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Multi-tier sustainable supply chain relationships (MSSCR) are complex with involvement of multiple organisations, practices, objectives, and interconnectivities. These complexities make it difficult to effectively study MSSCR using traditional empirical statistical correlative research. In MSSCR the relationship between the focal firm and sub-supplier may be affected by the relationship between the focal firm and direct-supplier, and the relationship between the direct-supplier and the sub-supplier. This paper introduces a research methodology, based on K-Means clustering, rough set theory, and cluster membership to investigate complex relationships across multi-tier sustainable supply chain triads. Collaborative advantage variables including knowledge-sharing routines, relation-specific investments, complementary capabilities, effective governance mechanisms, and long-term commitment are conceptually presented to evaluate relationships among MSSCR practices and sustainability performance. Insights for practitioners and researchers are provided. Research insights can be gained by analytically providing alternative explanatory and equifinality relationships amongst variables and multi-pair organisations. The methodology can mitigate the endogeneity problem, such as omitted factors (variables), measurement error, even in small sample data situations. Directions for future research are discussed. [ABSTRACT FROM AUTHOR]

Cognitive computation has leveraged the capabilities of computer algorithms, rendering it an exceptionally efficient approach for addressing multi-attribute group decision-making (MAGDM) problems. Due to the stability of MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and the capability of evidential reasoning (ER) to combine information from multiple sources, the technique of multigranulation probabilistic rough sets (MG PRSs) holds great promise for solving MAGDM problems. Thus, a new and stable method for MAGDM is proposed. Initially, three forms of multigranulation Pythagorean fuzzy probabilistic rough sets (MG PF PRSs) are constructed using MULTIMOORA approaches. Next, the hierarchical clustering method is employed to cluster similar decision information and consolidate the decision-makers' preferences. Representatives are chosen from each category to simplify information fusion calculations and reduce complexity by reducing the model's dimensionality. Following that, the rankings obtained from the three methods are fused using ER. Ultimately, the validity of our method is revealed via a case analysis on chickenpox cases from the UCI data set by employing cognitive analysis. The paper outlines a method for MAGDM that provides significant advantages. Specifically, the use of MULTIMOORA improves the stability of decision results, while the incorporation of ER reduces the overall uncertainty of entire decision processes. [ABSTRACT FROM AUTHOR]

The miRNA is a tiny, single-stranded RNA of nearly 22 nucleotides long that is transcribed from DNA and controls the genes in protein synthesis process. As expression levels of miRNAs vary significantly between cancerous and non-cancerous cells. Therefore, miRNAs can play a vital role in the development of cancer. Cancer classification from miRNA gene expression data is an area of interest to the bioinformatics and computational biology researches in recent past. However, traditional machine learning classifiers often do not produce the desired results due to lack of training patterns present in miRNA data. Additionally they are not often able to deal with overlapping, vague, uncertain, ambiguous and indiscernible cancer subtypes classes of the miRNA data. Motivated from the above said issues, we propose a novel semi-supervised fuzzy-rough based extreme learning machine (SSFRELM) method. Two stages are involved in the proposed method, where in the first stage, the soft class labels of the unlabeled samples are assigned using fuzzy-rough set theory, those are subsequently applied on the semi-supervised extreme learning machine in the second stage. The proposed SSFRELM method can improve classification accuracy since it utilizes unlabeled patterns together with limited labeled patterns in the learning process to develop the semi-supervised extreme learning machine and can handle the overlapping, vague, uncertainty, ambiguity, and indiscernibility usually present in miRNA gene expression data as it uses fuzzy-rough set theory. The proposed method is assessed using eight publicly available miRNA gene expression datasets from five different cancer types with respect to various classification evaluation measures in comparison to four other state-of-the-art methods. Experimental results justify that the proposed method outperformed the other counter-parts methods for cancer pattern classification. Paired t-test results also confirm the statistical significance of the better results achieved by the proposed SSFRELM over other methods for most of the cases. [ABSTRACT FROM AUTHOR]

This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization of these innovative ideals is accomplished by employing the (α , β) -cut of intuitionistic fuzzy sets in the context of BCK-algebras. [ABSTRACT FROM AUTHOR]

Rough set theory is a methodology that defines the definite or probable membership of an element for exploring data with uncertainty and incompleteness. It classifies data sets using lower and upper approximations to model uncertainty and missing information. To contribute to this goal, this study presents a newer approach to the concept of rough sets by introducing a new type of neighborhood called j-transitive neighborhood or j-TN. Some of the basic properties of j-transitive neighborhoods are studied. Also, approximations are obtained through j-TN, and the relationships between them are investigated. It is proven that these approaches provide almost all the properties provided by the approaches given by Pawlak. This study also defines the concepts of lower and upper approximations from the topological view and compares them with some existing topological structures in the literature. In addition, the applicability of the j-TN framework is demonstrated in a medical scenario. The approach proposed here represents a new view in the design of rough set theory and its practical applications to develop the appropriate strategy to handle uncertainty while performing data analysis. [ABSTRACT FROM AUTHOR]

Aptamers are very interesting peptide molecules or oligonucleic acid. They are used to bind particular target molecules. Aptamers play vital roles in various practical applications and physiological functions. Consequently, several diseases can be treated using therapies based on aptamer proteins and designing the binding of aptamers to specific proteins is essential to advance understanding into processes of interaction between aptamer-protein. Despite the wide applications of aptamers, identification of interaction between aptamer protein is always inadequate and challenging. Therefore, it is necessary to develop a computational approach for achieving good predictions of interaction between aptamer-protein. In the present study, a novel method for enhancing the prediction of interacting aptamer-target pairs based on sequence features obtained from both aptamers and their target proteins by employing a novel k-mean based intuitionistic fuzzy rough feature selection method is proposed. Firstly, an intuitionistic fuzzy rough set model based on k nearest neighbour concept is proposed. Then, a novel feature selection technique is introduced by using this model. Furthermore, non-redundant and relevant features are selected from training as well as testing datasets by using proposed feature selection technique. Secondly, SMOTE (Synthetic Minority Oversampling Technique) is applied to obtain the optimal balanced training and testing datasets. Thirdly, we apply various machine learning algorithms on optimally balanced reduced training and testing datasets to evaluate their performances. Experimental results shows that the best prediction performance is obtained by boosted random forest learning algorithm. Using a 10 fold cross-validation test, the proposed method is a good performer, with sensitivity of 91.3, 86.4, specificity of 91.9, 84.8, overall accuracy of 91.60%, 85.60%, Mathews correlation coefficient of 0.832, 0.713, AUC (area under curve) of 0.969, 0.908, and g-means of 91.5, 85.5 on optimal balanced reduced training and testing datasets consisting of aptamer-protein interacting pairs. Finally, a comparative study of the best obtained results with the existing best results is presented, which clearly indicates that our proposed approach is the best performing approach till date. [ABSTRACT FROM AUTHOR]

Attribute reduction is a typical topic in the field of rough sets. As an extension of this topic, test cost sensitive attribute reduction has garnered considerable attention in recent years, and scholars have made many achievements. However, existing research commonly operates under the assumption that test costs are exact values, disregarding the challenges associated with quantifying test costs accurately in certain real-world contexts. In light of the situation, this paper employs the form of interval values to represent the possible range of test costs and then studies the problem of attribute reduction based on interval-valued test costs. Firstly, a theoretical model for interval-valued test cost sensitive attribute reduction is constructed by utilizing a ranking method of intervals. In this model, some important concepts and properties are discussed. Especially, considering that the risk attitudes of different decision-makers may affect the decision results, an optimization problem related to risk attitude is formulated. Secondly, a backtracking algorithm and a heuristic algorithm are developed for tackling the optimization problem, along with the application of a competition strategy to enhance the heuristic algorithm's performance. Finally, the performance of the two algorithms is evaluated on multiple UCI datasets, and comparisons are drawn with several state-of-the-art attribute reduction methods. Experimental analyses well illustrate the effectiveness and superiority of the suggested algorithms. It is hoped that this work provides new insights into cost sensitive attribute reduction from the perspective of cost uncertainty and provides a reference for decision-making problems. [ABSTRACT FROM AUTHOR]

Hyperautomation acts as a real digital transformation with the support of several cutting-edge cognitive computation methods that include robotic process automation, natural language processing, artificial intelligence, and other emerging ones, which is conducive to processing complex industrial processes via extending the range of various data-driven cognitive decision-making algorithms. The study of air quality evaluations (AQE) plays a significant role in ensuring healthy atmospheric environments. In view of the objective existence of uncertainties, AQE can be modeled and addressed by a typical data-driven automated decision-making problem, and hyperautomation can provide a reasonable solution via associating with a variety of techniques. This article explores hyperautomation for AQE via evidential three-way large-scale group decision-making (LSGDM) in an intuitionistic fuzzy (IF) setting. First, the notion of intuitionistic fuzzy sets (IFSs) is incorporated into the paradigm of multi-granularity (MG) three-way decisions (TWD), and the model of adjustable MG IF probabilistic rough sets (PRSs) is developed. Second, an IF clustering analysis with the improved technique for order preference by similarity to ideal solution (TOPSIS) method is conducted to affirm representative members within a decision group. Third, a novel IF LSGDM method is built via adjustable MG IF PRSs and the evidence reasoning (ER) method. Finally, a case study in the setting of AQE is studied by using the presented evidential three-way LSGDM method. Corresponding experimental analyses are carried out for illustrating the efficiency of hyperautomation for AQE. In general, the proposed method improves the performance of information fusion by virtue of adjustable MG IF PRSs, and the TOPSIS method avoids the influence of subjective factors on decision results. Meanwhile, the evaluation information of decision-makers (DMs) is fully analyzed by means of the ER method, which can provide more explainable decision results. [ABSTRACT FROM AUTHOR]

Rough sets (RSs) and fuzzy sets (FSs) are designed to tackle the uncertainty in the data. By taking into account the control or reference parameters, the linear Diophantine fuzzy set (LD-FS) is a novel approach to decision making (DM), broadens the previously dominant theories of the intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), and q-rung orthopair fuzzy set (q-ROFS), and allows for a more flexible representation of uncertain data. A promising avenue for RS theory is to investigate RSs within the context of LD-FS, where LD-FSs are approximated by an intuitionistic fuzzy relation (IFR). The major goal of this article is to create a novel method of roughness for LD-FSs employing an IFR over dual universes. The notions of lower and upper approximations of an LD-FS are established by using an IFR, and some axiomatic systems are carefully investigated in detail. Moreover, a link between LD-FRSs and linear Diophantine fuzzy topology (LDF-topology) has been established. Eventually, based on lower and upper approximations of an LD-FS, several similarity relations are investigated. Meanwhile, we apply the recommended model of LD-FRSs over dual universes for solving the DM problem. Furthermore, a real-life case study is given to demonstrate the practicality and feasibility of our designed approach. Finally, we conduct a detailed comparative analysis with certain existing methods to explore the effectiveness and superiority of the established technique. [ABSTRACT FROM AUTHOR]

Objective: Technological advances have led to drastic changes in daily life, and particularly healthcare, while traditional diagnosis methods are being replaced by technology-oriented models and paper-based patient healthcare records with digital files. Using the latest technology and data mining techniques, we aimed to develop an automated clinical decision support system (CDSS), to improve patient prognoses and healthcare delivery. Our proposed approach placed a strong emphasis on improvements that meet patient, parent, and physician expectations. We developed a flexible framework to identify hepatitis, dermatological conditions, hepatic disease, and autism in adults and provide results to patients as recommendations. The novelty of this CDSS lies in its integration of rough set theory (RST) and machine learning (ML) techniques to improve clinical decision-making accuracy and effectiveness. Methods: Data were collected through various web-based resources. Standard preprocessing techniques were applied to encode categorical features, conduct min-max scaling, and remove null and duplicate entries. The most prevalent feature in the class and standard deviation were used to fill missing categorical and continuous feature values, respectively. A rough set approach was applied as feature selection, to remove highly redundant and irrelevant elements. Then, various ML techniques, including K nearest neighbors (KNN), linear support vector machine (LSVM), radial basis function support vector machine (RBF SVM), decision tree (DT), random forest (RF), and Naive Bayes (NB), were employed to analyze four publicly available benchmark medical datasets of different types from the UCI repository and Kaggle. The model was implemented in Python, and various validity metrics, including precision, recall, F1-score, and root mean square error (RMSE), applied to measure its performance. Results: Features were selected using an RST approach and examined by RF analysis and important features of hepatitis, dermatology conditions, hepatic disease, and autism determined by RST and RF exhibited 92.85 %, 90.90 %, 100 %, and 80 % similarity, respectively. Selected features were stored as electronic health records and various ML classifiers, such as KNN, LSVM, RBF SVM, DT, RF, and NB, applied to classify patients with hepatitis, dermatology conditions, hepatic disease, and autism. In the last phase, the performance of proposed classifiers was compared with that of existing state-of-the-art methods, using various validity measures. RF was found to be the best approach for adult screening of: hepatitis with accuracy 88.66 %, precision 74.46 %, recall 75.17 %, F1-score 74.81 %, and RMSE value 0.244; dermatology conditions with accuracy 97.29 %, precision 96.96 %, recall 96.96 %, F1-score 96.96 %, and RMSE value, 0.173; hepatic disease, with accuracy 91.58 %, precision 81.76 %, recall 81.82 %, F1-Score 81.79 %, and RMSE value 0.193; and autism, with accuracy 100 %, precision 100 %, recall 100 %, F1-score 100 %, and RMSE value 0.064. Conclusion: The overall performance of our proposed framework may suggest that it could assist medical experts in more accurately identifying and diagnosing patients with hepatitis, dermatology conditions, hepatic disease, and autism.

The COVID-19 pandemic has not only caused loss of life but also significantly affected people's emotional state. These emotional impacts have had serious consequences on societies and economies around the world. In order to repair these devastations in society, it is important to analyse these emotional effects in depth. In this study, the effects of the pandemic on human emotions are analysed using soft computing techniques. A rule-based approach is proposed for the analysis with the help of a rough set. The proposed method is based on two main components. The first one is the process of selecting the optimal subset (OFS) from the whole feature set with the help of k best known feature selection approaches. The second component involves the use of rough clustering methods to generate rules on the selected feature subset OFS. In the study, the first real data set called " Real World Concern Dataset", which is obtained from emotional responses to COVID-19, was used. The dataset consists of 5,000 items (2,500 short + 2,500 long). In the experimental studies, the proposed approach was tested with both labelled and unlabelled data, and it was observed that effective results were obtained with an accuracy rate of over 85%. It was also found that people were highly concerned about the future due to the pandemic.

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 The dimension and size of data is growing rapidly with the extensive applications of computer science and lab based engineering in daily life. Due to availability of vagueness, later uncertainty, redundancy, irrelevancy, and noise, which imposes concerns in building effective learning models. Fuzzy rough set and its extensions have been applied to deal with these issues by various data reduction approaches. However, construction of a model that can cope with all these issues simultaneously is always a challenging task. None of the studies till date has addressed all these issues simultaneously. This paper investigates a method based on the notions of intuitionistic fuzzy (IF) and rough sets to avoid these obstacles simultaneously by putting forward an interesting data reduction technique. To accomplish this task, firstly, a novel IF similarity relation is addressed. Secondly, we establish an IF rough set model on the basis of this similarity relation. Thirdly, an IF granular structure is presented by using the established similarity relation and the lower approximation. Next, the mathematical theorems are used to validate the proposed notions. Then, the importance-degree of the IF granules is employed for redundant size elimination. Further, significance-degree-preserved dimensionality reduction is discussed. Hence, simultaneous instance and feature selection for large volume of high-dimensional datasets can be performed to eliminate redundancy and irrelevancy in both dimension and size, where vagueness and later uncertainty are handled with rough and IF sets respectively, whilst noise is tackled with IF granular structure. Thereafter, a comprehensive experiment is carried out over the benchmark datasets to demonstrate the effectiveness of simultaneous feature and data point selection methods. Finally, our proposed methodology aided framework is discussed to enhance the regression performance for IC50 of Antiviral Peptides.

Purpose: To identify the key risk factors for venous thromboembolism (VTE) in urological inpatients based on the Caprini scale using an interpretable machine learning method. Methods: VTE 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. Results: Following 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. Conclusions: The 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. [ABSTRACT FROM AUTHOR]

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]

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office 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.)

In this article, we study the zero-divisor graphsΓ(Zn) of rings of integers modulo η as information systems L(Γ(Zn)) using equivalence classes and rough sets. Equivalence classes are referred as granules and partitions are referred as indiscernible partitions. We define an indiscernibility relation on the vertex set and identify different sets of attributes that induce the same indiscernibility partition. A reduct is a minimal subset of attributes which yields the same partition as the original attribute set. We compute all reducts of the defined information system and classify them in to two types including: (i) the set P of all prime divisors of η and (ii) the set consisting of P/pi, prime powers of P/pi in the prime factorization of η and the elements of the form P/pi pj, where pj ε P/pi . Moreover, we give the structures and the cardinalities of the attribute subsets whose removal yields a different indiscernibility partition than that of the set of all attributes, referred as essential sets. We prove that the essential sets of L(Γ(Zn)) either consist of two prime divisors of η or one prime divisor P/pi combined with prime powers of P/pi . Further, we determine the lower and upper approximations of various vertex subsets to study the properties of the zero-divisor graphs. We also study properties of the rough membership function forΓ(Zn). Furthermore, we introduce the class-based discernibility matrix induced by indiscernibility classes of zero divisors and determine general form of its entries. We also prove that the minimal entries of the class-based discernibility matrix coincide with the essential sets ofΓ(Zn). Based on these results, we determine information-granularity measures corresponding to the notable partitions of Γ(Zn) and provide an example to establish consistency of the proved results with these well-known measures. Thus, starting from introducing an information system, we investigate the components of granular computing and utilize our findings to compute information granularity measures, contributing to a deeper understanding of the zero divisor graphs via rough set theory. [ABSTRACT FROM AUTHOR]

Worldwide, the healthcare system is greatly impacted by the changing requirements of the people. Diabetes is a long-lasting condition that can lead to serious complications if not controlled correctly. It is divided into Type 1 (TID) and Type 2 (T2D) diabetes. Research shows that almost 90% of Diabetes cases are T2D, with TID making up around 10% of all Diabetes cases. This paper suggests a Rough-Neuro classification model for identifying Type 2 Diabetes, which includes a two-stage process. The approach includes utilising Rough sets JohnsonReducer to eliminate unnecessary features or characteristics and multi-layer perceptron for illness categorization. The suggested technique seeks to reduce the amount of input characteristics, which results in a reduction in the time needed to train the neural network and the storage space required. The findings show that decreasing the amount of input characteristics results in a lower neural network training time, enhances model performance, and reduces storage needs by 63%. It is worth mentioning that a smaller neural network with only seven hidden layers, trained for 1000 epochs with a learning rate of 0.01, attained the best performance, but time and storage were much decreased. [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]

In this article, we study the zero-divisor graphsΓ(Zn) of rings of integers modulo η as information systems L(Γ(Zn)) using equivalence classes and rough sets. Equivalence classes are referred as granules and partitions are referred as indiscernible partitions. We define an indiscernibility relation on the vertex set and identify different sets of attributes that induce the same indiscernibility partition. A reduct is a minimal subset of attributes which yields the same partition as the original attribute set. We compute all reducts of the defined information system and classify them in to two types including: (i) the set P of all prime divisors of η and (ii) the set consisting of P/pi, prime powers of P/pi in the prime factorization of η and the elements of the form P/pi pj, where pj ε P/pi . Moreover, we give the structures and the cardinalities of the attribute subsets whose removal yields a different indiscernibility partition than that of the set of all attributes, referred as essential sets. We prove that the essential sets of L(Γ(Zn)) either consist of two prime divisors of η or one prime divisor P/pi combined with prime powers of P/pi . Further, we determine the lower and upper approximations of various vertex subsets to study the properties of the zero-divisor graphs. We also study properties of the rough membership function forΓ(Zn). Furthermore, we introduce the class-based discernibility matrix induced by indiscernibility classes of zero divisors and determine general form of its entries. We also prove that the minimal entries of the class-based discernibility matrix coincide with the essential sets ofΓ(Zn). Based on these results, we determine information-granularity measures corresponding to the notable partitions of Γ(Zn) and provide an example to establish consistency of the proved results with these well-known measures. Thus, starting from introducing an information system, we investigate the components of granular computing and utilize our findings to compute information granularity measures, contributing to a deeper understanding of the zero divisor graphs via rough set theory. [ABSTRACT FROM AUTHOR]

Discussion related to exact sequences is an essential tool in module theory. The exact sequences are generalized to U-exact sequences, and X-sub-exact sequences. The concept of X-sub-exact sequences can be used to generalize basis and free modules. Besides, the rough set theory is a mathematical tool for dealing with uncertainty and vagueness problems. The advancement of the algebraic concept into the rough set theory is expeditious. Several structures are developed in rough set theory, such as groups, semigroups, rings, and modules. In this research, we provide a rough X-sub-exact sequence of a rough module over a rough ring. Furthermore, we investigate the properties related to the intersection of a finite number of rough modules over the rough ring. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct the lattice structure for Z-soft covering based rough set. First, we define an equivalence relation R' on a universal set to obtain the equivalence classes induced by Z-soft covering-based rough set. Also, we define a relation RS on the family of Z-soft covering-based rough set (TS) to show that the relation RS is a poset on TS. Second, we define two operations join ∨ and meet ∧ on TS. Using these two operations, we prove that every pair of elements of RS has a least upper bound and a greatest lower bound and as a result, TS is a lattice. Finally, we develop a novel Multiple Attribute Group Decision Making (MAGDM) model using Z-soft covering based rough set in medical diagnosis to determine the patients at high risk of chronic kidney disease using the collected data from the UCI Machine Learning Repository. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Beijing University of Technology is the property of Journal of Beijing University of Technology, Editorial Department 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.)

The rough set (RS) and multi-granulation rough set (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, bipolarity refers to the explicit handling of positive and negative aspects of data. In this paper, with the help of bipolar fuzzy preference relation (BFPR) and bipolar fuzzy preference δ -covering (BFP δ C), we put forward the idea of BFP δ C based optimistic multi-granulation bipolar fuzzy rough set (BFP δ C-OMG-BFRS) model and BFP δ C based pessimistic multi-granulation bipolar fuzzy rough set (BFP δ C-PMG-BFRS) model. We examine several significant structural properties of BFP δ C-OMG-BFRS and BFP δ C-PMG-BFRS models in detail. Moreover, we discuss the relationship between BFP δ C-OMG-BFRS and BFP δ C-PMG-BFRS models. Eventually, we apply the BFP δ C-OMG-BFRS model for solving multi-criteria decision-making (MCDM). Furthermore, we demonstrate the effectiveness and feasibility of our designed approach by solving a numerical example. We further conduct a detailed comparison with certain existing methods. Last but not least, theoretical studies and practical examples reveals that our suggested approach dramatically enriches the MGRS theory and offers a novel strategy for knowledge discovery, which is practical in real-world circumstances. [ABSTRACT FROM AUTHOR]

The main weakness of complex and sizeable fuzzy rule systems is the complexity of data interpretation in terms of classification. Classification interpretation can be affected by reducing rules and removing important rules for several reasons. Based on the results of experiments using the fuzzy grid partition (FGP) approach for high-dimensional data, the difficulty in generating many fuzzy rules still increases exponentially as the number of characteristics increases. The solution to this problem is a hybrid method that combines the advantages of the rough set method and the FGP method, which is called the fuzzy grid partition rough set (FGPRS) method. In the Irish data, the rough set approach reduces the number of characteristics and objects so that data with excessive values can be minimized, and the fuzzy rules produced using the FGP method are more concise. The number of fuzzy rules produced using the FGPRS method at K=2 is 50%; at K=K+1, it is reduced by 66.7% and at K=2 K, it is reduced by 75%. Based on the findings of the data collection classification test, the FGPRS method has a classification accuracy rate of 83.33%, and all data can be classified. [ABSTRACT FROM AUTHOR]

Optimal scale selection of multi-scale decision system (MDS) is an effective method to reduce data complexity, and there are a series of detailed analysis methods. However, the optimal scale combination (OSC) of MDS is often not unique, and there is no comparison method between OSCs. Meanwhile, multi-scale data is difficult to obtain, there is no effective method to convert single-scale data into MDS. Therefore, we propose a method for simplifying dynamic data by converting it to MDS and selecting the best OSC of it. Firstly, we propose the concepts of classes number vector and classes number matrix from the perspective of the number of equivalence classes. And we further introduce the generation methods of MDS and generalized MDS using clustering methods, respectively. Secondly, for the problem where the OSC cannot be compared in MDS, we transform it into a multi-attribute decision making problem and use relevant decision methods to obtain the best OSC, which is remembered as global OSC. Subsequently, we propose the concepts of local OSC and global OSC and design corresponding algorithms to find the global OSC. Furthermore, we combine the above two types of algorithms to propose a method for simplifying dynamic single scale data and consider the impact of dynamic data on the model. Finally, we validate the effectiveness of the proposed method through numerical experiments. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The significance of studying voting behaviour is underscored by its ability to gauge the continuity or divergence of electoral politics from historical trends, elucidating the real impact of the transformative ballot box, and contributing to the examination of democracy as a value among both masses and elites. Additionally, it aids in comprehending the intricate process of political socialization. Methods: An inherent strength of the rough set lies in its reliance solely on raw data, devoid of external inputs. The decision-theoretic rough set framework, an evolution of the rough set, has garnered widespread application across diverse domains, serving as a proficient tool for acquiring knowledge, particularly in navigating situations marked by vagueness and uncertainty. Despite the proliferation of mathematical models designed to discern people's voting behavior, a decision-based rough set recommendation remains noticeably absent in existing literature. This paper introduces an innovative three-way decision approach grounded in linguistic information for identifying voting behavior. The proposed approach is based on a hybrid probabilistic rough fuzzy model incorporating linguistic information and providing insights into voting patterns. Results: The three-way decision hybrid models are tested on people and a highly satisfactory result was achieved for identifying their voting behaviours. The justification of results was validated through the mathematical process. Conclusion: A practical illustration is provided to highlight the importance of this hybrid model and to confirm its usefulness in identifying and forecasting voting behaviour

Abstract The rough set (RS) and multi-granulation rough set (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, bipolarity refers to the explicit handling of positive and negative aspects of data. In this paper, with the help of bipolar fuzzy preference relation (BFPR) and bipolar fuzzy preference $$\delta $$ δ -covering (BFP $$\delta $$ δ C), we put forward the idea of BFP $$\delta $$ δ C based optimistic multi-granulation bipolar fuzzy rough set (BFP $$\delta $$ δ C-OMG-BFRS) model and BFP $$\delta $$ δ C based pessimistic multi-granulation bipolar fuzzy rough set (BFP $$\delta $$ δ C-PMG-BFRS) model. We examine several significant structural properties of BFP $$\delta $$ δ C-OMG-BFRS and BFP $$\delta $$ δ C-PMG-BFRS models in detail. Moreover, we discuss the relationship between BFP $$\delta $$ δ C-OMG-BFRS and BFP $$\delta $$ δ C-PMG-BFRS models. Eventually, we apply the BFP $$\delta $$ δ C-OMG-BFRS model for solving multi-criteria decision-making (MCDM). Furthermore, we demonstrate the effectiveness and feasibility of our designed approach by solving a numerical example. We further conduct a detailed comparison with certain existing methods. Last but not least, theoretical studies and practical examples reveals that our suggested approach dramatically enriches the MGRS theory and offers a novel strategy for knowledge discovery, which is practical in real-world circumstances.

Rough set theory is an advanced uncertainty tool that is capable of processing sophisticated real-world data satisfactorily. Rough approximation operators are used to determine the confirmed and possible data that can be obtained by using subsets. Numerous rough approximation models, inspired by neighborhood systems, have been proposed in earlier studies for satisfying axioms of Pawlak approximation spaces (P-approximation spaces) and improving the accuracy measures. This work provides a formulation a novel type of generalized approximation spaces (G-approximation spaces) based on new neighborhood systems inspired by $ \mathbb{I}_j $-neighborhoods and ideal structures. The originated G-approximation spaces are offered to fulfill the axiomatic requirements of P-approximation spaces and give more information based on the data subsets under study. That is, they are real simulations of the P-approximation spaces and provide more accurate decisions than the previous models. Several examples are provided to compare the suggested G-approximation spaces with existing ones. To illustrate the application potentiality and efficiency of the provided approach, a numerical example for Chikungunya disease is presented. Ultimately, we conclude our study with a summary and direction for further research.

Abstract 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.

Abstract This paper constructs a two-layer road data asset revenue allocation model based on a modified Shapley value approach. The first layer allocates revenue to three roles in the data value realization process: the original data collectors, the data processors, and the data product producers. It fully considers and appropriately adjusts the revenue allocation to each role based on data risk factors. The second layer determines the correction factors for different roles to distribute revenue among the participants within those roles. Finally, the revenue values of the participants within each role are synthesized to obtain a consolidated revenue distribution for each participant. Compared to the traditional Shapley value method, this model establishes a revenue allocation evaluation index system, uses entropy weighting and rough set theory to determine the weights, and adopts a fuzzy comprehensive evaluation and numerical analysis to assess the degree of contribution of participants. It fully accounts for differences in both the qualitative and quantitative contributions of participants, enabling a fairer and more reasonable distribution of revenues. This study provides new perspectives and methodologies for the benefit distribution mechanism in road data assets, which aid in promoting the market-based use of road data assets, and it serves as an important reference for the application of data assetization in the road transportation industry.

Machine learning algorithms investigate relationships in data to deliver useful outputs. However, past models required complete datasets as a prerequisite. In this study, rough set-based machine learning was applied using real-world incomplete datasets to generate a prediction model of biochar's adsorption capacity based on key attributes. The predictive model consists of if–then rules classifying properties by fulfilling certain conditions. The rules generated from both complete and incomplete datasets exhibit high certainty and coverage, along with scientific coherence. Based on the complete dataset model, optimal pyrolysis conditions, biomass characteristics and adsorption conditions were identified to maximize tetracycline adsorption capacity (> 200 mg/g) by biochar. This study demonstrates the capabilities of rough set-based machine learning using incomplete practical real-world data without compromising key features. The approach can generate valid predictive models even with missing values in datasets. Overall, the preliminary results show promise for applying rough set machine learning to real-world, incomplete data for generating biomass and biochar predictive models. However, further refinement and testing are warranted before practical implementation. Highlights: • It is the first explainable AI-based rough set model to study the tetracycline adsorption capacity of biochar. • Usage of an incomplete Practical dataset through RSML evaded the biasness due to imputations. • Higher accuracy and precision of incomplete Practical datasets revealed the uniqueness of the model. [ABSTRACT FROM AUTHOR]

Rough Set (RS) theory is a useful mathematical strategy to handle uncertainty. In 1982, Pawlak presented the idea, and numerous authors have undertaken in-depth studies on RS in both ordinary cases and fuzzy situations. In terms of both the theoretical investigations and the practical applications, progress in this field of RS theory has yielded favorable outcomes over the last three decades and it is typically considered to be an extension of classical sets. A universe in RS is separated by two subsets known as lower and upper approximations. Upper approximations are nonempty intersections of equivalence classes, whereas lower approximations are subsets of the set. In this study, rough sets are examined when the universe set has a ring structure. The main contribution of this study is to focus on rough fuzzy prime and semi-prime ideals of the gamma ring structure and explain certain respects of its upper and lower approximations. The goal of this research is to investigate some of the characterizations of prime and semi-prime ideals and prove some related results. Moreover, the study discusses rough fuzzy ideals (RFI) in Γ Residue class and gives some findings. [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]

Bipolar complex fuzzy set (BCFS) is a more advanced and powerful phenomenon as it consists of two-dimensional data with positive and negative impacts of an element. It can solve the data consisting of the positive and negative impacts of an element which is a bipolar fuzzy set (BFS). It also covers the two-dimensional complex data which is a complex fuzzy set (CFS). Due to these attributes, BFS and CFS are less useful in comparison with BCFS to capture vagueness, complexity, and ambiguity in the data. Furthermore, lower and upper approximations based on equivalency relations constitute another significant phenomenon known as rough set (RS). This structure is also more powerful in dealing with real-life dilemmas. Rather than comparing the RS and BCFS, we combine both phenomena to handle the complexity more powerfully to deal with such types of phenomena that are not handled by other structures. So, by combining both phenomena, we introduce a novel structure known to be bipolar complex fuzzy rough set (BCFRS) in this manuscript. After that, we define some important operations, some significant properties related to this structure, and some aggregation operators (AOs) to solve decision-making (DM) problems related to cyber security. We address a practical application of cyber security (C-S) in computing for the protection of critical data to demonstrate the usefulness of the multi-attribute DM (MADM) approach. Based on the various criteria and attributes given by the experts, we find the best and better alternative to the C-S by applying the MADM approach. We get the e Ã4 as the best and finest alternative by using bipolar complex fuzzy rough (BCFR) weighted arithmetic averaging (BCFRWAA), BCFR ordered weighted arithmetic averaging (BCFROWAA), and BCFR ordered weighted geometric averaging (BCFROWGA) operators. And, by using BCFR weighted geometric averaging (BCFRWGA), we get the e Ã3 as the finest alternative. Lastly, to prove the superiority, validity, and generalization of our unique established theory, we give a detailed comparative study of our established work with several prevalent theories. [ABSTRACT FROM AUTHOR]