Rough Set Research Articles

Learning trustworthy model from noisy labels based on rough set for surface defect detection

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.

Explainable Prediction Technique for Analyzing Information Disorder Using Fuzzy Rough Sets

A persistent challenge in the domain of social media pertains to the comprehension and representation of information disorder incidents, which include but are not limited to erroneous information, theories of conspiracy, and racial discrimination. These issues frequently become apparent in the written content of posts that are shared on networking platforms and multiple sites. The complexity of information disorder research stems from the wide range of internet epidemic genres and the diverse effects that such information can have on people. Furthermore, the difficulty is exacerbated by the emergence of generative AI models that are capable of generating information that is difficult to identify as synthetic. The findings can assist analysts and decision-makers in acquiring a more in-depth comprehension of the phenomenon occurring in the field of information disorder. Hence, Information Disorder Prediction using Fuzzy Rough Set (IDP-FRS) has been proposed to predict the disinformation in the collected domain accurately and identify fake and real information. Through the incorporation of fuzzy sets of data into modelling and prediction techniques, the research improves the accuracy and interpretability of models, hence facilitating the discovery of disinformation in a more trustworthy manner. Moreover, the introduction of explainable prediction approaches gives users the ability to make educated choices concerning the appropriateness and dissemination of information, which in turn promotes openness and confidence in predictive models.

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.

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.

Multi-index evaluation on reinforcement programs for frame structures based on life cycle theory and time-varying reliability

Under the mandates of economic and environmental sustainability, the consideration of reinforcement engineering must extend beyond mere enhancement effects and short-term project costs. As a long-term engineering activity, reinforcement significantly impacts urban economies and environments. Although extensive research has evaluated the costs or environmental impacts of reinforcement engineering based on the whole life cycle theory, existing studies often focus on single indicators without adequately integrating them with other domains. Using a reinforced concrete frame structure as a case study, this paper develops a combined evaluation decision-making model integrating the Analytic Hierarchy Process for subjective assessment and an enhanced Rough Set method for objective evaluation. This model comprehensively assesses the seismic performance, economic costs, and environmental impacts of various reinforcement strategies. The results indicate that the combined strategy of enlarging column sections and carbon fiber reinforced polymer strengthening beams performs best in seismic performance, long-term economic benefits, and environmental impacts. Grounded in practical projects, this study adjusts the whole life cycle cost model to better align with engineering maintenance realities and introduces Rough Set theory to address deficiencies in objective indicator weighting. This research offers insights and guidance for leveraging information technology in resolving multi-criteria evaluation decision-making challenges in reinforcement engineering solutions.

An insightful multicriteria model for the selection of drilling technique for heat extraction from geothermal reservoirs using a fuzzy-rough approach

Geothermal energy stands out as an exceptional renewable resource for power generation, offering a consistent power production without the intermittency issues. Despite its potential to deliver a consistent supply of electricity on demand, geothermal adoption is hindered due to substantial costs. Utilising the most effective drilling method can alleviate this challenge by boosting efficiency and reducing operational costs. The primary goal of this study is to identify the best drilling method for extracting heat from geothermal reservoirs. This optimised approach facilitates better access to geothermal reservoirs, leading to increased heat recovery rates and improved project viability. Traditional methods often fall short in evaluating optimal drilling alternatives due to uncertainties. To address this, our research introduces an innovative paradigm that integrates novel T-Spherical Hesitant Fuzzy Rough (T−SHFR) set, method for the removal effects of criteria with a geometric mean and ranking alternatives with weights of criterion hybrid Multiple Criteria Decision-Making (MCDM) techniques. By leveraging the novel T−SHFR concept, our approach allows for a comprehensive assessment of various factors. This holistic evaluation ensures an exhaustive comprehension of the decision-making environment. The study reveals that reservoir characteristics play a significant role in selecting a sustainable drilling alternative. Furthermore, directional drilling appears as the most promising method with higher energy yields followed by slim hole drilling. The robustness and credibility of these findings are established through sensitivity and comparative analyses, indicating the potential applicability of this MCDM method to analogous challenges in different contexts. The findings of the ranking techniques were validated using Spearman's rank correlation coefficient, which revealed a positive and notable correlation. This research will empower stakeholders to make informed decisions, thereby enhancing the overall efficiency and sustainability of geothermal energy projects.

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.

The green development in China through the lens of complex cybernetics: Insight for a new era

Measuring the level of green development is far from being a well-assessed problem, due to both the broad meaning of green development and the presence of randomness in environmental changes. In this paper, we develop the sustainable development evaluation index system from different perspectives, including resource utilization, green development management, green development quality, environmental protection, growth quality and green lifestyle. This evaluation index system is further viewed as a cybernetic system. Following a rough set approach, we properly address the issue of uncertainty and develop a robust estimation methodology. Neighborhood rough set and rough set methods based on genetic algorithms (GAs) have been used to identify the key indicators within the system. First, the results illustrate how a cybernetic approach deals with green policy and economic growth. Second, such a cybernetic approach provides new insights into identifying the main attributes for a sustainable development. Finally, stategies of improving green development in different parts of China are provided, concluding this paper.

Advanced image analysis for medical diagnostics: a system for segmentation and classification using level set methods and AI algorithms

This work aims to implement and utilize an advanced computer system for image analysis and processing through artificial intelligence. The system will evaluate images from multiple sources. As a result, a comprehensive e-Medicus system will be developed to capture and analyze X-ray data and classify cancer cells. This innovative tool, with its unique features tailored for medical facilities, will assist them in capturing and analyzing X-ray images and CT scan results. The e-Medicus system offers several benefits for medical facilities, including efficient automation of photo analysis, tracking changes in a patient's condition over time, and facilitating the identification of medical changes and data classification. A multimedia presentation of the change process will use the contour set function, allowing for topological changes in solution properties. The system integrates novel procedures and algorithms from theoretical computer science and numerical mathematics, leveraging neural networks, genetic algorithms, semantic networks, image ontology, rough set theory, contour set methods, and hybrid algorithms. These developed algorithms enhance methods and concepts in image segmentation, gathering, transmitting, storing, extracting, and effectively presenting information.

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

New categories of coverings in terms of rough fuzzy sets

New categories of coverings in terms of rough fuzzy sets

Algebraic rough sets via algebraic relations

Algebraic rough sets via algebraic relations

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-label-Specific Features Learning Algorithm Based on Label Importance and Fuzzy Rough Set

Multi-label-Specific Features Learning Algorithm Based on Label Importance and Fuzzy Rough Set

Retraction Note: Framework to forecast environment changes by optimized predictive modelling based on rough set and Elman neural network

Retraction Note: Framework to forecast environment changes by optimized predictive modelling based on rough set and Elman neural network

Attribute reduction using self-information uncertainty measures in optimistic neighborhood extreme-granulation rough set

The pessimistic and optimistic neighborhood multi-granulation rough sets (PNMRS and ONMRS) have been applied to attribute reduction. Nonetheless, the setting of the granulation space in both models is usually based on expert experience or continuous trials, which are poorly interpretable. Besides, the dependency, an important attribute evaluation function in PNMRS and ONMRS, only considers classification information in the lower approximation and ignores that of the upper approximation, affecting its evaluation effect. Thus, we firstly propose the pessimistic and optimistic neighborhood extreme-granulation rough sets (PNERS and ONERS) based on the minimum granulation space, avoiding the unobjective setting of the granulation space. However, PNERS describes knowledge with low accuracy, and therefore we construct two self-information uncertainty measures in ONERS and propose the joint self-information that is more suitable for attribute reduction as it takes full consideration of classification information in the lower and upper approximations. Then, an attribute reduction method using the joint self-information is designed, and Fisher Score is introduced into our method to decrease time cost when processing high dimensional data. Extensive experiments validate that our method is able to achieve superior reduction and classification results on different dimensional datasets.

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.

Supervised spectral feature selection with neighborhood rough set

Spectral feature selection, an excellent dimensionality reduction method, is extensively used in knowledge mining and protein sequence analysis. However, the graph representation derived from data with potential noises significantly impacts feature selection performance. Similarly, its performance deteriorates when label information is ignored, as the selected features have poor discrimination ability. To overcome these drawbacks, this article optimizes neighborhood structure and further constructs the conditional entropy based on neighborhood purity to generate a precise graph representation incorporating label information to enhance the compactness of intra-class samples and increase the dispersion between inter-class samples. Then this article proposes a novel spectral feature selection method. Specifically, the method dynamically learns the precise graph representation from low-dimension space, which can effectively preserve the local structure of data, and the global structure is preserved by introducing a constraint term that maintains the graph representation before and after dimension reduction. Additionally, ℓ2,1-norm is introduced to ensure row sparsity and select the valuable features. The alternative optimization algorithm is employed to solve the optimization problem and its convergence is theoretically analyzed. Finally, to assess the performance of the proposed method, a series of comprehensive experiments are performed on several real-world datasets.

Financial multidimensional assessment of a green hydrogen generation process via an integrated artificial intelligence-based four-stage fuzzy decision-making model

It is widely accepted that there is an urgent need to make green hydrogen (GH2) projects financially viable to reduce global warming. However, any form of improvements to these GH2 projects lead to substantial cost increase. Due to this cost increase, making many improvements negatively affects the financial profitability of hydrogen projects. This is why there is a need for new advanced financial priority analysis tools so that it is easier to develop GH2 projects globally. Accordingly, the aim of this study is to identify and then define the most important factors affecting GH2 generation projects. To achieve this aim, this work proposes a new fuzzy multi-criteria decision-making model based on artificial intelligence (AI). First, experts are weighted with AI technique. Second, the missing evaluations are filled via a recommender system. Third, criteria weights are calculated by the M-SWARA technique integrated with quantum picture fuzzy rough (QPFR) sets. Finally, GH2 energy generation processes are listed by the QPFR-VIKOR approach. Overall, the main contribution of this study is the generation of a comprehensive AI oriented fuzzy decision-making model to make a detailed evaluation with respect to the financial potential improvements of the GH2 generation projects. The main originality of this model is the consideration of AI to calculate the weights of the criteria. Similarly, another benefit of the proposed model, that increases its superiority against other models, is the completion of missing evaluations by experts thanks to the recommender system. It is concluded that the most important criterion affecting green hydrogen investments is organizational effectiveness.