integration of various neural networks for fundamental nursing teaching materials was presented. The automatic classification method of teaching resources was designed by extracting the characteristics of teaching resources, establishing the model of multiple neural network integration, and designing the classification index of basic nursing teaching resources. The experimental findings suggest that this technique has higher chi-square test parameters and better outcomes for the automated classification of large instructional materials than the classic rough set automatic classification method.

Rough Set Based Classification and Feature Selection Using Improved Harmony Search for Peptide Analysis and Prediction of Anti-HIV-1 Activities

AIDS, which is caused by the most widespread HIV-1 virus, attacks the immune system of the human body, and despite the incredible endeavors for finding proficient medication strategies, the continuing spread of AIDS and claiming subsequent infections has not yet been decreased. Consequently, the discovery of innovative medicinal methodologies is highly in demand. Some available therapies, based on peptides, proclaim the treatment for several deadly diseases such as AIDS and cancer. Since many experimental types of research are restricted by the analysis period and expenses, computational methods overcome the issues effectually. In computational technique, the peptide residues with anti-HIV-1 activity are predicted by classification method, and the learning process of the classification is improved with significant features. Rough set-based algorithms are capable of dealing with the gaps and imperfections present in real-time data. In this work, feature selection using Rough Set Improved Harmony Search Quick Reduct and Rough Set Improved Harmony Search Relative Reduct with Rough Set Classification framework is implemented to classify Anti-HIV-1 peptides. The primary objective of the proposed methodology is to predict the peptides with an anti-HIV-1 activity using effective feature selection and classification algorithms incorporated in the proposed framework. The results of the proposed algorithms are comparatively studied with existing rough set feature selection algorithms and benchmark classifiers, and the reliability of the algorithms implemented in the proposed framework is measured by validity measures, such as Precision, Recall, F-measure, Kulczynski Index, and Fowlkes–Mallows Index. The final results show that the proposed framework analyzed and classified the peptides with a high predictive accuracy of 96%. In this study, we have investigated the ability of a rough set-based framework with sequence-based numeric features to classify anti-HIV-1 peptides, and the experimentation results show that the proposed framework discloses the most satisfactory solutions, where it rapidly congregates in the problem space and finds the best reduct, which improves the prediction accuracy of the given dataset.

Neighborhood Rough Neural Network Approach for COVID-19 Image Classification.

The rapid spread of the new Coronavirus, COVID-19, causes serious symptoms in humans and can lead to fatality. A COVID-19 infected person can experience a dry cough, muscle pain, headache, fever, sore throat, and mild to moderate respiratory illness, according to a clinical report. A chest X-ray (also known as radiography) or a chest CT scan are more effective imaging techniques for diagnosing lung cancer. Computed Tomography (CT) scan images allow for fast and precise COVID-19 screening. In this paper, a novel hybridized approach based on the Neighborhood Rough Set Classification method (NRSC) and Backpropagation Neural Network (BPN) is proposed to classify COVID and NON-COVID images. The proposed novel classification algorithm is compared with other existing benchmark approaches such as Neighborhood Rough Set, Backpropagation Neural Network, Decision Tree, Random Forest Classifier, Naive Bayes Classifier, K- Nearest Neighbor, and Support Vector Machine. Various classification accuracy measures are used to assess the efficacy of the classification algorithms.

Uncertainty Measure for Multisource Intuitionistic Fuzzy Information System

Multisource information systems and multigranulation intuitionistic fuzzy rough sets are important extended types of Pawlak’s classical rough set model. Multigranulation intuitionistic fuzzy rough sets have been investigated in depth in recent years. However, few studies have considered this combination of multisource information systems and intuitionistic fuzzy rough sets. In this paper, we give the uncertainty measure for multisource intuitionistic fuzzy information system. Against the background of multisource intuitionistic fuzzy information system, each information source is regarded as a granularity level. Considering the different importance of information sources, we assign different weights to them. Firstly, the paper proposes an optimal source selection method. Secondly, we study the weighted generalized, weighted optimistic, and weighted pessimistic multigranularity intuitionistic fuzzy rough set models and uncertainty measurement methods in the multisource intuitionistic fuzzy information system, and we further study the relationship between the three models and related properties. Finally, an example is given to verify the validity of the models and methods.

A study of fixed point sets based on Z-soft rough covering models

<abstract><p>Z-soft rough covering models are important generalizations of classical rough set theory to deal with uncertain, inexact and more complex real world problems. So far, the existing study describes various forms of approximation operators and their properties by means of soft neighborhoods. In this paper, we propose the notion of $ Z $-soft rough covering fixed point set (briefly, $\mathcal{Z}$-$\mathcal{SRCFP}$-set) induced by covering soft set. We study the conditions that the family of $ \mathcal{Z} $-$ \mathcal{SRCFP} $-sets become lattice structure. For any covering soft set, the $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is a complete and distributive lattice, and at the same time, it is also a double p-algebra. Furthermore, when soft neighborhood forms a partition of the universe, then $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is both a boolean lattice and a double stone algebra. Some main theoretical results are obtained and investigated with the help of examples.</p></abstract>

Evaluation of importance for condition attributes based on quality of decision reducts

Relative or decision reducts belong with mechanisms dedicated to feature selection, and they are embedded in rough set approach to data processing. Algorithms for reduct construction typically aim at dimensionality reduction aspect, searching for smallest reducts, which are considered as the most advantageous from the point of view of knowledge representation. However, classifiers build on reduced data models, based on reducts, can significantly vary in performance. Therefore, to ensure quality of predictions, other characteristics of reducts, apart from their cardinalities, need to be taken into account. The paper presents research in which estimation of reduct quality through their characteristics was reflected in calculation of the proposed weighting factors leading to attribute rankings. These rankings were next employed in the process of filtering decision rules, inferred by classic rough set approach. Constructed rule-based classifiers were applied in the stylometric domain to solve a task of authorship attribution.

Spatial rough set-based geographical detectors for nominal target variables

Spatial rough set theory is an extension of classical rough set theory that is designed to handle spatial data. Different from its classical analog, spatial rough set theory approximates nominal target variables in each local region, thereby enabling the local explanatory power of various factors on these nominal target variables to be determined. Based on spatial rough set theory, this paper describes two new uncertainty indices for measuring the spatial heterogeneity of the local explanatory power on nominal target variables. Moreover, three new spatial rough set-based geographical detectors are proposed. With the help of the uncertainty indices, these detectors measure the spatial explanatory power of different factors, compare their importance, and detect feature interactions. Experiments are conducted using two publicly accessible datasets to demonstrate the effectiveness of the proposed geographical detectors and evaluate their performance against that of geographical detectors based on q-statistics. The results show that the proposed detectors are effective in processing nominal variables and can be used to complement existing q-statistics-based geographical detectors.

Characteristic numbers and approximation operators in generalized rough approximation system

Covering rough set theory and binary relation based rough set theory are regarded as two important different generalizations of Z. Pawlak's classical rough set theory. In fact, when serial relations are considered, they are the same thing. If R is a serial relation from a universe U to another universe V, then {{R−1(y)}:y∈V} is a covering of U and {{R(x)}:x∈U} is a covering of V. In a covering approximation space (U,C), the relation R defined as R(x)={C∈C:x∈C} is just a serial relation from U to V=C. So U and V have the same status and (U,V,R) is indeed a whole, then (U,V,R) is called an Approximation System in order to take a comprehensive study from a new and higher perspective. By introducing nthl neighborhoods and kthr neighborhoods recursively, a new set of upper and lower approximation operators is established, and the Approximation System is further referred to as the Generalized Rough Approximation System (GRAS). In order to describe some stability of the Approximate System, characteristic numbers such as l-cycle number, r-cycle number, link number and connect number are also introduced. From there, partitions of GRAS can be constructed and sub-GRAS can be defined. This makes the whole of GRAS modularized, which is a big simplification when it comes to solving real problems. In addition, some applications of characteristic numbers and approximation operators are illustrated by examples, and the Boolean matrix calculation formulas of all approximations are proved. Finally, the important special GRAS (U,U,R) is studied in detail and an application example is given.

Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

Double-local rough sets for efficient data mining

As an important extension of classical rough sets, local rough set model is effective to handle large data sets with small amounts of labeled data, which has an obvious advantage in improving computational performance. However, the existing mining algorithms based on local rough sets are still computationally time-consuming in processing large-scale labeled data sets. To overcome this limitation, we propose an enhanced local rough set framework called double-local rough sets, by introducing the notion of local equivalence classes. Under this framework, we define the lower deletion matrix, the upper addition matrix, and the upper deletion matrix. Based on these matrices, we develop a fast iteration method for computing the approximations, which is vital for attribute reduction and knowledge discovery. Furthermore, a fast attribute reduction method is presented by accelerating the calculation of stop criteria and attribute significance measures, which can obtain the same attribute reduct as its original local rough set version. Theoretical analysis and experimental results indicate that the proposed algorithms in double-local rough sets significantly outperform their original counterparts in classical local rough sets.

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.

Gait and Full Body Movement Dataset of Autistic Children Classified by Rough Set Classifier

Gait and body movement are a window to human brain which make these activities unique for each person. These activities are used to diagnose some disorders related to parts of brain which causes have not been known such as Autism Disorders (AD). The traditional diagnostic methods of AD are time-consuming and highly dependent on clinician’s judgment which is based on behaviour assessment. This approach leads to subjective interpretations that differ from doctor to another and affect by strengths and weaknesses of patient. Therefore this paper aims to diagnosis of AD based on gait and body movement analysis. At first, Kinect v2 uses to create a 3D dataset, which includes three dimensional joints positions, joints trajectories video, skeleton movement video captured by Kinect v2, and color videos captured by Samsung Note 9 camera. This paper also aims to classify children with autism from normal children by proposed system based on four stages: Augmentation of the database by using seven transformations to deal with small number of autism cases; Extracting features that we think play an important role in classification; Reducing data dimensions using Principal Component Analysis; using Rough Set to classify dataset. Results show that classification is 92% after augmentation.

On local multigranulation covering decision-theoretic rough sets

Multi-granulation decision-theoretic rough sets uses the granular structures induced by multiple binary relations to approximate the target concept, which can get a more accurate description of the approximate space. However, Multi-granulation decision-theoretic rough sets is very time-consuming to calculate the approximate value of the target set. Local rough sets not only inherits the advantages of classical rough set in dealing with imprecise, fuzzy and uncertain data, but also breaks through the limitation that classical rough set needs a lot of labeled data. In this paper, in order to make full use of the advantage of computational efficiency of local rough sets and the ability of more accurate approximation space description of multi-granulation decision-theoretic rough sets, we propose to combine the local rough sets and the multigranulation decision-theoretic rough sets in the covering approximation space to obtain the local multigranulation covering decision-theoretic rough sets model. This provides an effective tool for discovering knowledge and making decisions in relation to large data sets. We first propose four types of local multigranulation covering decision-theoretic rough sets models in covering approximation space, where a target concept is approximated by employing the maximal or minimal descriptors of objects. Moreover, some important properties and decision rules are studied. Meanwhile, we explore the reduction among the four types of models. Furthermore, we discuss the relationships of the proposed models and other representative models. Finally, illustrative case of medical diagnosis is given to explain and evaluate the advantage of local multigranulation covering decision-theoretic rough sets model.

Condition attributes, properties of decision rules, and discretisation: Analysis of relations and dependencies

When mining of input data is focused on rule induction, knowledge, discovered in exploration of existing patterns, is stored in combinations of certain conditions on attributes included in rule premises, leading to specific decisions. Through their properties, such as lengths, supports, cardinalities of rule sets, inferred rules characterise relations detected among variables. The paper presents research dedicated to analysis of these dependencies, considered in the context of various discretisation methods applied to the input data from stylometric domain. For induction of decision rules from data, Classical Rough Set Approach was employed. Next, based on rule properties, several factors were proposed and evaluated, reflecting characteristics of available condition attributes. They allowed to observe how variables and rule sets changed depending on applied discretisation algorithms.