Rough Set Model Research Articles

Sequential rough set: a conservative extension of Pawlak’s classical rough set

Rough set theory is an important approach to deal with uncertainty in data mining. However, Pawlak’s classical rough set has low fault-tolerance on concept approximation based on knowledge granules, which may influence the classification accuracy in practical application. To address this problem, the present paper proposes a novel sequential rough-set model that is proved to be a conservative extension of Pawlak’s classical rough set. As a result, it effectively improves the fault-tolerance ability, classification accuracy and concept approximation accuracy of the latter without any additional assumption. Based on the properties and theoretical analysis of the proposed model, an algorithm is presented to automatically determine the sequential thresholds and compute the three regions for the given concept. Experiments on real data verify the validity of the algorithm, and also show the stable improvement on the two types of accuracy.

Local fuzzy rough attribute reduction for large-scale mixed data with limited missing labels based on local fuzzy self information

The advent of the era of big data is accompanied by the generation of large-scale data of various types. Extracting the potential value and rules from such data has always been a challenge. Due to various external and internal factors, it is commonplace for large-scale data to exhibit the phenomenon of missing limited labels. In addressing a large-scale mixed information system with limited label missing (LSMDISLML), local neighborhood rough set model (LNRS-model) is typically employed. However, the identical neighborhood radius is often used by such model when confronted with numerical attributes, which could potentially attenuate the classification capability of the data. Local fuzzy rough set model (LFRS-model) can overcomes this point. This paper studies local fuzzy rough attribute reduction for large-scale mixed data with limited missing labels based on LFRS-model via local fuzzy self information and overlap degree function. First, leveraging the statistical distribution of data as a foundation, fuzzy relations on the entire sample set are established, which has the advantage of being able to use different fuzzy similarity radii to calculate similarity, thereby adapting to different data distributions. Subsequently, the samples with missing labels are discarded as they constitute a small proportion of the entire sample set and have little impact on overall performance of dataset. The limited computing resources and storage space are focused on the sample set with complete labels (denoted as target set). Thereafter, based on the target set, local fuzzy λ-upper and lower approximations are defined, and LFRS-model is constructed. This model not only reduces processing time and sources of error in large-scale data but also improves data quality and enhances the reliability of the experimental results. Then, local fuzzy λ-self information is introduced and used to design a local fuzzy rough attribute reduction algorithm in a LSMDISLML. Furthermore, a overlap degree function is introduced to evaluate and reorder the attributes based on their importance, prioritizing the elimination of redundant attributes with high overlap and low importance from the preordered attribute set. This strategy effectively improves the efficiency of obtaining the optimal subset. Finally, a series of experiments are carried out. The experiment results demonstrate that the designed algorithm exhibits excellent performance in classification tasks and outlier detection tasks, surpassing existing four algorithms.

An Extension of VIKOR Approach for MCDM Using Bipolar Fuzzy Preference δ-Covering Based Bipolar Fuzzy Rough Set Model

Bipolarity highlights the positive and negative facets of a certain dilemma. This script aims to propose a novel multi-criteria decision-making (MCDM) approach based on bipolar fuzzy preference δ-covering based bipolar fuzzy rough set (BFPδC-BFRS) model by combining the VIKOR (VIseKriterijumska Optimizacija I Kompromisno Rasenje) scheme. The VIKOR scheme is viewed as a beneficial MCDM strategy, particularly in situations where an expert is incapable of making the right decision at the beginning of system design. The VIKOR method works well for problems with competing attributes because it operates under the presumptions that compromise is acceptable in conflict resolution, the expert seeks a solution that is extremely close to the best, and all developed attributes are taken into consideration when processing the various alternatives. In this study, firstly, we proposed an integrated MCDM based on BFPδC-BFRSs using the VIKOR methodology. Moreover, we solve a real-world illustration to show the effectiveness of the expanded VIKOR approach. Finally, we demonstrate a detailed comparative analysis of the proposed methodology with some prevalent decision-making approaches to substantiate the accountability of the recommended scheme.

Covering rough set models, fuzzy rough set models and soft rough set models induced by covering similarity

In order to study the rule of quantity characteristics of rough set theory, a novel notion of covering similarity in a covering approximation space is introduced. Based on this new notion, novel covering rough set models, novel fuzzy rough set models and novel soft rough set models are defined. Further, the concept of similarity matrix is presented, and then the matrix calculation formulas of all the new concepts and new models are deduced. Moreover, aim to better solve the practical problems by comparing the similarity, a concept of similarity interval is introduced, then the covering classification is carried out and a partial order of all the classes is derived. Finally, a few practical examples are given to illustrate the simple applications of all the new concepts and models in this paper.

Noise-resistant fuzzy multineighbourhood rough set-based feature selection with label enhancement and its application for multilabel classification

Noise pollution in process of feature selection greatly reduces the classification efficacy of multilabel data, and the estimation of label descriptions is insufficient because of the lack of label enhancement for label distribution learning. To overcome the limitations, this work presents a noise-resistant fuzzy multineighbourhood rough set-based feature selection methodology with label enhancement and its application for multilabel classification. First, under the fuzzy T-equivalence relation, to construct new adaptive fuzzy neighbourhood class, the multineighbourhood radius set on feature space is integrated with fuzzy neighbourhood radius via sample interval on label space; then, the adaptive fuzzy multineighbourhood granules are obtained. Second, by integrating the parameterized fuzzy decision of labels and adaptive fuzzy multineighbourhood granules, noise-resistant lower and upper approximations via fuzzy multineighbourhood are constructed. A noise-resistant multilabel fuzzy multineighbourhood rough set model and its noise-resistant approximate accuracy can be proposed. Third, the description degree of label is computed to design label proportion after label enhancement. Certain fuzzy multineighbourhood entropy measures are developed to obtain label enhancement-based mutual information. When the algebraic and information perspectives are fused, label enhancement-based mutual information with fuzzy multineighbourhood via approximate accuracy is presented to evaluate the final association relationship between the features and label sets. Finally, a multilabel feature selection strategy via label enhancement will be constructed to obtain the best feature subset. The experimental results applied to 14 multilabel datasets indicate that this algorithm is significant.

Intuitionistic Fuzzy Sequential Three-Way Decision Model in Incomplete Information Systems

As an effective method for uncertain knowledge discovery and decision-making, the three-way decisions model has attracted extensive attention from scholars. However, in practice, the existing sequential three-way decision model often faces challenges due to factors such as missing data and unbalanced attribute granularity. To address these issues, we propose an intuitionistic fuzzy sequential three-way decision (IFSTWD) model, which introduces several significant contributions: (1) New intuitionistic fuzzy similarity relations. By integrating possibility theory, our model defines similarity and dissimilarity in incomplete information systems, establishing new intuitionistic fuzzy similarity relations and their cut relations. (2) Granulation method innovation. We propose a density neighborhood-based granulation method to partition decision attributes and introduce a novel criterion for evaluating attribute importance. (3) Enhanced decision process. By incorporating sequential three-way decision theory and developing a multi-level granularity structure, our model replaces the traditional equivalent relation in the decision-theoretic rough sets model, thus advancing the model’s applicability and effectiveness. The practical utility of our model is demonstrated through an example analysis of “Chinese + vocational skills” talent competency and validated through simulation experiments on the UCI dataset, showing superior performance compared to existing methods.

Dominance-Based Rough Set Model in Hesitant Fuzzy Information Systems

Hesitant fuzzy information systems have been widely applied in decision-making due to their ability to handle uncertain information. In addition, dominance relationships are often taken into account in many practical decision-making problems. Therefore, it is of great significance to conduct research on hesitant fuzzy information systems involved with dominance relations. In this study, we introduce dominance relations in a hesitant fuzzy information system to make it a dominance-based hesitant fuzzy information system, which can provide a solid new idea for comparing hesitant fuzzy elements. Furthermore, a hesitant fuzzy dominance-based rough set model is constructed, and an attribute reduction method is designed to simplify the dominance-based hesitant fuzzy information system. Further, we propose lower and upper approximation discernibility matrices in the dominance-based hesitant fuzzy decision information system to extract decision rules. In addition, two numerical examples are given to demonstrate the effectiveness of the proposed attribute reduction methods.

Correction: Intuitionistic fuzzy rough set model based on k-means and its application to enhance prediction of aptamer–protein interacting pairs

Correction: Intuitionistic fuzzy rough set model based on k-means and its application to enhance prediction of aptamer–protein interacting pairs

Neighborhood margin rough set: Self-tuning neighborhood threshold

The neighborhood threshold in the neighborhood rough set has a significant impact on the neighborhood relation. When the neighborhood threshold of an object exceeds the critical value, the labels of objects in the neighborhood are not completely consistent, and the critical value of each object often differs. Most existing neighborhood rough set models cannot adaptively regulate the neighborhood threshold. In this paper, we introduce a novel neighborhood rough set model that incorporates a self-tuning mechanism for the neighborhood threshold, taking into account the distribution of objects across different areas. The neighborhood margin is a measure proposed to assess the condition of neighborhoods, and it is calculated by subtracting the neighborhood threshold from the closest distance between heterogeneous elements. The neighborhood margin accurately represents the local state of the neighborhood, taking into account decision information. The margin neighborhood is proposed with a self-tuning the neighborhood threshold. Finally, we introduce the margin neighborhood rough set model and margin neighborhood-based attribute reduction algorithm, and explore the relationship between the proposed model and the neighborhood rough set model. The experiment examines the performance of reducts under various measures, and demonstrates that the neighborhood margin rough set reduces the uncertainty of neighborhood granules effectively, leading to excellent classification performance compared to other neighborhood-based SOTA models.

Simplified rough sets

Z. Pawlak first proposed the rough set (RS) in 1982. For over forty years, scholars have developed a large number of RS models to solve various data problems. However, most RS models are designed based on inherent rules, and their mathematical structures are similar and complex. For this reason, the efficiency of RS methods in analyzing data has not been significantly improved. To address this issue, we propose some new rules to simplify traditional RS models. These simplified RS models, which are equivalent to traditional RS models, can mine data more quickly. In this paper, we take Pawlak RS as an example to compare the computational efficiency between the simplified Pawlak RS (SPRS) and the traditional RSs. Numerical experiments confirm that the computational efficiency of the SPRS is not only far superior to that of traditional Pawlak RS (TPRS), but also higher than that of most existing RSs.

Neighborhood-related q-rung orthopair fuzzy covering-based rough set models and their applications for multi-attribute decision making

Neighborhood-related q-rung orthopair fuzzy covering-based rough set models and their applications for multi-attribute decision making

Identification of key risk factors for venous thromboembolism in urological inpatients based on the Caprini scale and interpretable machine learning methods

PurposeTo identify the key risk factors for venous thromboembolism (VTE) in urological inpatients based on the Caprini scale using an interpretable machine learning method.MethodsVTE risk data of urological inpatients were obtained based on the Caprini scale in the case hospital. Based on the data, the Boruta method was used to further select the key variables from the 37 variables in the Caprini scale. Furthermore, decision rules corresponding to each risk level were generated using the rough set (RS) method. Finally, random forest (RF), support vector machine (SVM), and backpropagation artificial neural network (BPANN) were used to verify the data accuracy and were compared with the RS method.ResultsFollowing the screening, the key risk factors for VTE in urology were “(C1) Age,” “(C2) Minor Surgery planned,” “(C3) Obesity (BMI > 25),” “(C8) Varicose veins,” “(C9) Sepsis (< 1 month),” (C10) “Serious lung disease incl. pneumonia (< 1month) ” (C11) COPD,” “(C16) Other risk,” “(C18) Major surgery (> 45 min),” “(C19) Laparoscopic surgery (> 45 min),” “(C20) Patient confined to bed (> 72 h),” “(C18) Malignancy (present or previous),” “(C23) Central venous access,” “(C31) History of DVT/PE,” “(C32) Other congenital or acquired thrombophilia,” and “(C34) Stroke (< 1 month.” According to the decision rules of different risk levels obtained using the RS method, “(C1) Age,” “(C18) Major surgery (> 45 minutes),” and “(C21) Malignancy (present or previous)” were the main factors influencing mid- and high-risk levels, and some suggestions on VTE prevention were indicated based on these three factors. The average accuracies of the RS, RF, SVM, and BPANN models were 79.5%, 87.9%, 92.6%, and 97.2%, respectively. In addition, BPANN had the highest accuracy, recall, F1-score, and precision.ConclusionsThe RS model achieved poorer accuracy than the other three common machine learning models. However, the RS model provides strong interpretability and allows for the identification of high-risk factors and decision rules influencing high-risk assessments of VTE in urology. This transparency is very important for clinicians in the risk assessment process.

Multi-modal incomplete label information three-way bidirectional decision-making: Applications of disease assessment

Disease assessment involves two stages of decision-making process. The first process is to infer the development trend of the disease through the existing judgment conditions, which is to make a positive estimation (prediction) decision. The second process is to update the judgment conditions for different disease states and optimize the clinical assessment evidence by fusing disease progression data, that is, to make a reverse evaluation (optimization) decision by reviewing historical diagnostic and treatment data to summarize the best judgment conditions for the disease characteristics. Therefore, we construct a three-way bidirectional decision method for multi-modal incomplete labeling information, considering the mixed data features with no labels and labels, and the bidirectional decision features of positive prediction and reverse optimization. Specifically, the method first introduces semi-supervised learning (SSL) into the rough sets, constructs a rough sets model based on cosine similarity relation, generates pseudo-labels for incomplete information, and explains the positive prediction decision process principle. Second, the gradient space is constructed on the predictive information system by the three-way decision-making principle, the loss function formed by the combination of KL divergence and cross entropy loss function is used to find the direction of the fastest decline in attribute information value, and the optimal decision rule and the automatic updating strategy of the threshold value are obtained. At the same time, the principle of the reverse optimization decision process is explained. Finally, multimodal information from pathological tissue images is used to evaluate clinical progress problem. A pathological tissue images dataset includes 2000 colorectal cancer and 300 kidney disease cases used for simulation experiments. The proposed three-way bidirectional decision-making model can be widely applied to actual decision-making scenarios for evaluating clinical progress of different diseases. Compared with previous studies, this method can realize objective calculation and automatic update of threshold and loss values and effectively solve complex prediction and optimization decision-making problems.

The novel WASPAS method for roughness of bipolar fuzzy sets based bipolar fuzzy covering

The research employs Covering-based Rough Set and Fuzzy Set theories to handle uncertainty in data analysis. However, when dealing with data uncertainty and bipolarity in various scenarios, the Bipolar Fuzzy Set (BFS) theory proves advantageous by simultaneously managing positive and negative information. Other sets, such as traditional fuzzy sets, often fail to capture this duality, leading to less comprehensive data analysis. This study pioneers a new methodology called the Theory of Roughness of Bipolar Fuzzy Sets, integrating Fuzzy Covering, Monotone Fuzzy Covering, and Bipolar Fuzzy Covering to propose an innovative decision-making approach. This novel concept undergoes comprehensive structural analysis. By incorporating the bipolar fuzzy covering based bipolar fuzzy rough set ( BFCBFRS ) model into conventional decision-making methods like the WASPAS technique, the research introduces a fresh perspective to address Multi-Criteria Decision-Making ( MCDM ) challenges. The efficacy of this extended method is evaluated by applying it to agricultural diagnosis, demonstrating its superiority over existing approaches through comparative analysis.

Feature selection based on neighborhood complementary entropy for heterogeneous data

In practical applications, there exists a large amount of heterogeneous data consisting of a mixture of numerical and categorical data, which are more complex and difficult to handle than a single class. In recent years, feature selection for heterogeneous data has received more and more attention from scholars. However, the current research on feature selection for heterogeneous data seldom takes into account the fineness of the granularity structure and the complementary information contained in the complements of each granularity. Addressing the shortcomings of existing efforts, this paper introduces complementary entropy into the neighborhood rough set model to define an uncertainty measurement system in heterogeneous data, and constructs the corresponding feature selection algorithm. First, the neighborhood complementary entropy and its associated uncertainty measures based on neighborhood relation are defined, and the relevant theoretical properties of these uncertainty measures are investigated. Then, based on the proposed uncertainty measures, a significance function is defined to assess the importance of candidate features. Next, a feature selection method for heterogeneous data is designed using neighborhood complementary entropy. Finally, the feasibility of the method proposed in this paper is demonstrated through an experimental comparative analysis with various existing feature selection methods.

Attribute reduction with fuzzy divergence-based weighted neighborhood rough sets

Neighborhood rough sets are well-known as an interesting approach for attribute reduction in numerical/continuous data tables. Nevertheless, in most existing neighborhood rough set models, all attributes are assigned the same weights. This may undermine the capacity to select important attributes, especially for high-dimensional datasets. To establish attribute weights, in this study, we will utilize fuzzy divergence to evaluate the distinction between each attribute with the whole attributes in classifying the objects to the decision classes. Then, we construct a new model of fuzzy divergence-based weighted neighborhood rough sets, as well as propose an efficient attribute reduction algorithm. In our method, reducts are considered under the scenario of the α-certainty region, which is introduced as an extension of the positive region. Several related properties will show that attribute reduction based on the α-certainty region can significantly enhance the ability to identify optimal attributes due to reducing the influence of noisy information. To validate the effectiveness of the proposed algorithm, we conduct experiments on 12 benchmark datasets. The results demonstrate that our algorithm not only significantly reduces the number of attributes compared to the original data but also enhances classification accuracy. In comparison to some other state-of-the-art algorithms, the proposed algorithm also outperforms in terms of classification accuracy for almost all of datasets, while also maintaining a highly competitive reduct size and computation time.

Intuitionistic fuzzy rough set model based on k-means and its application to enhance prediction of aptamer–protein interacting pairs

Intuitionistic fuzzy rough set model based on k-means and its application to enhance prediction of aptamer–protein interacting pairs

Label distribution feature selection based on hierarchical structure and neighborhood granularity

Label Distribution Learning (LDL) addresses label ambiguity in datasets but struggles with high-dimensional data due to irrelevant features. Label Distribution Feature Selection (LDFS) methods can effectively unravel the issues, but they often overlook the advantages of utilizing hierarchical relationships among data, which can improve feature discriminability. Furthermore, these methods inadequately consider the granulation process, directly affecting the important features’ identification. To overcome these challenges, this study proposes a novel LDFS approach incorporating hierarchical structures and neighborhood granularity. Our algorithm proceeds in three stages: initially, it forms a multi-granular representation of data to reveal hierarchical relationships; subsequently, in the granulation process, it employs a variable precision rough set model, leveraging neighborhood granularity for a nuanced feature relevance assessment; and finally, it synthesizes these findings via a fusion strategy, culminating in a hierarchical feature ranking. Extensive experiments are conducted on thirteen benchmark datasets against five different algorithms in terms of six evaluation metrics. The results show that our method outperforms competitors in about 80% of the cases, demonstrating its effectiveness and generalization.

A Novel generalization of sequential decision-theoretic rough set model and its application

This paper introduces a refined and broadened version of decision-theoretic rough sets (DTRSs) named Generalized Sequential Decision-Theoretic Rough Set (GSeq-DTRS), which integrates the three-way decision (3WD) methodology. Operating through multiple levels, this iterative approach aims to comprehensively explore the boundary region. It introduces the concept of generalized granulation, departing from conventional equivalence-relation-based structures to incorporate similarity/tolerance relations. GSeq-DTRS addresses the limitations encountered by its predecessor, Seq-DTRS, particularly in managing sequential procedures and integrating new attributes. A notable advancement is its seamless handling of continuous-scale datasets through a defined Generalized Granular Structure (GGS), enabling classification across multiple levels without necessitating reduction of attributes. A refined version of conditional probability (CP), aligned with tolerance classes, enhances the approach, supported by a meticulously designed algorithm. Extensive experimental analysis conducted on two datasets sourced from https://www.kaggle.com demonstrates the efficacy of the procedure for both continuous and discrete datasets, effectively classifying probable elements into POS or NEG regions based on their membership. Unlike traditional Seq-DTRS, it does not require reduction of attributes at each new level. Additionally, the algorithm exhibits lower sensitivity to parametric values and yields results in fewer iterations. Thus, its potential impact on decision-making processes is readily apparent.

A novel adaptive neighborhood rough sets based on sparrow search algorithm and feature selection

Neighborhood rough sets-based methods have been widely used for feature selection. However, the existing methods have some problems in neighborhood construction, such as the application of the same neighborhood radius for all samples. Thus, this paper proposed a novel adaptive neighborhood rough set model based on Sparrow Search Algorithm (SSA) to tackle the above problems, and applied the model to feature selection. First, we reconsidered the problems mentioned above from the viewpoint of optimization where the neighborhood radius of the target sample is considered as the solution to the optimization, and the maximum percentage of the label of the neighborhood formed is considered as the target to the optimization. Second, SSA is introduced to design the adaptive neighborhood construction to tackle the optimization problem where all candidate neighborhood radii of the target sample are considered as sparrows, the maximum and minimum distances between the target sample and other samples are considered as the search range, and the maximum label rate defined in this paper is considered as the search target. Then, a novel adaptive neighborhood rough set model is proposed by using the adaptive neighborhood construction. Third, we proposed a feature selection algorithm based on the adaptive neighborhood rough set model. Finally, the experimental results on seventeen datasets demonstrate the effectiveness of our algorithm. The running time of the proposed algorithm is at least one time less than classical algorithms under the condition that the classification performance is better, the accuracy increases 3% and the balanced accuracy increases 4%.