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Nano topology is a modern type of topology based on rough sets, introducing nano open sets and their properties. This study explores the new properties of nano-β-open sets and nano-closures in nano topological space, providing some equivalent definitions, theorems, and lemmas for illustration. The effectiveness of incorporating nano β-open sets in medical decision-making is demonstrated in diagnosing breast cancer in two cases for women. Results indicated that utilizing nano open sets enhanced the accuracy, sensitivity, and specificity of cancer diagnosis. Additionally, an algorithm has been developed to aid clinicians in diagnosing breast cancer infections. The overarching objective is to provide physicians with a valuable tool to make informed decisions and reach optimal conclusions in patient care. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy information systems (TFISs-2), one interesting form of complex data, are extensions of fuzzy information systems. Uncertainty measurement and attribute reduction of TFISs-2 are key issues when describing and analyzing complex fuzzy data. However, existing researches mainly focus on the traditional fuzzy data, and seldom consider type-2 fuzzy data. This paper focuses on finding an effective indicator to measure the uncertainty of TFISs-2, and carries out the research of attribute reduction based on this indicator. Firstly, the weighted membership distance and the weighted membership similarity are defined, which are used to describe the relation between two objects in TIFSs-2, and σ similarity relations are introduced. Secondly, a fuzzy neighborhood structure is defined based on σ similarity relations. The classical rough set model is extended on TFISs-2, and the definitions of upper and lower approximation, accuracy and roughness are given. Then, a novel indicator called σ self-information is used to describe the uncertainty of TFISs-2, and a heuristic greedy selection attribute reduction algorithm is proposed. Finally, the experimental results show that the constructed uncertainty measurement indicator is suitable for TFISs-2, and the proposed attribute reduction method is effective. This study is beneficial to promote the understanding of complex fuzzy data, and contributes to the data analysis and processing of TFISs-2. [ABSTRACT FROM AUTHOR]

Rough Set (RS) is a relatively new technique for making imprecise and uncertain decisions. It is an emerging area of ambiguous mathematics associated with fuzzy set theory. In comparison with fuzzy sets and other theories, RS has more advantages. Unlike statistics, evidence theory, and fuzzy set theory, RS theory does not require any additional or preliminary information about data. RS theory deals with approximating arbitrary subsets of the universe using two subsets namely lower and upper approximation. The advantage of RS is that rough approximations can be expanded into fuzzy environments which aids in solving a wide variety of realtime problems. The goal of this study is to focus on Rough Fuzzy Prime Ideals (RFPI) in ring structure and explain specific aspects of its upper and lower approximations. Furthermore, Rough Fuzzy Ideal (RFI) and RFPI notions and characteristics are described. [ABSTRACT FROM AUTHOR]

In this paper rudiments of the theory will be outlined, and basic concepts of the theory will be illustrated by a simple tutorial example, concerning churn modeling in telecommunications. Real life applications require more advanced extensions of the theory but we will not discuss these extensions here. Rough set theory has an overlap with many other theories dealing with imperfect knowledge, e.g., evidence theory, fuzzy sets, Bayesian inference and others. Nevertheless, the theory can be regarded as an independent, complementary, not competing, discipline in its own rights. [ABSTRACT FROM AUTHOR]

The "greenization" of papermaking enterprise behavior is an important approach to transition towards to environmental protection and green development mode. Aiming at the problem that it is difficult to quantitatively evaluate the green behavior performance of papermaking enterprises, a new model of green behavior performance evaluation of papermaking enterprises is proposed based on rough set and cloud model theory. Firstly, the factors influencing the green behavior performance of papermaking enterprises are identified, and an evaluation index system for the green behavior of papermaking enterprises is established. Secondly, using rough set theory, the weight of each layer in the index system is determined. Subsequently, considering the fuzziness and uncertainty of index evaluation, the cloud model is employed to construct the performance evaluation model of green behavior of papermaking enterprises. The weights are combined with the evaluation model to finally calculate the performance level of green behavior of papermaking enterprises. Finally, a comprehensive evaluation is conducted, taking the green behavior performance of a papermaking enterprise as the research object. The results show that: (1) The green behavior performance level of the papermaking enterprise is in a good level, but there are pollution penalties caused by inadequate management in pollutant discharge management. In terms of energy structure, coal is the main source of energy, and a large amount of oxides are emitted. (2) The calculation results of the evaluation method are basically consistent with the actual situation. It can reflect the actual effect of the green behavior of the enterprise, and verify the reliability, rationality and effectiveness of the model [ABSTRACT FROM AUTHOR]

Purpose: In recent years, rough set theory has evolved as one of the most promising classification techniques. One of the cardinal uses of rough set theory is its application for rule generation. The purpose of this paper is to propose a real-time fabric inspection technique. This work deals with the multi-class classification of fabric defects using rough set theory. Design/methodology/approach: This technique focuses on the classification of fabric defects using the effective decision rules envisaged by rough set theory. In the proposed work, the six features of 50 images have been used for multiclass classification of fabric defects. Findings: In this work, 40 images were used for generation of decision rules and 10 unseen images were used for validation out of which nine images are accurately predicted by the proposed technique. Originality/value: The proposed method accurately identified 9 out of 10 testing defects. The obtained decision rules provide an insight about the classification method which ensures that the prediction accuracy can be improved further by framing more robust decision rules with the help of a large training data set. Thus, with the support of modern computational systems this method is potent in getting recognition from the textile industry as a real-time classification technique. [ABSTRACT FROM AUTHOR]

An information system is a type of knowledge representation, and attribute reduction is crucial in big data, machine learning, data mining, and intelligent systems. There are several ways for solving attribute reduction problems, but they all require a common categorization. The selection of features in most scientific studies is a challenge for the researcher. When working with huge datasets, selecting all available attributes is not an option because it frequently complicates the study and decreases performance. On the other side, neglecting some attributes might jeopardize data accuracy. In this case, rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information; nonetheless, investigating all available combinations of attributes will result in some problems. Furthermore, because attribute reduction is primarily a mathematical issue, technical progress in reduction is dependent on the advancement of mathematical models. Because the focus of this study is on the mathematical side of attribute reduction, we propose some methods to make a reduction for information systems according to classical rough set theory, the strength of rules and similarity matrix, we applied our proposed methods to several examples and calculate the reduction for each case. These methods expand the options of attribute reductions for researchers. [ABSTRACT FROM AUTHOR]

Text Summarization is the technique of shortening a long text but having all the relevant and significant topics conveyed in the text. As the number of journal articles published every year is growing steadily, the relevance of research on journal article summarization also increases. In this work, six extractive summarization methods are implemented and compared with the results of four standard methods applied to the dataset of journal articles. Precision, Recall and F-measure of Rouge-1, Rouge-2, Rouge-L and Rouge-Lsum measures are analyzed. Eight features are used in the implementation of the sum of features method and the BernoulliRBM method. It is observed from the experiments conducted that the Rough set method and the K-Means clustering and summarization method have high rouge scores in 10 out of the 12 measures analyzed here. The recall of the generated summary by the Roughset method is further improved when the first part of the article is used as a heuristic yard in calculating the similarity score with selected sentences. [ABSTRACT FROM AUTHOR]

The theory of rough set is a robust approach to face uncertainty by classifying the data under study into three main regions. The main principles of this theory are approximation operators and accuracy measures, so improving them has been a major goal for several works. The intrinsic aim of this study is to create new methods with high accuracy measures to classify subsets of data. These methods are established by combining an ideal structure with four types of maximal neighbourhoods. The essential characterizations and properties of these methods are amply studied. Thereafter, the relationships between these methods are elucidated with the assistance of some numerical examples. In this regard, we prove that the approximation operators and accuracy measures induced from rough set model defined by intersection minimal-maximal neighborhoods are the best. In addition to that, some comparisons are provided to demonstrate the importance of the introduced techniques compared to the previous ones in terms of improving the approximation operators and increasing the values of accuracy. Finally, a numerical example is given to confirm the efficiency of the followed techniques to maximize the value of accuracy and shrink the boundary regions compared to the existing techniques. [ABSTRACT FROM AUTHOR]

The objective of this work is to classify the mind mapping decisions "like", "dislike" and "neutral" in Epilepsy patients by applying the concepts of rough sets. An effective rough set-based classification of mental status in epilepsy patients has been computed using the features such as meditation, familiarity, theta, attention, appreciation, beta, mental effort, delta, alpha and gamma. The significance of features is considered as conditional attributes and the expected mood is represented as decision attributes. To analyze the impact of the features, the cardinality and rough set-based approximation are computed. Grey Relational Analysis (GRA) algorithm is applied for classification of patient decision is either like or dislike or neutral. The experimental results on classification of mind mapping of epilepsy patients using rough set-based approximation yields 95% accuracy. [ABSTRACT FROM AUTHOR]

In surface defect detection, some regions remain ambiguous and cannot be distinctly classified as abnormal or normal. This challenge is exacerbated by subjective factors, including workers' emotional fluctuations and judgment variability, resulting in noisy labels that lead to false positives and missed detections. Current methods depend on additional labels, such as clean and multi-labels, which are both time-consuming and labor-intensive. To address this, we utilize Rough Set theory and Bayesian neural networks to learn a trustworthy model from noisy labels for Surface Defect Detection. Our approach features a novel pixel-level representation of suspicious areas using lower and upper approximations, and a novel loss function that emphasizes both precision and recall. The Pluggable Spatially Bayesian Module (PSBM) we developed enhances probabilistic segmentation, effectively capturing uncertainty without requiring extra labels or architectural modifications. Additionally, we have devised a 'defect discrimination confidence' metric to better quantify uncertainty and assist in product quality grading. Without the need for extra labeling, our method significantly outperforms state-of-the-art techniques across three types of datasets and enhances seven types of classic networks as a pluggable module, without compromising real-time computing performance. For further details and implementation, our code is accessible at https://github.com/ntongzhi/RoughSet-BNNs. • A Rough Set-based method was proposed for noise label handling in defect detection. • Enhances robustness to noisy data without extra labels or network changes. • Experiments across datasets and models prove the method's effectiveness and utility. [ABSTRACT FROM AUTHOR]

In most of the scientific research feature selection is a challenge for researcher. Selecting all available features is not an option as it usually complicates the research and leads to performance drop when dealing with large datasets. On the other hand, ignoring some features can compromise the data accuracy. Here the rough set theory presents a good technique to identify the redundant features which can be dismissed without losing any valuable information, however, exploring all possible combinations of features will end with NP-hard problem. In this research we propose adopting a heuristic algorithm to solve this problem, Polar Bear Optimization PBO is a metaheuristic algorithm provides an effective technique for solving such kind of optimization problems. Among other heuristic algorithms it proposes a dynamic mechanism for birth and death which allows keep investing in promising solutions and keep dismissing hopeless ones. To evaluate its efficiency, we applied our proposed model on several datasets and measured the quality of the obtained minimal feature set to prove that redundant data was removed without data loss. [ABSTRACT FROM AUTHOR]

The manhole sealing performance of a kettle agitator directly affects the production efficiency and safety of the whole pressure vessel. This paper investigated the market demand for the reliability of manhole seal rings. First, the objective weight was determined by the rough set method and the subjective weight was determined by an analytic hierarchy process. The subjective weight and objective weight were integrated organically to obtain a scientific and effective comprehensive evaluation model. Then, the method of Quality Function Deployment is applied to transform the user requirements into the technical characteristics of the seal ring. The technical c haracteristics of the sealing ring are converted into the influencing factors of the reliability of the sealing ring by the transformation matrix, and the weight of the factors is determined according to the triangular fuzzy number. Finally, the most important factors affecting the reliability of the seal ring were studied by finite element analysis. This paper provides a theoretical basis for studying the reliability design of seal ring. [ABSTRACT FROM AUTHOR]

Feature selection technique attempts to select and remove irrelevant features while ensuring that an informative subset of features remains in the dataset. The performance of a classifier often depends on the feature subset used for the robust classification task. In the medical and healthcare application domain, classification accuracy plays a vital role. The higher level of false negatives in medical diagnosis systems may raise the risk of patients not employing the necessary treatment they need. In this article, we have proposed an unsupervised feature selection method that underlines the concepts of rough set theory for the task of classification of high-dimensional datasets. Experiments are carried out on seven public domain healthcare and life science related datasets. The obtained experimental results justify the significance of the proposed method over five other state-of-the-art feature selection methods. [ABSTRACT FROM AUTHOR]

Groundwater has a great influence on the stability of expansive soft rock roadway. Therefore, hydrogeological factors must be considered in the classification and evaluation of rock mass quality of expansive soft rock engineering. Based on a practical project, this paper uses PCA extension model to classify the hydrogeology of expansive soft rock roadway. Then the rough set theory is introduced into the weight calculation of each influencing factor. Finally, the RS method is established and the reliability of the model is evaluated. The results show that the weight value of RQD is the largest, which is very important to the stability of surrounding rock, and the classification prediction results are basically consistent with the actual values. The model has good engineering applicability and practical value. This study provides a reference for the hydrogeological classification and stability prediction of expansive soft rock roadway, slope and underground cavern in the future. [ABSTRACT FROM AUTHOR]

As an extension of partition, fuzzy β -covering can provide a more realistic and accurate description of incomplete information. In this paper, we mainly integrate the idea of fuzzy β -covering with dual hesitant fuzzy (DHF) information and construct some novel three-way decision (3WD) models with DHF covering-based rough set. Firstly, we propose the notions of DHF β -covering, DHF β -minimal description and DHF β -maximal description, and then construct three types of DHF neighborhood operators. Meanwhile, we introduce DHF conditional probability by using DHF neighborhood operator. Secondly, in terms of DHF conditional probability, DHF covering-based probabilistic rough set, DHF covering-based decision-theoretic rough set and their 3WD models are established. In light of DHF neighborhood operator, we propose two pairs of optimistic and pessimistic DHF decision evaluation functions and build two 3WD models through them. Lastly, a numerical example is employed to elaborate the application of the above models, which is effective and credible to medicine screening for Alzheimer's disease. • Proposed neighborhood operators in dual hesitant fuzzy environment. • Three-way decision based on dual hesitant fuzzy probabilistic rough sets. • Three-way decision based on dual hesitant fuzzy decision-theoretic rough sets. • Three-way decision based on dual hesitant fuzzy decision evaluation functions. • Experiment on medication screening of Alzheimer's disease are given. [ABSTRACT FROM AUTHOR]

Some learners couldn't get ideal learning results from distance education, to find out the root of this problem, their learning behavior and initiative should be analyzed in real time. However, in existing research results, the collected distance learning behavior data of learners are not pertinent enough, the extraction methods of big data are not proper enough, and the analysis models of learning behavior are not scientific enough. For these reasons, this paper analyzed the autonomous learning behavior of learners during distance reading based on big data, and gave the analysis contents and methods. In the text, a sequence diagram transformation method that is selfadaptive to long and short sequences had been introduced to process the learning behavior data of learners, who were then classified according to the features of different autonomous learning behavior sequences. Then, an attribute reduction algorithm based on improved Bayesian fuzzy rough set was adopted for attribute reduction, and the behavior indexes that are closely related to the autonomous learning effect of learners were selected for correlation analysis. After that, this paper proposed a method for detecting nonautonomous learning behavior based on multiple time scales, combining shortterm autonomous learning pattern with long-term autonomous learning behavior and resource access behavior, this paper also analyzed the typical autonomous learning pattern of learners through the learning of hidden layer features. At last, experimental results proved the effectiveness of the proposed analysis method. [ABSTRACT FROM AUTHOR]

The decision-theoretic rough set model based on Bayesian decision theory proposes a framework for studying rough set approximations using probabilistic theory, it has become an important research direction of rough set theory. In order to extend the theory of decision-theoretic rough set, this article is devoted to studying the fuzzy decision-theoretic rough set model in type-2 fuzzy conditional information systems. The type-2 fuzzy similarity relations are induced though computing the measure of similarity between objects for each attribute. Then, we use intersection operation of type-2 fuzzy sets to aggregate the multiple induced fuzzy similarity relations. Next, a fuzzy decision-theoretic rough set approach for type-2 fuzzy conditional information systems is proposed by means of inclusion degree of type-2 fuzzy sets. Finally, an example is considered to illustrate the effectiveness of the proposed method, which is helpful for applying these theories to deal with practical issues. [ABSTRACT FROM AUTHOR]

In data processing, measurement of uncertainty is one of the significant evaluation tools, which can describe the uncertainty essence of data. So far, there are few measurable tools to study the uncertainty of type-2 fuzzy information systems (TFISs-2) (the expanded models of fuzzy information systems). This paper is devoted to looking for effective indicators to describe the uncertainty of TFISs-2. The fuzzy T cos -similarity relations are first introduced, which are generated by TFISs-2 based on Gaussian kernel. Then, the fuzzy information structures are defined on account of this fuzzy T cos -similarity relation. Next, two measures constructed from the upper and lower approximations are given for TFISs-2, that is, δ -accuracy and δ -roughness, which are used to reflect the degree of accuracy and inaccuracy of information by numerical form. Furthermore, by combining roughness and entropy, the δ -rough entropy is investigated. Finally, the practicability of proposed measures is tested by a numerical experiment. The experimental results show that the δ -rough entropy is efficacious and applicable for TFISs-2. [ABSTRACT FROM AUTHOR]

This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic models. The weighted method and the Karush-Kuhn-Tucker optimality condition are combined to obtain the Pareto front of each model. The nature of the problem solutions is characterized according to newly proposed definitions. The location of efficient solutions depending on the lower/upper approximation set is discussed. The aim of the proposed solution procedure for the BL-MRNPP is to avoid solving four problems. A numerical example is solved to indicate the applicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Rough set is an important method for dealing with incomplete information systems. In incomplete information systems, the most common way to determine the relation between two samples is the tolerance relation. However, the condition for the tolerance relation to determine those samples may belong to the same category is very lenient, which makes the reduction rate low when using the rough set generated by this relation to select features. In response to the above problems, we design the neighborhood equivalence tolerance relation to solve them. Different from other improved tolerance relations, firstly, the relation designed in this paper does not require additional threshold to accomplish the above goals, which will avoid the trouble caused by the given threshold. Secondly, we notice that most of the current improvements for this kind of problems are computationally cumbersome, and the relation designed in this paper is simple and effective. Based on this, we construct a neighborhood rough set model that handles incomplete information by using this relation, introduce its properties, expound the properties that a reduction set should satisfy, quantify the importance of conditional attributes with attribute dependence degree, which provides the basis for the design of feature selection algorithm. Finally, the greedy strategy is used to design a forward feature selection algorithm. Experimental results show that the model is effective in dealing with incomplete information systems. The feature selection algorithm has the smallest size of the average reduced subset on twelve datasets, and maintains the accuracy of the classifier, which verifies that the feature selection algorithm can effectively deal with incomplete information systems. ● As the judgment of tolerance relation is very lenient, the existing improvement methods either rely on the probability distribution of attribute values in the information system, or need to give a additional threshold. To solve the above problems, this paper improves the tolerance relation, and the improved binary relation only relies on the existing information system itself, without giving additional threshold. ● Rough set in incomplete information systems can only select more attributes to refine the knowledge granules when making feature selection due to the lenient judgment of tolerance relation, which is equivalent to making up for the problems caused by tolerance relation when selecting attributes, but this will lead to low reduction rate. In this paper, we use the newly proposed binary relation to construct neighborhood rough set model in incomplete information systems, and use this model to make feature selection, which improves the problem of low reduction rate above, while maintaining the accuracy of the classifier. [ABSTRACT FROM AUTHOR]

Attribute reduction is a fundamental problem in rough set theory and serves as an effective data reduction technique. The minimal test cost attribute reduction problem poses a more challenging task built upon the classical reduction problem and finds widespread applications in the real world. The development of efficient heuristic algorithms is crucial for effectively addressing this problem. However, research efforts utilizing local search algorithms for solving the minimal test cost attribute reduction problem remain limited. This paper aims to combine the graph-based rough set attribute reduction method with the effectiveness of local search algorithms known for solving the set covering problem. It proposes a method to transform the minimal test cost attribute reduction problem into a set covering problem and a four-stage branch local search algorithm based on the set covering is designed to solve the minimal test cost attribute reduction problem, which includes three core algorithmic techniques to further improve the practical performance of the algorithm. Extensive experiments are conducted to evaluate the effectiveness of the proposed algorithms, comparing them against various existing algorithms. The experimental results demonstrate that the proposed algorithms achieve fewer attributes and lower test costs within an acceptable running time, while maintaining competitive classification accuracy. • We propose the equivalence between minimal test cost attribute reduction problem (MTCARP) and set covering problem (SCP). • We propose two algorithms for MTCARP (GRF-NuSC1 and GRF-NuSC2). • GRF-NuSC1 and GRF-NuSC2 can efficiently transform the MTCARP into the SCP. • GRF-NuSC2 employs unique stage settings and a branching strategy. • GRF-NuSC2 surpasses most of existing algorithms in achieving the minimal test cost. [ABSTRACT FROM AUTHOR]

Insider threat is a severe problem for many computer departments since they have an authorization to do some assigned tasks. They can easily seek security for any organizational computer vulnerability. Protocol "Insider Threat Detection and Prevention Protocol: ITDP" is designed to detect whether a requesting "IT user" is an authentic IT user who has been allocated rights to a particular application. The User's knowledge and behavior are used to classify whether the user is authentic. The statistical classification technique is used to predict whether the guest is authentic. The best classification technique is linear binary discriminant function analysis with 98.3% of accuracy in insider threat detection classification. [ABSTRACT FROM AUTHOR]

Reduction of attributes in an information system (IS) is a basic step for IS analysis. The original rough set model of Pawlak depends on an equivalence relation which is strongly constraints. This paper aims to use similarity classes and similarity degrees to obtain a reduction of IS and indicate an approach by using an example from biochemistry to get a quantitative structure activity relationship (QSAR). Moreover, signs of each attribute and degrees of memberships are computed to give a decision by using the degree of similarity. The suggested approach gives an increase in decision-making and decision accuracy. [ABSTRACT FROM AUTHOR]

Simultaneous quality reliability analysis can detect the weak links in production process as early as possible, which can significantly improve product reliability. Aiming at the reliability in product quality, a model based on rough set and Bayesian network (RS-BN) is proposed in this paper. Simplify expert knowledge and reduce product quality factors using rough set theory, and the minimal product quality rules can be obtained. Then the Bayesian network is constructed and trained by the minimum rules. Based on the minimal rules, the complexity of Bayesian network structure and the difficulties of product reliability analysis are largely decreased. To verify the performance of the proposed RS-BN model, a competition dataset is utilized and four evaluation indicators are investigated, i.e., accuracy, F1-score, recall, and precision. Experimental results indicated that the proposed model is superior to the other three comparative models. [ABSTRACT FROM AUTHOR]

This paper aims to originate two new notions that are soft rough Pythagorean fuzzy set and Pythagorean fuzzy soft rough set, and investigate some important properties of soft rough Pythagorean fuzzy set and Pythagorean fuzzy soft rough set in detail. Furthermore, classical representations of Pythagorean fuzzy soft rough approximation operators are presented. Then the proposed operators are applied on decision-making problem in which the experts provide their preferences in Pythagorean fuzzy soft rough environment. Finally through an illustrative example, it is shown that how the proposed operators work in decision-making problems. [ABSTRACT FROM AUTHOR]

Fuzzy rough bi-level multi-objective nonlinear programming problem (FRBMNPP) moved toward becoming rise normally in various real applications. In this article we develop bi-level multi-objective nonlinear programming problem (BMNPP), in which the objective functions have fuzzy nature and the constraints represented as a rough set. The fuzzy objective functions converted into deterministic ones by utilizing the α -cut methodology. Thus the FRBMNPP become a rough BMNPP which is transformed into two problems corresponding to the upper and lower approximation models. The Karush-Kuhn-Tucker (KKT) method and two models of technique of order preferences by similarity to ideal solution (TOPSIS) approach are developed to solve such problem. At last, applicability and efficiency of the two TOPSIS models and KKT method, suggested in this study, are presented through an algorithm and a numerical illustration. [ABSTRACT FROM AUTHOR]

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Abstract In order to predict the service life of large centrifugal compressor impeller correctly, the rough set and fuzzy Bandelet neural network are combined to construct the novel prediction model which can give full play to theirs advantages. The attribute reduction algorithm based rough set and clustering method is firstly designed to optimize the inputting variables of fuzzy Bandelet neural network. And then the prediction model based on fuzzy Bandelet neural network is proposed, the Bandelet function is used as the excitation function of hidden layer and is combined with fuzzy theory to improve the prediction effectiveness of the prediction model. The training algorithm of fuzzy Bandelet neural network is designed based on improved genetic algorithm, the improved genetic algorithm introduces the adaptive differential evolution method into the traditional genetic algorithm, which can effectively optimize the parameters of fuzzy Bandelet neural network. Finally, the original 30 input variables of fuzzy Bandelet neural network are reduced to 9 input nodes based on rough set using 500 remanufacturing impellers as research objects. The service life of remanufacturing impeller is predicted based on three prediction models, and simulation results show that the fuzzy Bandelet neural network optimized by improved genetic algorithm has highest prediction precision and efficiency, which can correctly predict the service life of remanufacturing impeller. Highlights • Fuzzy Bandelet neural network is constructed based on Bandelet transform. • Service life prediction model is established by rough set and fuzzy Bandelet neural network. • Prediction effectiveness of service life of remanufactured impeller are improved. [ABSTRACT FROM AUTHOR]

Feature selection is one of the key steps in text classification. To some extent, it can affect the performance of text classification. In this paper, we firstly proposed an optimized document frequency-based word frequency and document frequency and then presented the feature resolution based on the optimized document frequency. Meanwhile, we introduced rough set into feature selection and provided an attribute reduction algorithm based on the correlation matrix of equivalence classes. We finally put forward a feature selection method combining the presented feature resolution with the provided attribute reduction algorithm. The proposed feature selection method firstly employs the presented feature resolution to select some valuable text features and filter out useless terms to reduce the sparsely of text feature spaces, and then it uses the provided attribute reduction algorithm to eliminate redundant features. The comparative experimental results show that the proposed feature selection method has certain advantages in consumed time, macro-average, micro-average, and average classification accuracy. [ABSTRACT FROM AUTHOR]

Nowadays, databases expand rapidly due to electronically generated information from different fields like bioinformatics, census data, social media, business transactions, etc. Hence, feature selection/attribute reduction in databases is necessary in order to reduce time, cost, storage and noise for better accuracy. For this purpose, the rough set theory has been played a very significant role, but this theory is inefficient in case of real-valued data set due to information loss through discretization process. Hybridization of rough set with intuitionistic fuzzy set successfully dealt with this issue, but it may radically change the outcome of the approximations by adding or ignoring a single element. To handle this situation, we reconsider the hybridization process by introducing intuitionistic fuzzy quantifiers into the idea of upper and lower approximations. Supremacy of intuitionistic fuzzy quantifier over VPRS and VQRS is presented with the help of some examples. A novel process for feature selection is given by using the degree of dependency approach with intuitionistic fuzzy quantifier-based lower approximation. A greedy algorithm along with two supportive examples is presented in order to demonstrate the proposed approach. Finally, proposed algorithm is implemented on some benchmark datasets and classification accuracies for different classifiers are compared. [ABSTRACT FROM AUTHOR]

In the process of product design, the knowledge of product ecological design is growing with the increasing of environmental requirements of product. In the process of knowledge acquisition of product ecological design, massive redundant or insignificant design data will affect designers' efficiency, and it is necessary to reduce these data. In this paper, taking the automobile reducer as an example, the ontology expression model is established for the ecological design knowledge needed in the design process. Starting from the rough set knowledge, the rough set theory is applied to reduce the attributes and remove the redundancy. Finally, the accurate data which meets the design requirements is obtained, and the design efficiency and precision are improved. [ABSTRACT FROM AUTHOR]

Feature selection is the key issue of unstructured data mining related fields. This paper presents a dimensionality reduction method which uses a rough set as the feature selection tool. Different from previous rough set based classification algorithm, it takes feature cooccurrence into account when make attribution reduction to get a more accurate feature subset. The novel method called Feature Cooccurrence Quick Reduction algorithm is in this article. Experimental results show it has a high efficiency in dimensionality reduction- time consumption by approximately 23% less than traditional rough set based dimensionality reduction methods. Moreover, classification based on the feature set selected by Feature Co-occurrence Quick Reduction algorithm is more precise. The proposed algorithm is helpful to us for refining knowledge from massive unstructured data. [ABSTRACT FROM AUTHOR]

Among various tasks of feature reduction, how to search qualified features and then construct the corresponding reduct which satisfies a given constraint is a hot topic. Constraint is the pre-defined condition in feature reduction, it rules two crucial aspects: 1) when the process of searching can be terminated to construct reduct; 2) whether a feature/set of features should be added into reduct pool or not. Obviously, such a task of feature reduction is constraint-dependent. However, some limitations may naturally emerge: 1) constraint-independent features are ignored; 2) fixed constraint hinders the diverse evaluations of features; 3) selected features based on single constraint are powerless to data perturbation. Therefore, an Ensembler Mixed with Pareto Optimality (EmPo) is developed in this study. Firstly, the principle of Restricted Pareto Optimality is proposed to identify constraint-independent features before performing constraint related searching, which indicates a two-stages strategy to feature reduction. Naturally, diverse evaluations of features are achieved in such a process. Secondly, a data perturbation w.r.t. either sample or feature aspect is employed to obtain multiple reductions of features. The objective is to further improve the stability of the classification results based on those multiple reducts. It should also be emphasized that EmPo is a general framework, and most existing approaches to feature reduction can be embedded into it to further improve their performances. Finally, the effectiveness of our EmPo is validated over 20 datasets within 4 different ratios of noisy label. • Propose a framework for selecting qualified features. • Investigate the shortcomings of some existing methods. • The quality of features is related to evaluation conditions. • Ensemble strategy is useful in selecting features. [ABSTRACT FROM AUTHOR]

Accurately forecasting power load is essential for utilities to effectively manage their resources, reduce operational costs, and provide improved customer service. However, the current load forecasting lacks the ability to deeply explore data, thus failing to accurately predict both short-term trends and volatility ranges. To address this issue, we construct a novel combined forecasting system based on rough sets, information granulation, deep learning, and multi-objective optimization. In this study, we follow the reasonable granulation criterion for granular computing, which aims to improve the reasonableness and specificity of granular interval prediction under the determination of granularity level, and innovatively propose a novel multi-objective optimization algorithm that can simultaneously constrain the reasonable granulation criterion and theoretically demonstrate the obtained Pareto-optimal solution. Four simulation experiments were conducted using the Australian dataset to evaluate the performance of our proposed system in predicting trend changes and fluctuation ranges of power load. Our results demonstrate that the developed system effectively predicts the trend changes and fluctuation range of power load. Specifically, our system showed a deterministic prediction performance improvement of 13.39% and a granularity interval prediction performance improvement of 6.67% compared to the baseline model. Moreover, we conducted a series of discussion tests to validate the superiority of our system, which further confirmed the effectiveness of our proposed approach. • A multivariate intelligent granularity combination forecasting system (MGCFS) is constructed. • A novel clustering algorithm based on intelligent optimization is presented for information granulation. • Pareto optimal solution is proved theoretically. • A multi- objective swarm intelligent optimization technique is proposed. [ABSTRACT FROM AUTHOR]

Knowledge reduction is an essential issue in data mining. However, most of the existing studies consider the problem of knowledge reduction in a single-scale system. When the system expands to a multi-scale information system (MIS), the existing methods are not available. To overcome this challenge, we design a universal framework to reduce attributes and select optimal scales (OSs) based on the dominance relation in ordered information systems (OISs). Firstly, we analyze the effect of scale on rough approximations and correlation measures in multi-scale ordered information systems (MOISs). Secondly, the relation between attribute reduction and OS selection is explored in OISs. Moreover, the corresponding algorithms are designed around both tasks. Due to our universal framework considering the decisions at the finest, optimal and coarsest scale, our study is an extension of the three-way decision. Thirdly, a novel MOIS construction algorithm is explored to transform an OIS into an MIS. Thus, the proposed reduction algorithms can be operated in any OIS. Experiments substantiate that models trained by data at the OS can improve their stability and the attribute reduction task is also suitable for the proposed algorithm. • A universal framework is explored to reduce attributes and select optimal scales. • A novel multi-scale ordered information system construction algorithm is designed. • The influence of scale on rough approximations and correlation measures is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of parameter selection and uncer-tainty measurement for a variable precision probabilistic rough set. Firstly, within the framework of the variable precision probabilistic rough set model, the rela-tive discernibility of a variable precision rough set in probabilistic approximation space is discussed, and the conditions that make precision parameters α discernible in a variable precision probabilistic rough set are put forward. Concurrently, we consider the lack of predictability of precision parameters in a variable precision probabilistic rough set, and we propose a systematic threshold selection method based on relative discernibility of sets, using the concept of relative discernibility in probabilistic approximation space. Furthermore, a numerical example is applied to test the validity of the proposed method in this paper. Secondly, we discuss the problem of uncertainty measurement for the variable precision probabilistic rough set. The concept of classical fuzzy entropy is introduced into probabilistic approxi-mation space, and the uncertain information that comes from approximation space and the approximated objects is fully considered. Then, an axiomatic approach is established for uncertainty measurement in a variable precision probabilistic rough set, and several related interesting properties are also discussed. Thirdly, we study the attribute reduction for the variable precision probabilistic rough set. The definition of reduction and its characteristic theorems are given for the variable precision probabilistic rough set. The main contribution of this paper is twofold. One is to propose a method of parameter selection for a variable precision probabilistic rough set. Another is to present a new approach to measurement uncertainty and the method of attribute reduction for a variable precision probabilistic rough set. [ABSTRACT FROM AUTHOR]

Copyright of Journal Européen des Systèmes Automatisés is the property of International Information & Engineering Technology Association (IIETA) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Feature selection has been a significant task for data mining and pattern recognition. It aims to choose the optimal feature subset with the minimum redundancy and the maximum discriminating ability. This paper analyzes the feature selection method from two aspects of data and algorithm. In order to deal with the redundant features and irrelevant features in high-dimensional & low-sample data and low-dimensional & high-sample data, the feature selection algorithm model based on the granular information is presented in this paper. Thus, our research examines experimentally how granularity level affects both the classification accuracy and the size of feature subset for feature selection. First of all, the improved binary genetic algorithm with feature granulation (IBGAFG) is used to select the significant features. Then, the improved neighborhood rough set with sample granulation (INRSG) is proposed under different granular radius, which further improves the quality of the feature subset. Finally, in order to find out the optimal granular radius, granularity λ optimization based on genetic algorithm (ROGA) is presented. The optimal granularity parameters are found adaptively according to the feedback of classification accuracy. The performance of the proposed algorithms is tested upon eleven publicly available data sets and is compared with other supervisory methods or evolutionary algorithms. Additionally, the ROGA algorithm is applied to the enterprise financial dataset, which can select the features that affect the financial status. Experiment results demonstrate that the approaches are efficient and can provide higher classification accuracy using granular information. [ABSTRACT FROM AUTHOR]

The minimum vertex cover problem (MVCP) and minimum weighted vertex cover problem (MWVCP) have been used in a variety of applications. This paper focuses on a view of test-cost-sensitive rough set for MWVCP. We first provide a method to convert a minimum weight vertex cover of a graph into a minimal test cost attribute reduct of a test-cost-sensitive decision table. Then, an induced test-cost-sensitive decision table from an undirected weighted graph is established. On the foundation of the induced decision table, an improved heuristic algorithm for finding minimum weight vertex covers is proposed, it can avoid a mass of redundant computation. Furthermore, to improve efficiency, a quantum-behaved particle swarm optimization with immune mechanism is presented, which can avoid the phenomenon of premature, improve the global searching ability, and enhance the convergence speed. The results of the experiment show the advantages and limitations of the proposed algorithms compared with state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In the process of attribute reduction, the importance degree of a condition attribute is generally measured by means of the dependence degree between the condition attribute and the decision attribute set. If the dependence degree of the condition attribute is 0, we generally think that the condition attribute does not affect the decision results of the decision table and can be directly deleted form the condition attribute set. However, to some extent, it cuts off the connection of the condition attribute and other attributes, resulting in a great loss of valuable information in the decision table. Therefore, based on the fact that the dependency degree of the condition attribute set is more credible than the dependency degree of a single condition attribute, this paper researches the dependency degree of the condition attribute set and puts forward a calculation method for dependency degree of condition attribute set using a discernibility matrix. This paper also presents and proves a theorem to improve the proposed method. The proposed method can quickly get the discernibility matrix and can directly calculate the dependency degree of the condition attribute set. The theoretical analysis and the simulation experiment comparison results all show that the proposed method has better effectiveness and lower time complexity. [ABSTRACT FROM AUTHOR]

Fuzzy time series forecasting is an emergent research topic. In fuzzy time series model design, accuracy of forecast is dependent on two major issues: (1) Efficient data partitioning (2) Establishing Fuzzy logical relationships for Prediction. In this study, a new data partitioning technique based on rough-fuzzy approach has been proposed. Then, for the prediction purpose, a novel rule selection criterion has been adopted. In addition to that a mechanism is devised to deal with the situation when there is no matching rule present in the training data. Motivation for the present work is to overcome the drawback of existing high-order fuzzy time series models by avoiding the computations of complicated fuzzy logical relationship considering all previous states at a time and then explicit matching of those rules. The proposed work produces output of improved accuracy with selective rules only. In this high order model fuzzy logical relationships for each time lag are established separately and predictions are combined at the end to produce final result. Performance of the model is evaluated using TAIEX dataset. This idea also outperforms the some of the recent fuzzy time series forecasting models using the same dataset, in terms of forecast accuracy. [ABSTRACT FROM AUTHOR]

To improve the prediction capacity of stock price trend, an integrated prediction method is proposed based on Rough Set (RS) and Wavelet Neural Network (WNN). RS is firstly introduced to reduce the feature dimensions of stock price trend. On this basis, RS is used again to determine the structure of WNN, and to obtain the prediction model of stock price trend. Finally, the model is applied to prediction of stock price trend. The simulation results indicate that, through RS attribute reduction, the structure of WNN prediction model can be simplified significantly with the improvement of model performance. The directional symmetry values of prediction, corresponding to SSE Composite Index, CSI 300 Index, All Ordinaries Index, Nikkei 225 Index and Dow Jones Index, are 65.75%, 66.37%, 65.97%, 65.52% and 66.75%, respectively. The prediction results are better than those obtained by other neural networks, SVM, WNN and RS-WNN, which verifies the feasibility and effectiveness of the proposed method of predicting stock price trend. [ABSTRACT FROM AUTHOR]

A concept of intuitionistic fuzzy rough set based on approximations plays a vital role in coping with uncertainty. Aczel-Alsina t-norm and t-conorm are the most flexible operational laws based on the parameter for fuzzy frameworks. In multi-attribute group decision-making (MAGDM), the aim of this article is to develop some tools based on norm operations for the information fusion. In this article, intuitionistic fuzzy rough Aczel-Alsina weighted geometric operators are developed and studied their properties. Based on these operators, MAGDM algorithm is presented. The developed aggregation operators (AOs) are compared with some existing AOs, and their significance is discussed. [ABSTRACT FROM AUTHOR]

Rough K-Means (RKM) is a well-known unsupervised clustering algorithm based on rough set logic that is utilized in a wide range of applications. However, when dealing with complex problems like image segmentation, it is frequently trapped in local optima during execution, resulting in undesirable segmentation results. To handle the issue in a realistic computing time, this study develops a Lévy–Cauchy Arithmetic Optimization Algorithm (LCAOA), an enhanced form of AOA, for performing rough clustering. The Levy flight and Cauchy distribution help in exploration and exploitation, respectively, in the proposed LCAOA. Therefore, well-balanced exploration and exploitation have been incorporated into LCAOA, which is a major problem of classical AOA. Opposition-based learning is also incorporated into LCAOA to maintain an efficient population during the optimization process. As the segmentation efficacy is somewhat dependent on the selection of color spaces caused by the non-illumination of regions, the suggested method employs the CIELab color space. The suggested method is compared to conventional and Nature-Inspired Optimization Algorithms (NIOA)-based state-of-the-art image segmentation techniques over traditional color images, color pathology images, and leaf images. The proposed clustering methodology outperforms all other examined clustering algorithms, according to the results of the experiments. For example, proposed LCAOA-based rough clustering gives average Feature Similarity Index (FSIM) values of 0.9513, 0.9688, and 0.9769 for traditional color images with 4, 6, and 8 clusters, respectively. The proposed technique is associated with an average FSIM value of 0.9525 for cluster number 2 in images of oral pathology. Lastly, for leaf images, the proposed approach yields a mean FSIM value of 0.9759 with an accuracy of greater than 97% for cluster number 2. • Arithmetic Optimization Algorithm (AOA) based rough clustering has been introduced. • Enhancement of AOA is performed by Lévy–Cauchy based mutation. • Opposition based learning is also incorporated into AOA. • The proposed clustering method uses CIELab color space. • The proposed method is compared against state-of-art segmentation methods. [ABSTRACT FROM AUTHOR]

The identification of regions of social vulnerability to earthquake disaster and factors contributing to social vulnerability is significant for effective earthquake disaster risk management. To assess social vulnerability to earthquake disaster, this paper applied a rough set to construct an evaluation model of social vulnerability based on catastrophe progression. Following in-depth literature researches, an assessment model of social vulnerability to earthquake disaster in Sichuan Province, China, based on the catastrophe progression method was established. A rough set attribute reduction method was adopted to eliminate irrelevant social vulnerability indicators and optimize the proposed model. Finally, a catastrophe progression method for social vulnerability to earthquake disaster is developed to overcome the subjectivity of the index weight assignment of social vulnerability indicators in the currently used social vulnerability assessment method. The application of our method to Sichuan Province indicates large regional differences in terms of social vulnerability to earthquake disasters. The results show that the northeastern and central areas of Sichuan Province belong to the high social vulnerability category; in particular, Guangyuan is the most vulnerable region. These findings will provide policymakers with a scientific basis for their earthquake disaster risk management strategies. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C -soft sets and CC -soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR -approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR -hemirings ( k -ideal and h -ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example. [ABSTRACT FROM AUTHOR]

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)