Fuzzy Rough Set Theory Research Articles

Exploring Climate Interactions: A Fuzzy Rough Set Theory Approach

Analysing climate change is challenging due to climate data’s intricate and dynamic nature. The primary issue is starting with high dimensionality. High dimensionality impacts the model’s performance, computation time, cost, and accuracy. Feature selection can be employed as a strategy to address the issue of dimensionality reduction, resulting in more precise insights and the identification of more explicit patterns. Various techniques are used for feature selection. Still, there is scope for progress in this field. This study uses fuzzy rough set theory (FRST) to perform feature selection in the analysis of climatic data. The dataset in the present study, obtained from Kaggle, is an authentic climate change dataset in the real world. FRST effectively addresses uncertainty and vagueness in climate data by identifying the most relevant temperature parameters and treating them as the deciding attribute. We identified 25 reducts from the original dataset using FRST. Compared to the original dataset, the best reducts had good classification accuracy. It indicates that FRST reducts preserve the essential features of the original climate data, assuring the reduced dataset’s integrity and relevance. FRST was more accurate than usual climate data analysis methods, proving its efficacy.

FRRI: A novel algorithm for fuzzy-rough rule induction

Interpretability is the next frontier in machine learning research. In the search for white box models — as opposed to black box models, like random forests or neural networks — rule induction algorithms are a logical and promising option, since the rules can easily be understood by humans. Fuzzy and rough set theory have been successfully applied to this archetype, almost always separately. As both approaches offer different ways to deal with imprecise and uncertain information, often with the use of an indiscernibility relation, it is natural to combine them. The QuickRules [20] algorithm was a first attempt at using fuzzy rough set theory for rule induction. It is based on QuickReduct, a greedy algorithm for building decision superreducts. QuickRules already showed an improvement over other rule induction methods. However, to evaluate the full potential of a fuzzy rough rule induction algorithm, one needs to start from the foundations. Accordingly, the novel rule induction algorithm, Fuzzy Rough Rule Induction (FRRI), we introduce in this paper, uses an approach that has not yet been utilised in this setting. We provide background and explain the workings of our algorithm. Furthermore, we perform a computational experiment to evaluate the performance of our algorithm and compare it to other state-of-the-art rule induction approaches. We find that our algorithm is more accurate while creating small rulesets consisting of relatively short rules.

Fuzzy–Rough Analysis of ESG Ratings and Financial and Growth Ratios on the Stock Returns of Blue-Chip Stocks in Taiwan

This study uses fuzzy–rough analysis to investigate the influence of Environmental, Social, and Governance (ESG) ratings, along with critical financial and growth ratios, on the stock returns of blue-chip companies in Taiwan. The growing importance of ESG factors in investment decisions underscores the need to understand their impact on stock performance. By integrating the fuzzy–rough set theory, which accommodates uncertainty and imprecision in data, we analyze the complex relationships between ESG ratings, traditional financial metrics (such as ROE, return on equity), and stock returns. Our findings provide insights into how ESG considerations, alongside financial indicators, drive the returns of Taiwan’s blue-chip stocks. Three public-listed companies were evaluated using this approach, and the results are consistent with the actual stock performance. This research contributes to the field by offering a robust methodological approach to assess the nuanced effects of ESG factors on financial performance, thus aiding investors and management teams in making informed decisions.

Short-Term Electrical Load Forecasting Based on Fuzzy Rough Set Feature Selection and Multi-kernel Extreme Learning Machine

As the complexity of power systems increases, accurate load forecasting becomes crucial. This paper proposes a method for short-term electrical load forecasting that integrates fuzzy rough set (FRS) theory and multi-kernel extreme learning machine (MKELM) to improve both the accuracy and reliability of load predictions. First, we introduce the FRS theory for pre-selecting features. Next, we use correlation analysis (CA) to get rid of redundant features and choose the most important ones as prediction targets. Second, we introduce a novel prediction model based on the multi-kernel extreme learning machine (MKELM), utilizing an enhanced differential evolution algorithm (DEA) to optimize the kernel function’s parameters and the model’s weights. This approach allows for effective adaptation to various feature subsets. Experimental results on actual power load data demonstrate that our approach achieves high accuracy and reliability in short-term load forecasting. Moreover, comparative evaluations reveal that the proposed method outperforms alternative prediction models on key metrics. ANOVA and multiple comparisons further validate the statistical significance and superiority of the proposed method.

Modeling methods for deep fuzzy inference systems based on feature selection

A bottom-up, layer-by-layer feature selection modeling method is proposed for deep fuzzy inference systems. By selecting features in the input space, redundant and interfering features in each layer's input space can be removed. The selected features have been appropriately ordered to avoid the randomness of features within the feature sliding window. Based on fuzzy rough set theory, the matching degree between the fuzzy granules associated with the conditional feature set and those associated with the decision feature is used as a likelihood function. The λ-AIC criterion with a penalty term have been redefined as an evaluation index for features. The obtained model is compared to four baseline models and an existing deep fuzzy rule classification system. The results show that the feature selection-based deep fuzzy inference system effectively improves data classification performance and efficiency. Compared to four rough set-based feature selection methods based on different measures, the method proposed is more convincing in terms of accuracy and the number of features selected. Compared to the modeling method where input space features are randomly shuffled, the feature sorting modeling method performs better and avoids the instability in model accuracy caused by randomness.

An oversampling algorithm of multi-label data based on cluster-specific samples and fuzzy rough set theory

Imbalanced class distributions are common in real-world scenarios, including datasets with multiple labels. One widely acknowledged approach to addressing imbalanced distributions is through oversampling, a technique that both balances the class distribution and improves the effectiveness of classification models. However, when generating synthetic data for multi-label datasets, complexities arise due to the presence of multiple-label sets, which require careful placement and labeling. We propose MLCSMOTE-FRST, an algorithm for synthetic data generation based on label-specific clustering and fuzzy rough set theory. Generation ratios and dependency samples are provided by clusters specific to each label, with a focus on the overall label distribution and the distribution within each cluster. The labels are supported by intra-cluster positive samples, determined using fuzzy rough set theory, which helps to capture the consensus label set. Experimental results on multi-label datasets using four classifiers demonstrate the effectiveness of the proposed method in terms of macro-F1 and micro-F1 scores.

Consistency approximation: Incremental feature selection based on fuzzy rough set theory

Fuzzy Rough Set Theory (FRST)-based feature selection has been widely used as a preprocessing step to handle dynamic and large datasets. However, large-scale or high-dimensional datasets remain intractable for FRST-based feature selection approaches due to high space complexity and unsatisfactory classification performance. To overcome these challenges, we propose a Consistency Approximation (CA)-based framework for incremental feature selection. By exploring CA, we introduce a novel significance measure and a tri-accelerator. The CA-based significance measure provides a mechanism for each sample in the universe to keep members with different class labels within its fuzzy neighbourhood as far as possible, while keeping members with the same label as close as possible. Furthermore, our tri-accelerator reduces the search space and decreases the computational space with a theoretical lower bound. The experimental results demonstrate the superiority of our proposed algorithm compared to state-of-the-art methods on efficiency and classification accuracy, especially for large-scale and high-dimensional datasets.

Classification of artificial intelligence tools for civil engineering under the notion of complex fuzzy rough Frank aggregation operators

In recent days researchers have tried to handle the maximum information and use those techniques and methods in which there is no chance of data loss or loss of information is minimum. The structure like fuzzy set and complex fussy set cannot discuss the upper and lower approximations. Moreover, we can observe that a fuzzy rough set cannot discuss the second dimension and in this case, there is a chance of data loss. To cover all these issues in previous ideas, the notion of a complex fuzzy rough set in Cartesian form is the demand of the day because this structure can discuss the second dimension as well as upper and lower approximations. For this purpose, in this manuscript, we have developed the theory of complex fuzzy relation and complex fuzzy rough set in Cartesian form. Moreover, we have initiated the fundamental laws for complex fuzzy rough numbers based on Frank t-norm and t-conorm. The fundamental tools that can convert the overall input into a single output are called aggregation operators (AOs). So based on the characteristics of AOs, we have defined the notion of complex fuzzy rough Frank average and complex fuzzy rough Frank geometric AOs. The utilization of the developed theory is necessary to show the importance and validity of the delivered approach. So based on developed notions, we have defined an algorithm for this purpose along with an illustrative example. We have utilized the introduced structure for the classification of AI tools for civil engineering. Moreover, the comparative analysis of the delivered approach shows the advancement of the introduced structure as compared to existing notions.

Assessing indoor positioning system: A q-spherical fuzzy rough TOPSIS analysis

This study investigates advanced data collection methodologies and their implications for understanding employee and customer behavior within specific locations. Employing a comprehensive multi-criteria decision-making framework, we evaluate various technologies based on four distinct criteria and four technological alternatives. To identify the most effective technological solution, we employ the q-spherical fuzzy rough TOPSIS method, integrating three key parameters: lower set approximation, upper set approximation, and parameter q (where q ≥ 1). Our novel approach combines the TOPSIS method with q-spherical fuzzy rough set theory, providing deeper insights into data-driven decision-making processes in corporate environments. By comparing our proposed framework with existing multi-criteria decision-making methodologies, we demonstrate its strength and competitiveness. This research contributes to enhancing decision-making capabilities in corporate settings and beyond.

A novel intuitionistic fuzzy rough instance selection and attribute reduction with kernelized intuitionistic fuzzy C-means clustering to handle imbalanced datasets

Due to advancement of internet and lab based technologies, large volume of high dimensional data are generated every day. These data usually consisted of several issues such as class imbalance, noise, later uncertainty, irrelevant and/or redundant features, and redundancy in size. These issues degrade the overall performance measures of the various machine learning algorithms. An efficient method to cope with such issues for a large sized datasets is to apply efficient data reduction techniques. In the recent years, numerous data reduction techniques have been presented based on fuzzy rough set theory to tackle these obstacles. However, building such a method that can handle all the above mentioned issues simultaneously is still a challenging task. In this study, we handle all these obstacles simultaneously by introducing a novel approach to obtain the reduced dataset by combining kernelized intuitionistic fuzzy C-means with intuitionistic fuzzy rough set model. Intuitionistic fuzzy rough set handles the vagueness and uncertainty in a better way than fuzzy set aided models as it takes use of membership, non-membership as well as hesitancy to capture the uncertainty of real-valued datasets. To generate the membership and non-membership grades, kernelized intuitionistic fuzzy C- means based notion is introduced. Further, an intuitionistic fuzzy rough set model is established by addressing lower and upper approximations based on a novel similarity relation. Moreover, all the necessary conditions are justified with the relevant mathematical theorems. Next, this model is employed for dimensionality reduction based on the concept of discernibility matrix by using the idea of different classes’ ratios to avoid the noise. Thereafter, positive region is defined with the help of lower approximation. The positive region information is applied to tackle problematic instances available in both minority and majority class for the imbalanced dataset after generation of artificial samples by synthetic minority oversampling technique (SMOTE). A comprehensive experimental study is added to show the effectiveness of the proposed technique. Finally, a framework is established to improve the prediction of animal toxin peptides.

Variation of New Energy Vehicle Product Scores Based on Fuzzy Rough Set Theory and Cellular Automaton

This study investigates the fluctuation in product scores of new energy vehicles (NEVs) using a combination of fuzzy rough set theory and cellular automaton. By integrating these two methodologies, we aim to provide a comprehensive understanding of how NEV product scores evolve over time. Firstly, the fuzzy rough set theory is employed to handle the uncertainty and imprecision inherent in NEV product evaluation, optimizing the selection of influential factors. Subsequently, a cellular automaton model is utilized to simulate the dynamic changes in NEV product scores, incorporating factors identified through fuzzy rough set theory. Through this combined approach, we can continuously monitor and analyze the variations in NEV product scores, enabling stakeholders to make informed decisions for improving product competitiveness and market performance. This study contributes to the advancement of methodologies for evaluating NEV products and offers insights into the dynamic nature of their competitive landscape.

Hybrid similarity relation based mutual information for feature selection in intuitionistic fuzzy rough framework and its applications

Fuzzy rough entropy established in the notion of fuzzy rough set theory, which has been effectively and efficiently applied for feature selection to handle the uncertainty in real-valued datasets. Further, Fuzzy rough mutual information has been presented by integrating information entropy with fuzzy rough set to measure the importance of features. However, none of the methods till date can handle noise, uncertainty and vagueness simultaneously due to both judgement and identification, which lead to degrade the overall performances of the learning algorithms with the increment in the number of mixed valued conditional features. In the current study, these issues are tackled by presenting a novel intuitionistic fuzzy (IF) assisted mutual information concept along with IF granular structure. Initially, a hybrid IF similarity relation is introduced. Based on this relation, an IF granular structure is introduced. Then, IF rough conditional and joint entropies are established. Further, mutual information based on these concepts are discussed. Next, mathematical theorems are proved to demonstrate the validity of the given notions. Thereafter, significance of the features subset is computed by using this mutual information, and corresponding feature selection is suggested to delete the irrelevant and redundant features. The current approach effectively handles noise and subsequent uncertainty in both nominal and mixed data (including both nominal and category variables). Moreover, comprehensive experimental performances are evaluated on real-valued benchmark datasets to demonstrate the practical validation and effectiveness of the addressed technique. Finally, an application of the proposed method is exhibited to improve the prediction of phospholipidosis positive molecules. RF(h2o) produces the most effective results till date based on our proposed methodology with sensitivity, accuracy, specificity, MCC, and AUC of 86.7%, 90.1%, 93.0% , 0.808, and 0.922 respectively.

A fuzzy rough granular ensemble learning based on the feature selection with chi-square1

Neighborhood granulation is a classical granulation method. Although it is adequate for clustering and classification tasks, its granules are more complex, and the data representation is binary. This paper proposes a new granulation method based on the neighborhood granulation. Firstly, a detailed definition of the granular form is given with fuzzy rough set theory. Then, a modified fuzzy rough discriminant function is proposed based on neighborhood systems. The samples are globally granulated on single features to construct granules and on multiple features to construct granular vectors. Also, a feature selection technique based on the Chi-square, which strikingly reduces the complexity of the fuzzy rough granular vectors, is introduced to address the disadvantage of the fuzzy rough granular vectors. An ensemble model structure is also proposed in the paper for the mixed nature of fuzzy rough granular vectors. The paper makes a detailed comparison between the fuzzy rough granulation and the neighborhood granulation. The results show that fuzzy rough granulation has higher computational efficiency and classification performance. Finally, a detailed comparison is made between the fuzzy rough granular ensemble model and various classical ensemble algorithms. The final results show that the fuzzy rough granular ensemble model has better robustness and generalization.

Research on automatic detection of gradual fault of high voltage electric energy metering transformer based on fuzzy rough set and whale optimization algorithm

Based on fuzzy rough set and whale optimization algorithm, the automatic fault detection method of high-voltage electric energy metering transformer is studied to improve the fault diagnosis effect and efficiency. On the basis of constructing the mathematical model of gradual fault of high-voltage electric energy metering transformer, the fuzzy rough set theory is used to reduce the data attributes of fault samples, eliminate similar attributes, determine the minimum fault feature set, and complete the fault feature selection, which is used as the input of the fault detection model based on Whale Optimization Algorithm-based Support Vector Machine (WOA-SVM). After the kernel parameters and penalty factors of SVM are optimized by whale optimization algorithm, the type of gradual fault of high-voltage electric energy metering transformer is identified. The experimental results show that the reduced fault attributes are distributed differently in the sample data, and the fault detection accuracy can be improved by 9.5 % through fault feature selection. The fault diagnosis model with Gaussian radial basis function, kernel parameter of 0.05 and penalty factor of 10 has the best performance. This method can identify the gradual fault types of high-voltage electric energy metering transformers, and the fault diagnosis effect is outstanding.

Distributed Feature Selection for Power System Dynamic Security Region Based on Grid-Partition and Fuzzy-Rough Sets

In order to satisfy the requirements of modern online security assessment of power systems with continuously increasing complexity in terms of structure and scale, it is desirable to develop a power system dynamic security region (DSR) analysis. However, data-driven methods suffer from expensive model training costs and overfitting when determining DSR boundaries with high-dimensional grid features. Given this problem, a distributed feature selection method based on grid partition and fuzzy-rough sets is proposed in this paper. The method first employs the Louvain algorithm to partition the power grid and divide the original feature set so that high-dimensional features can be allocated to multiple computational units for distributed screening. At this point, the connections between features of different computational units are minimized to a relatively low level, thereby avoiding large errors in the distributed results. Then, an incremental search algorithm based on the fuzzy-rough set theory (FRST) is used for feature selection at each computational unit, which can effectively take into account the intrinsic connections between features. Finally, the results of all computational units are integrated in the coordination unit to complete the overall feature selection. The experimental results based on the IEEE-39 bus system show that the proposed method can help simplify the power system DSR analysis with high-dimensional features by screening the critical features. And compared with other commonly used filter methods, it has higher screening accuracy and lower time costs.

Evaluation and ranking of fuzzy sets under equivalence fuzzy relations as [formula omitted]certainty and [formula omitted]possibility

In this paper, we deal with a finite collection of fuzzy sets that are used to represent a given linguistic variable in real-world problems. These fuzzy sets are usually represented as fuzzy singletons, fuzzy numbers, or fuzzy G-numbers. In many cases, there are significant interactions between elements of a given set, so it is useful to evaluate and rank elements while taking the degree of interactions into consideration. To find the degree of interaction, we develop a fuzzy equivalence relation based on a similarity function and a triangular norm operator. The compositions of the (max -(T-norm)) and (min -(S-norm)) cause the membership function to change from the minimum values (certainty version) to the maximum values (possibility version). These concepts are also useful for improving fuzzy data mining, rough fuzzy set theory, etc. Furthermore, two indices, α and β, are introduced to determine the degree of certainty (α-certainty) and degree of possibility (β-possibility). Examples are provided to compare the proposed method with the existing method. After comparing the experimental results, it can be concluded that the proposed approach is satisfactory for many situations. Finally, we apply the proposed methodology to evaluate the results of a hospital efficiency study conducted for the Office of Inspector General(OIG)-Eastern Virginia Department of Health and Human Services.

Research on Industrial Economics Models in Rapid Development of Digital Economy

Abstract Amidst the rapid evolution of the digital economy, this research positions fuzzy rough set theory at the forefront of industrial economic modeling, acknowledging its profound capability to manage uncertain information. This theory’s analytical precision facilitates a deep dive into the dynamics of industrial economic growth, enabling the refinement of industrial structures for sustainable development. Our empirical investigation into region A’s grain industry showcases a remarkable output growth of 272.88% from 2008 to 2018, with a model accuracy exceeding 95%. Analysis on cost inputs further demonstrates how innovation in science and technology plays a crucial role in cost reduction. By leveraging fuzzy rough set theory, this work contributes significantly to the strategic development of industrial economics, offering a robust methodology for data-driven analysis and forecasting in industrial sectors.

Exploiting fuzzy rough entropy to detect anomalies

Anomaly detection has been used in a wide range of fields. However, most of the current detection methods are only applicable to certain data, ignoring uncertain information such as fuzziness in the data. Fuzzy rough set theory, as an essential mathematical model for granular computing, provides an effective method for processing uncertain data such as fuzziness. Fuzzy rough entropy has been proposed in fuzzy rough set theory and has been employed successfully in data analysis tasks such as feature selection. However, it mainly uses the intersection operation, which may not effectively reflect the similarity between high-dimensional objects. In response to the two challenges mentioned above, distance-based fuzzy rough entropy and its correlation measures are proposed. Further, the proposed fuzzy rough entropy is used to construct the anomaly detection model and the Fuzzy Rough Entropy-based Anomaly Detection (FREAD) algorithm is designed. Finally, the FREAD algorithm is compared and analyzed with some mainstream anomaly detection algorithms (including COF, DIS, INFLO, LDOF, LoOP, MIX, ODIN, SRO, and VarE algorithms) on some publicly available datasets. Experimental results indicate that the FREAD algorithm significantly outperforms other algorithms in terms of performance and flexibility. The code is publicly available online at https://github.com/optimusprimeyy/FREAD.

Fusing multi-scale fuzzy information to detect outliers

Outlier detection aims to find objects that behave differently from the majority of the data. Existing unsupervised approaches often process data with a single scale, which may not capture the multi-scale nature of the data. In this paper, we propose a novel information fusion model based on multi-scale fuzzy granules and an unsupervised outlier detection algorithm with the fuzzy rough set theory. First, a multi-scale information fusion model is formulated based on fuzzy granules. Then we employ fuzzy approximations to define the outlier factor of multi-scale fuzzy granules centered at each data point. Finally, the outlier score is calculated by aggregating the outlier factors of a set of multi-scale fuzzy granules. Experimental results demonstrate that the proposed method is comparable with or better than the leading outlier detection methods. The codes and datasets are publicly available online at https://github.com/ChenBaiyang/MFIOD.

Enhancing pancreatic cancer classification through dynamic weighted ensemble: a game theory approach

The significant research carried out on medical healthcare networks is giving computing innovations lots of space to produce the most recent innovations. Pancreatic cancer, which ranks among of the most common tumors that are thought to be fatal and unsuspected since it is positioned in the region of the abdomen beyond the stomach and can’t be adequately treated once diagnosed. In radiological imaging, such as MRI and CT, computer-aided diagnosis (CAD), quantitative evaluations, and automated pancreatic cancer classification approaches are routinely provided. This study provides a dynamic weighted ensemble framework for pancreatic cancer classification inspired by game theory. Grey Level Co-occurrence Matrix (GLCM) is utilized for feature extraction, together with Gaussian kernel-based fuzzy rough sets theory (GKFRST) for feature reduction and the Random Forest (RF) classifier for categorization. The ResNet50 and VGG16 are used in the transfer learning (TL) paradigm. The combination of the outcomes from the TL paradigm and the RF classifier paradigm is suggested using an innovative ensemble classifier that relies on the game theory method. When compared with the current models, the ensemble technique considerably increases the pancreatic cancer classification accuracy and yields exceptional performance. The study improves the categorization of pancreatic cancer by using game theory, a mathematical paradigm that simulates strategic interactions. Because game theory has been not frequently used in the discipline of cancer categorization, this research is distinctive in its methodology.