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The theories of rough sets (RSs) and soft sets (SSs) are practical mathematical techniques to accommodate data uncertainty. On the other hand, fuzzy bipolar soft sets (FBSSs) can address uncertainty and bipolarity in various situations. The key objective of this study is to establish the notions of rough fuzzy bipolar soft ideals in semigroup (SG), which is an extension of the idea of rough fuzzy bipolar soft sets in a SG. Also, we have analyzed the roughness in the bipolar fuzzy subsemigroup (BF-SSG) by employing a congruence relation (CR) defined on the SG and investigating several related characteristics. Further, the idea is expanded to the rough fuzzy bipolar soft ideal, rough fuzzy bipolar soft interior ideal, and rough fuzzy bipolar soft bi-ideal in SGs. Moreover, it is observed that CR and complete CR (CCR) are critical in developing rough approximations of fuzzy bipolar soft ideals. Therefore, their related characteristics are studied via CRs and CCRs. [ABSTRACT FROM AUTHOR]

Accurately and effectively detecting the growth position and contour size of apple fruits is crucial for achieving intelligent picking and yield predictions. Thus, an effective fruit edge detection algorithm is necessary. In this study, a fusion edge detection model (RED) based on a convolutional neural network and rough sets was proposed. The Faster-RCNN was used to segment multiple apple images into a single apple image for edge detection, greatly reducing the surrounding noise of the target. Moreover, the K-means clustering algorithm was used to segment the target of a single apple image for further noise reduction. Considering the influence of illumination, complex backgrounds and dense occlusions, rough set was applied to obtain the edge image of the target for the upper and lower approximation images, and the results were compared with those of relevant algorithms in this field. The experimental results showed that the RED model in this paper had high accuracy and robustness, and its detection accuracy and stability were significantly improved compared to those of traditional operators, especially under the influence of illumination and complex backgrounds. The RED model is expected to provide a promising basis for intelligent fruit picking and yield prediction. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Based on equivalence relation R on X, equivalence class [ x ] of a point and equivalence class [ A ] of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation axioms, metric spaces, proximity relations and uniformity structures on an approximation space (X , R) depending on the lower approximation and the upper approximation of rough sets. The properties and the possible implications of these definitions are studied. The generated approximation topology τ R on X is equivalent to the generated topologies associated with metric d, proximity δ and uniformity U on X. Separated metric spaces, separated proximity spaces and separated uniform spaces are defined and it is proven that both are associating exactly discrete topology τ R on X. [ABSTRACT FROM AUTHOR]

Reducing doctor-patient conflict is an important part of coordinating doctor-patient disputes and easing doctor-patient relationship, which is conducive to building a harmonious medical environment and promoting the healthy development of medical undertakings. This paper constructs a multi-decision-maker mixed conflict model based on rough set theory, puts forward the matrix operation expression of the conflict degree theory in the Pawlak model, and gives a more objective and scientific evaluation function. Combined with hot issues of doctor-patient conflict, the proposed multi-decision-maker mixed conflict model is applied to doctor-patient conflict, examines the doctor-patient relationship in the medical institution system from multiple internal perspectives, and calculates feasible solutions in the conflict system. The results show that high medical quality, high standardize medication, high institutional efficiency, high staff efficiency, high hospital benefits, high hospital revenue, medium employee development, medium equipment development, or high medical quality, high standardize medication, high institutional efficiency, medium staff efficiency, medium hospital benefits, high hospital revenue, high employee development, and high equipment development are important conditions for building a harmonious medical environment and reducing doctor-patient conflicts. [ABSTRACT FROM AUTHOR]

In order to address the problem of low algorithm efficiency caused by repeated calculation of the relative importance of attributes in the attribute reduction algorithm based on positive region, this paper proposed a fast attribute reduction algorithm based on knowledge rough entropy from the perspectives of attribute measurement and search strategy. Firstly, it introduced knowledge rough entropy into decision information systems by incorporating knowledge distance to measure the degree of knowledge roughness. Next, it employed knowledge rough entropy as the criterion for evaluating the significance of attributes, assessing the importance of individual attributes. Finally, it ranked all attributes based on attribute importance, and eliminated redundant attributes through dependency, so as to achieve rapid attribute reduction. The proposed algorithm was compared with other three algorithms in terms of running efficiency and classification accuracy on six publicly available datasets. The results demonstrate that the proposed algorithm improves running efficiency by 83.24%,28.77%, and 59.92% respectively compared to other three algorithms. Among the three classifiers, the classification accuracy increases on average by 0.83%,0.63%, and 1.37% respectively. Therefore, the proposed algorithm is able to achieve attribute reduction more quickly while ensuring classification performance. [ABSTRACT FROM AUTHOR]

As an important extension of the rough set theory, interval-set rough sets provide an effective method to solve the problem that the objective sets cannot be accurately expressed in the rough approximation process and to induce classification rules from incomplete information systems. In practical information systems, the value of an object's decision attribute may be set-valued due to missing decision information or multiple decision values. However, this situation is not considered by any of the existing rough set models. Therefore, to properly deal with the information system where decision attributes are set-valued, we construct the interval-set rough set model on the information system and study attribute reductions of interval-set rough sets. First, we define the information system where decision attributes are set-valued as an extended set-valued decision information system (ESVDIS) and construct the interval-set rough set model on the ESVDIS. Second, the accuracy and the roughness are extended to the interval-set approximation accuracy and the interval-set approximation roughness, respectively. The two extended measures can be used to measure the uncertainty caused by rough approximations. In addition, the dependency degree of interval-set rough sets called the interval-set dependency degree is defined to estimate the significance of attribute subsets. By adopting the interval-set dependency degree, we propose the definition of attribute reduction based on interval-set rough sets and design a heuristic attribute reduction algorithm. Finally, the effectiveness of the proposed attribute reduction algorithm is demonstrated using 12 public data sets. Experimental results show that the model is applicable to some fields, such as missing decision information and group decision-making. [ABSTRACT FROM AUTHOR]

We consider fuzzy rough sets defined on De Morgan Heyting algebras. We present a theorem that can be used to obtain several correspondence results between fuzzy rough sets and fuzzy relations defining them. We characterize fuzzy rough approximation operators corresponding to compositions of reflexive, transitive, mediate, Euclidean and adjoint fuzzy relations defined on De Morgan Heyting algebras using only a single axiom. [ABSTRACT FROM AUTHOR]

Clustering is the main task of machine learning, and is also the core work of granular computing, namely information granulation. At present, most of granular computing based clustering algorithms only utilize the granule features without taking the granule structure into account, especially in the information field where algebraic structure is widely used. From the perspective of granular computing, this paper proposes a clustering method based on algebraic granularity (CMAG). Firstly, the algebraic granularity is newly formulated with the granule structure of an algebraic binary operator. Secondly, the CMAG is proposed with granules of incorporating congruence partition and granule structure of homeomorphic projection. Finally, the CMAG is experimentally compared with the tolerance domain model and the quotient space model, and the results show that the CMAG has better structural completeness and practical robustness. The CMAG can enrich and extend the granular computing theory from granule structure, and will provide a theoretical basis for the combination of granular computing methods and machine learning theory. [ABSTRACT FROM AUTHOR]

An intrusion detection method using rough-fuzzy set and parallel quantum genetic algorithm (RFS-QGAID) is proposed in this paper. The RFS-QGAID is applied to solve the serious problems of determining the optimal antibodies subsets used to detect an anomaly. To obtain a simplified antibodies collection for high dimensional Log data sets, RFS is applied to delete the redundant antibody features and obtain the optimal antibodies features combination. Then, the optimal attitudes are entered into the QGA classifier for learning and training in the following stage. At last, the detected Log antigens are fed into RFS-QGAID, and we can classify the intrusion types. With RFS-QGAID, we give the simulations, the results on real Log data sets show that: the higher detection accuracy of RFS-QGAID is higher detection accuracy, but the false negative rate is lower for small samples sets, the adaptive performance is higher than other detection algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we use the notions of lower set LR(A) and the upper set UR(A) to define the interior operator intAR and the closure operator clAR associated with a set A in an approximation space (X,R). These operators generate an approximation topological space different from the generated Nano topological space in (X,R). Ideal approximation spaces (X,R, ℓ) based on an ideal ℓ joined to the approximation space (X,R) are introduced as well. The approximation continuity and the ideal approximation continuity are defined. The lower separation axioms Ti, i = 0, 1, 2 are introduced in the approximation spaces and also in the ideal approximation spaces. Examples are given to explain the definitions. Connectedness in approximation spaces and ideal connectedness are introduced and the differences between them are explained. The interior and the closure operators are deduced using a grill G defined on (X,R), yielding the same results. [ABSTRACT FROM AUTHOR]

Point cloud data generated by LiDAR sensors play a critical role in 3D sensing systems, with applications encompassing object classification, part segmentation, and point cloud recognition. Leveraging the global learning capacity of dot product attention, transformers have recently exhibited outstanding performance in point cloud learning tasks. Nevertheless, existing transformer models inadequately address the challenges posed by uncertainty features in point clouds, which can introduce errors in the dot product attention mechanism. In response to this, our study introduces a novel global guidance approach to tolerate uncertainty and provide a more reliable guidance. We redefine the granulation and lower-approximation operators based on neighborhood rough set theory. Furthermore, we introduce a rough set-based attention mechanism tailored for point cloud data and present the rough set transformer (RST) network. Our approach utilizes granulation concepts derived from token clusters, enabling us to explore relationships between concepts from an approximation perspective, rather than relying on specific dot product functions. Empirically, our work represents the pioneering fusion of rough set theory and transformer networks for point cloud learning. Our experimental results, including point cloud classification and segmentation tasks, demonstrate the superior performance of our method. Our method establishes concepts based on granulation generated from clusters of tokens. Subsequently, relationships between concepts can be explored from an approximation perspective, instead of relying on specific dot product or addition functions. Empirically, our work represents the pioneering fusion of rough set theory and transformer networks for point cloud learning. Our experimental results, including point cloud classification and segmentation tasks, demonstrate the superior performance of our method. [ABSTRACT FROM AUTHOR]

The establishment of the correspondence between the important features of the topside weld pool and the penetration state is a key link in penetration control. This article presents a scheme of variable gap welding penetration control based on rough-fuzzy modeling. By utilizing the basic concepts of variable precision rough sets and conditional information entropy, relevant algorithms for attribute reduction and rule extraction in decision information systems are addressed. Raw data for modeling are obtained through current–gap combination experiments, and then rough-set-based knowledge acquisition algorithms are used to generate classification rules for the penetration state. Based on the correspondence between the important features of the topside pool and the penetration state, a fuzzy control model is established. Welding experiments under variable gaps are conducted to examine the proposed control scheme, and the results indicate that the weld has good penetration and meets the requirements of welding specifications. [ABSTRACT FROM AUTHOR]

In this paper, two new uncertainty modeling concepts, namely strait soft set and strait rough set, between the structures of rough sets and soft sets, which will bring new perspectives to both theoretical and practical aspects, are presented. A reduction method of alternatives is given using strait soft sets. Another convenience arising from the structure of strait soft sets is that they allow the parameters to be combined. Thus, the fusion of parameters is defined and its use in soft set operations is demonstrated. Strait rough sets naturally contain the characteristics of the rough sets and also allow the parameters to be characterized. The strait soft set and strait rough set are supported by many examples and comparisons. In addition, a new decision-making approach based on the strait soft set and strait rough set is proposed and then followed by real-life applications to illustrate the computational processes. [ABSTRACT FROM AUTHOR]

In order to reduce the deficiency of single assignment of evaluation index weight.a multi-objective decision-making method based on rough set theory and technique for order preference by similarity to an ideal solution is proposed. According to the attribute importance and attribute dependency in the rough set theory, the objective weight of the evaluation index is calculated respectively, and it is properly integrated with the subjective weight of the evaluation index obtained by the binary contrast method to obtain the comprehensive weight of the evaluation index. On this basis, the decision matrix of each design scheme of the system is normalized, and the comprehensive weight of the evaluation index is assigned to the decision matrix to obtain the normalized weighted decision matrix of the evaluation index. The optimal design scheme and the worst design scheme among the alternatives are calculated by using the technique for order preference by similarity to an ideal solution, and the distance between each design scheme and the best and the worst design scheme is calculated, and then the corresponding fit degree of each scheme is calculated, so as to determine the optimal design scheme. Finally, it is compared with analytic hierarchy process and the rationality and practicability of this method are verified by the decision case of the design scheme of the tool change system of a NC machine tool manufacturing enterprise. [ABSTRACT FROM AUTHOR]

In this paper, a new uncertainty modelling concept called strait fuzzy set is introduced, which brings new perspectives to both theoretical and practical advances in fuzzy mathematics. This set type allows objects/points to be graded with fuzzy membership intervals that are partitions of [0,1] (so that the union of these partitions is [0,1] and their intersection is empty) instead of fuzzy membership degrees represented as exact values in [0,1]. Moreover, some basic operations and properties of strait fuzzy sets are studied in detail. The concept of strait fuzzy rough set is put forward and its theoretical aspects are discussed. In addition, two different similarity approaches are proposed for strait fuzzy sets and strait fuzzy rough sets, and applied to measure the similarity rates of vaccines against influenza viruses. [ABSTRACT FROM AUTHOR]

The relationship between Rough Set (RS) and algebraic systems has been long studied by mathematicians. RS is a growing research area that encourages studies into both real-world applications and the theory itself. In RS, a universe subset is characterized by a pair of ordinary sets called lower and upper approximations. In this study, we look attentively at the use of rough sets when the universe set has a ring structure. The main contribution of the paper is to concentrate on the study of rough fuzzy ideals concerning the gamma ring and to describe some properties of its lower and upper approximations. This paper deals with the connection between Rough Fuzzy Sets (RFS) and ring theory. The goal of this paper is to present the notion of Left Operator Rings (LOR) and Right Operator Rings (ROR) in the gamma ring structure. We introduce some basic concepts of rough fuzzy left and right operator rings. Furthermore, we investigate some characterizations of left and right operator rings and prove some theorems based on these results. [ABSTRACT FROM AUTHOR]

Issues in daily life, where making the best decisions is crucial, are frequently encountered. But, in the majority of these situations, the best course of action is uncertain. We must take into account a number of parameters in order to find the best possible solution to these difficulties. The best mathematical instrument for this is fuzzy soft set F S S theory in decision making. Nutrition is the process of supplying cells and organisms with the nutrients they need to grow and thrive and to sustain life. A healthy diet has the potential to prevent or mitigate numerous prevalent health issues. The purpose of this paper is to select a burning problem for the nutrition of students and successfully apply the F S S theory in decision making. We aim to prove that the approach to decision-making problems with imprecise data via F S S s is more accurate than other types of approaches, and we present a new approach to the F S S model and its applications in decision-making problems. [ABSTRACT FROM AUTHOR]

In March 2020, a cohort of 26 is treated critically ill hospitalized SARS-CoV-2 infected patients who received EEGs to assess unexplained altered mental status, loss of consciousness, or poor arousal and responsiveness. The objective of the present work is to develop a method that is able to automatically determine mental status of vigilance, i.e., a person's state of alertness. Such a task is relevant to diverse domains, where a person is expected or required to be in a particular state of mind. Aiming at the EEG feature selection and classification model in the identification of fatigue driving, the discretization algorithm using rough set theory is proposed to select the channel and EEG signal feature quantities. The support vector machine (SVM) is selected as the fatigue driving recognition model, and the risk of fatigue misjudgment is taken as SVM model parameters for model optimization. The experimental results of subjects show that compared with the principal component method, the rough set discretization algorithm selects fewer features, and the compatibility threshold 0.8. The number of features selected among the candidate features is 208. The features selected by different subjects are different and have an impact on the establishment of the support vector machine recognition model. Fatigue misjudgment risk control parameters can adjust the support vector machine recognition model error judgment risk. Even if the present approach is costly in computation time, it allows constructing a decision rule that provides an accurate and fast prediction of the alertness state of an unseen individual. [ABSTRACT FROM AUTHOR]

Ensemble clustering helps achieve fast clustering under abundant computing resources by constructing multiple base clusterings. Compared with the standard single clustering algorithm, ensemble clustering integrates the advantages of multiple clustering algorithms and has stronger robustness and applicability. Nevertheless, most ensemble clustering algorithms treat each base clustering result equally and ignore the difference of clusters. If a cluster in a base clustering is reliable/unreliable, it should play a critical/uncritical role in the ensemble process. Fuzzy-rough sets offer a high degree of flexibility in enabling the vagueness and imprecision present in real-valued data. In this paper, a novel fuzzy-rough induced spectral ensemble approach is proposed to improve the performance of clustering. Specifically, the significance of clusters is differentiated, and the unacceptable degree and reliability of clusters formed in base clustering are induced based on fuzzy-rough lower approximation. Based on defined cluster reliability, a new co-association matrix is generated to enhance the effect of diverse base clusterings. Finally, a novel consensus spectral function is defined by the constructed adjacency matrix, which can lead to significantly better results. Experimental results confirm that the proposed approach works effectively and outperforms many state-of-the-art ensemble clustering algorithms and base clustering, which illustrates the superiority of the novel algorithm. [ABSTRACT FROM AUTHOR]

Rough-based topology has become an important technique for decision making in numerous real-life problems. The main purpose of this research paper is to use some topological notions in the approximation space of a rough set. Firstly, some concepts of topological near open sets and rough concepts are presented. A new approximation structure based on the topological near open sets is introduced. We debate the properties of the new approximation structure. We included an algorithm for detecting COVID-19 infection by its side effects. We believe that our approach will be helpful for any future detection. [ABSTRACT FROM AUTHOR]

In this paper, the concept of rough representation of a rough topological group on a Banach space is explored. Mainly, the continuity and the irreducibility of rough representations are studied. [ABSTRACT FROM AUTHOR]

In this paper, a new type of L-fuzzy generalized neighborhood system is introduced and then novel L-fuzzy rough sets based on it are defined and discussed. It is verified that the proposed model is an extension of Pang's generalized neighborhood system-based pessimistic rough sets and so called L-fuzzy generalized neighborhood system-based pessimistic L-fuzzy rough sets. Firstly, the basic properties of the novel model are studied. To regain some Pawlak's properties which are lost in the novel model, the serial, reflexive, transitive and symmetric conditions for L-fuzzy general neighborhood systems are defined. Secondly, the axiomatic characterizations of the pessimistic L-fuzzy rough sets and that generated by serial, reflexive and symmetric L-fuzzy general neighborhood systems are given, respectively. Thirdly, a reduction theory preserving L-fuzzy approximation operators is established. Finally, one applied in information system, i.e., a new three-way decision model based on pessimistic L-fuzzy rough sets, is built. To show the effectiveness and reliability of our model, a practical example is presented. [ABSTRACT FROM AUTHOR]

The clinical diagnosis of heart disease in most situations is based on a difficult amalgamation of pathological and clinical information. Because of this complication, there is a significant level of curiosity among many diagnostic healthcare professionals and researchers who are keenly interested in the efficient, accurate, and early-stage forecasting of heart disease. Deep Learning Algorithms aid in the prediction of heart disease. The main focus of this paper is to develop a method for predicting heart disease through Modified Rough K means + + (MRK + +) clustering along with the Restricted Boltzmann Machine (RBM). This paper is categorized into two modules: (1) Propose a clustering component based on Modified Rough K-means + + ; (2) disease prediction based on RBM. The input Cleveland dataset is clustered using the stochastic probabilistic rough k-means + + clustering technique in the module for clustering. The clustered data is acquired and used in the RBM, and this hybrid structure is then used in the heart disease forecasting module. Throughout the testing procedure, the most valid result is chosen from the clustered test data, and the RBM classifier that correlates to the nearest cluster in the test data is based on the smallest distance or similar parameters. Furthermore, the output value is used to predict heart disease. There are three different types of experiments that are performed: In the first experiment comprises modifying the rough K-means + + clustering algorithm, the second experiment evaluates the classification result, and the third experiment suggests hybrid model representation. When the Hybrid Modified Rough k-means + + - RBM model is compared with any single model, it provides the highest accuracy. [ABSTRACT FROM AUTHOR]

In the field of rough set, feature reduction is a hot topic. Up to now, to better guide the explorations of this topic, various devices regarding feature reduction have been developed. Nevertheless, some challenges regarding these devices should not be ignored: (1) the viewpoint provided by a fixed measure is underabundant; (2) the final reduct based on single constraint is sometimes powerless to data perturbation; (3) the efficiency in deriving the final reduct is inferior. In this study, to improve the effectiveness and efficiency of feature reduction algorithms, a novel framework named parallel selector for feature reduction is reported. Firstly, the granularity of raw features is quantitatively characterized. Secondly, based on these granularity values, the raw features are sorted. Thirdly, the reordered features are evaluated again. Finally, following these two evaluations, the reordered features are divided into groups, and the features satisfying given constraints are parallel selected. Our framework can not only guide a relatively stable feature sequencing if data perturbation occurs but can also reduce time consumption for feature reduction. The experimental results over 25 UCI data sets with four different ratios of noisy labels demonstrated the superiority of our framework through a comparison with eight state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

As a key part of data preprocessing, namely attribute reduction, is effectively applied in the rough set field. The purpose of attribute reduction is to prevent too many attributes from affecting classifier operations and reduce the dimensionality of data space. Presently, in order to further improve the simplification performance of attribute reduction, numerous researchers have proposed a variety of methods. However, given the current findings, the challenges are: to reasonably compress the search space of candidate attributes; to fulfill multi-perspective evaluation; and to actualize attribute reduction based on guidance. In view of this, forward greedy searching to κ -reduct based on granular ball is proposed, which has the following advantages: (1) forming symmetrical granular balls to actualize the grouping of the universe; (2) continuously merging small universes to provide guidance for subsequent calculations; and (3) combining supervised and unsupervised perspectives to enrich the viewpoint of attribute evaluation and better improve the capability of attribute reduction. Finally, based on three classifiers, 16 UCI datasets are used to compare our proposed method with six advanced algorithms about attribute reduction and an algorithm without applying any attribute reduction algorithms. The experimental results indicate that our method can not only ensure the result of reduction has considerable performance in the classification test, but also improve the stability of attribute reduction to a certain degree. [ABSTRACT FROM AUTHOR]

Fuzzy rough sets and multi-granularity rough sets are essential extensions of Pawlak rough sets, which have become artificial intelligence research hotspots. Previous studies of the rough sets based on the fuzzy T-equivalence relation did not take the multi-granularity into account. The multi-granularity data is typically the multi-view cognition obtained by different granularity of the data, and its distinctive feature is that the data can be presented in different granularity spaces. In this paper, we integrate the idea of multi-granularity and propose four new models of "optimistic," "pessimistic," "optimistic-pessimistic," and "pessimistic-optimistic" decision-theoretic rough sets based on the fuzzy T-equivalence relation for the first time, followed by a preliminary analysis of the intrinsic relations and properties of these new decision-theoretic rough set models by a concrete example. At last, we use experiments to show the effectiveness of suggested models, proving that they are both rational and practical. [ABSTRACT FROM AUTHOR]

Approximate accuracy is an important concept in rough set theory, which is defined by upper and lower approximations. Generally speaking, the higher precision means the better application performance. The approximation accuracy can be improved by minimizing the upper approximation and maximizing the lower approximation. Recently, Zhou [52] introduced two types of fuzzy-covering based rough set models by using inclusion relation between fuzzy sets. In this paper, by replacing inclusion relation with implication degree, we investigate two new fuzzy covering-based rough set models. Compared with inclusion relationship, the inclusion degree can describe the contained relation between fuzzy sets in more detail. This makes our upper approximation smaller than Zhou's upper approximation, while the lower approximation is larger than Zhou's. Therefore, the approximate accuracy of our model is higher than that of Zhou. Furthermore, we apply the new model to the study of multi-attribute decision-making (MADM). Combined with the car buying problem, we demonstrate the effectiveness of our model and compare it with other methods. The results show that we can get the same optimal choice as other methods. However, according to Zhou's model, we cannot get the optimal choice. [ABSTRACT FROM AUTHOR]

In this paper, it is investigated how different features of membrane systems can be simulated by the boundary rule application. Firstly, it is discussed how the effect of maximally parallel mode can be obtained by non-cooperative boundary rules applied only in sequential mode, then it is also demonstrated how membrane dissolution, or the application of using promoters and inhibitors can be simulated. [ABSTRACT FROM AUTHOR]

Essentially, the problem solving of attribute reduction can be regarded as a process of reduct searching which will be terminated if a pre-defined restriction is achieved. Presently, among a variety of searching strategies, meta-heuristic searching has been widely accepted. Nevertheless, it should be emphasized that the iterative procedures in most meta-heuristic algorithms rely heavily on the random generation of initial population, such a type of generation is naturally associated with the limitations of inferior stability and performance. Therefore, a constraint score guidance is proposed before carrying out meta-heuristic searching and then a novel framework to seek out reduct is developed. Firstly, for each attribute and each label in data, the index called local constraint score is calculated. Secondly, the qualified attributes are identified by those constraint scores, which consist of the foundation of initial population. Finally, the meta-heuristic searching can be further employed to achieve the required restriction in attribute reduction. Note that most existing meta-heuristic searchings and popular measures (evaluate the significance of attributes) can be embedded into our framework. Comprehensive experiments over 20 public datasets clearly validated the effectiveness of our framework: it is beneficial to reduct with superior stabilities, and the derived reduct may further contribute to the improvement of classification performance. [ABSTRACT FROM AUTHOR]

Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs' psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies. [ABSTRACT FROM AUTHOR]

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhood systems inspired by the system of maximal neighborhood systems. We benefit from the symmetry between rough approximations (lower and upper) and topological operators (interior and closure) to structure the current generalized rough approximation spaces. First, we display two novel types of rough set models produced by maximal neighborhoods, namely, type 2 m ξ -neighborhood and type 3 m ξ -neighborhood rough models. We investigate their master properties and show the relationships between them as well as their relationship with some foregoing ones. Then, we apply the idea of adhesion neighborhoods to introduce three additional rough set models, namely, type 4 m ξ -adhesion, type 5 m ξ -adhesion and type 6 m ξ -adhesion neighborhood rough models. We establish the fundamental characteristics of approximation operators inspired by these models and discuss how the properties of various relationships relate to one another. We prove that adhesion neighborhood rough models increase the value of the accuracy measure of subsets, which can improve decision making. Finally, we provide a comparison between Yao's technique and current types of adhesion neighborhood rough models. [ABSTRACT FROM AUTHOR]

As nonassociative fuzzy logic connectives, it is important to study fuzzy rough set models using overlap functions that replace the role of t-norms. Overlap functions and t-norms are logical operators with symmetry. Recently, intuitionistic fuzzy rough set and multi-granulation fuzzy rough set models have been proposed based on overlap functions. However, some results (that contain five propositions, two definitions, six examples and a proof) must be improved. In this work, we improved the existing results. Moreover, to extend the existing fuzzy rough sets, a new fuzzy covering rough set model was constructed by using the generalized overlap function, and it was applied to the diagnosis of medical diseases. First, we improve some existing results. Then, in order to overcome the limitations of the fuzzy covering rough set model based on overlap functions, a fuzzy β -covering rough set model based on generalized overlap functions was established. Third, some properties of the fuzzy β -covering rough set model based on generalized overlap functions are discussed. Finally, a multi-criteria decision-making (MCDM) method of the fuzzy β -covering rough set based on generalized overlap functions was proposed. Taking medical disease diagnosis as an example, the comparison with other methods shows that the proposed method is feasible and effective. [ABSTRACT FROM AUTHOR]

A complex network in reality contains a large amount of information, but some information cannot be obtained accurately or is missing due to various reasons. An uncertain complex network is an effective mathematical model to deal with this problem, but its related research is still in its infancy. In order to facilitate the research into uncertainty theory in complex network modeling, this paper summarizes and analyzes the research hotspots of set pair analysis, rough set theory and fuzzy set theory in complex network modeling. This paper firstly introduces three kinds of uncertainty theories: the basic definition of set pair analysis, rough sets and fuzzy sets, as well as their basic theory of modeling in complex networks. Secondly, we aim at the three uncertainty theories and the establishment of specific models. The latest research progress in complex networks is reviewed, and the main application fields of the three uncertainty theories are discussed, respectively: community discovery, link prediction, influence maximization and decision-making problems. Finally, the prospect of the modeling and development of uncertain complex networks is put forward. [ABSTRACT FROM AUTHOR]

Humans are a vision-dominated species; what we perceive depends on where we look. Therefore, eye movements (EMs) are essential to our interactions with the environment, and experimental findings show EMs are affected in neurodegenerative disorders (ND). This could be a reason for some cognitive and movement disorders in ND. Therefore, we aim to establish whether changes in EM-evoked responses can tell us about the progression of ND, such as Alzheimer's (AD) and Parkinson's diseases (PD), in different stages. In the present review, we have analyzed the results of psychological, neurological, and EM (saccades, antisaccades, pursuit) tests to predict disease progression with machine learning (ML) methods. Thanks to ML algorithms, from the high-dimensional parameter space, we were able to find significant EM changes related to ND symptoms that gave us insights into ND mechanisms. The predictive algorithms described use various approaches, including granular computing, Naive Bayes, Decision Trees/Tables, logistic regression, C-/Linear SVC, KNC, and Random Forest. We demonstrated that EM is a robust biomarker for assessing symptom progression in PD and AD. There are navigation problems in 3D space in both diseases. Consequently, we investigated EM experiments in the virtual space and how they may help find neurodegeneration-related brain changes, e.g., related to place or/and orientation problems. In conclusion, EM parameters with clinical symptoms are powerful precision instruments that, in addition to their potential for predictions of ND progression with the help of ML, could be used to indicate the different preclinical stages of both diseases. [ABSTRACT FROM AUTHOR]

Deterioration of concrete structures is closely related to their service environment. Under different environmental conditions, the durability performance of structures will be different. To perform durability design based on local conditions and extend the service life of structures, it is necessary to divide their service environment based on the prevailing deterioration mechanism. In this study, considering Guangdong Province as an example, the environmental conditions affecting the durability of concrete structures are investigated and the geographical distribution of environmental conditions is analyzed, including ambient temperature, precipitation, corrosive gas, acid rain, and salt fog. The weights of the regional durability indexes are calculated by combining fuzzy clustering analysis with information entropy using rough set theory. Based on the assessment data of 1324 existing concrete structures, the durability geographic division map of Guangdong Province, including three regions (Chloride corrosion region, Acid rain‐carbonation coupling region, and Carbonation region), is constructed. This geographic division map is divided into a total of eight subregions by considering the subordinate factors in each region. The environmental characteristics of each region and its dominating deterioration mechanism for concrete structures are analyzed, and suggestions for durability design are provided. [ABSTRACT FROM AUTHOR]

This paper aims to increase the accuracy measure of the subgraph of a graph and generate new nano topologies on the power set of vertices and edges of a graph. Firstly, we introduce E j -neighborhoods and C j -neighborhoods which depend on vertices and edges of a simple directed graph by using j-neighborhoods for j ∈ { out , in , ∩ , ∪ } . Then, we apply these neighborhoods to present the concepts of E j -approximations and C j -approximations. We investigate their main properties and relationships among them. Besides, we define the accuracy measures of a subgraph with the help of these approximations and show that C j -accuracy measures are the highest when we compare these accuracy measures with the previous one. Furthermore, we generate new nano topologies via obtained approximations and illustrate that these topologies may not be comparable. Finally, we give an application in physics to elucidate the current approximations are more general. Throughout the paper, we summarize all comparisons with tables and give counterexamples to support the study. [ABSTRACT FROM AUTHOR]

As a useful extension of rough sets, multigranulation rough sets (MGRSs) can be used to deal with a variety of complex data. Numerous significant advances have been achieved by generalizing MGRSs. However, most of the existing findings of MGRSs are sensitive to misclassification and noise in data. Furthermore, the studies of attribute reduction based on MGRSs have received little attention. To fill such gaps, this paper proposes an extended model of MGRSs named variable precision multigranulation rough sets (VPMGRSs) by introducing rough membership function and approximation parameters in variable precision rough sets (VPRSs) into the multigranulation environment. After giving some basic properties of VPMGRSs, we investigate the relationships between VPMGRSs and VPRSs, pessimistic MGRSs, and generalized MGRSs. In addition, several VPMGRSs-based attribute reductions are introduced, and it is proved that some of them are equivalent when the parameters in the model meet specific requirements. Finally, we propose a heuristic algorithm for α -lower distribution reduct and illustrate its effectiveness and efficiency by a comparative experiment on real datasets. [ABSTRACT FROM AUTHOR]

Since Pawlak defined the notion of rough sets in 1982, many authors made wide research studying rough sets in the ordinary case and the fuzzy case. This paper introduced a new style of rough fuzzy sets based on a fuzzy ideal ℓ on a universal finite set X. New lower and new upper fuzzy sets are introduced, and consequently, fuzzy interior and fuzzy closure operators of a rough fuzzy set are discussed. These definitions, if ℓ is restricted to ℓ° = {ō}, imply the fuzzification of previous definitions given in the ordinary case, and moreover in the crisp case, we get exactly these previous definitions. The new style gives us a better accuracy value of roughness than the previous styles. Rough fuzzy connectedness is introduced as a sample of applications on the recent style of roughness. [ABSTRACT FROM AUTHOR]

Being an agro-based natural product, cotton always poses vagueness in the parameters. Hence, formulation of decision rules for prediction of cotton yarn quality from the imprecise cotton fiber properties is an intricate problem. Yarn tenacity is considered an imperative quality parameter in the cotton textile industry. Modelling of yarn tenacity has remained as the cynosure of research for textile engineers. In recent years, rough set theory has evolved as one of the most important techniques used for handling imprecise data. One of the cardinal uses of rough set theory is its application to rule generation. Our approach focuses on the elimination of the redundant data set in order to generate effective decision rules which retain the accuracy of the original data set. In this work rough set theory is employed to generate decision rules to predict yarn tenacity from six input parameters. The validation results prove that the generated 45 decision rules accurately predicted 14 out of 16 unknown test data. Thus, in the present competitive market, this model is potent for getting recognition from the textile industry. [ABSTRACT FROM AUTHOR]

Minimum vertex covering has been widely used and studied as a general optimization problem. We focus on one of its variation: minimum vertex cover of hypergraphs. Most existed algorithms are designed for general graphs, where each edge contains at most two vertices. Moreover, among these algorithms, rough set-based algorithms have been proposed recently and attract many researchers sight. However, they are not efficient enough when the number of nodes and hyperedges scale largely. To address these limitations, we propose a novel rough set-based approach by combining rough set theory with the stochastic local search algorithm. In this approach, three improvements have been introduced, i.e., (1) fast relative reduct construction method, which can quickly achieve a relative reduct, and it is based on low-complexity heuristics; (2) (p, q)-reverse incremental verification mechanism, which uses incremental positive region update technology to quickly verify whether a required attribute pair can be found; (3) adjusting iterative process rules, the main purposes of these rules are avoiding repeated computation and jumping out of local optimum. Finally, by comparing groups of benchmark graphs and hypergraphs with the existing algorithms based on rough sets, experimental results presents the advantages and limitations of our proposed approach. [ABSTRACT FROM AUTHOR]

Gene selection is an important technique to remove irrelevant genes and handle the problem of curse-of-dimensionality issue. In other words the objective of the gene selection problem is to find (a small number of) cancer responsible genes (called biomarkers) from large number of genes, which have highest class discernable property. Traditional gene selection techniques are often not scalable on large number of genes and they are not able to handle the problem of vagueness, indiscerniblity, ambiguity, overlappiness complex cancer subtypes classes as usually present in the microarray gene expression data. In this context, a novel greedy fuzzy vaguely quantified rough approach for feature (gene) selection (GFVQRFS) is proposed that handles curse-of-dimensionality issue, vagueness, indiscerniblity, ambiguity, overlapping and complex cancer subtypes classes. The proposed method is evaluated on eight publicly available microarray gene expression datasets and the results are compared with four other state-of-the-art methods namely, CFS-GA, CON-GA, CON-GS and FRFS-GA using three classifiers (viz., KNN, SVM and NB). Six different validity measures (viz., accuracy, precision, recall, macro average F 1 -measures, micro average F 1 -measures and kappa) are used to access the performance of the proposed GFVQRFS method with respect to the compared methods. The proposed method selects very less number of genes compared to those selected by the other counterpart methods. The experimental results reveal the edge of the proposed method over other counterpart methods for most of the datasets. [ABSTRACT FROM AUTHOR]

Many researchers have proposed algorithms to improve the network performance of vehicular ad hoc network (VANET) clustering techniques for different applications. The effectiveness of the clustering model is the most important challenge. The K-Means clustering algorithm is an effective algorithm for multi-clusters that can be used in VANETs. The problems with the K-Means algorithm concern the selection of a suitable number of clusters, the creation of a highly reliable cluster, and achieving high similarity within a cluster. To address these problems, a novel method combining a covering rough set and a K-Means clustering algorithm (RK-Means) was proposed in this paper. Firstly, RK-Means creates multi-groups of vehicles using a covering rough set based on effective parameters. Secondly, the K-value-calculating algorithm computes the optimal number of clusters. Finally, the classical K-Means algorithm is applied to create the vehicle clusters for each covering rough set group. The datasets used in this work were imported from Simulation of Urban Mobility (SUMO), representing two highway scenarios, high-density and low-density. Four evaluation indexes, namely, the root mean square error (RMSE), silhouette coefficient (SC), Davies–Bouldin (DB) index, and Dunn index (DI), were used directly to test and evaluate the results of the clustering. The evaluation process was implemented on RK-Means, K-Means++, and OK-Means models. The result of the compression showed that RK-Means had high cluster similarity, greater reliability, and error reductions of 32.5% and 24.2% compared with OK-Means and K-Means++, respectively. [ABSTRACT FROM AUTHOR]

Tooth decay is a common problem among people due to many factors, including neglect to clean teeth. Dental caries is becoming more common in a number of countries worldwide. This study aims to determine the prevalence of dental caries and how to treat this problem. We also implement fuzzy soft multifunction between fuzzy soft topological spaces which is Smarandache's generation of the notion. In this paper, we generated additional topologies for an information system based on a similarity relation. This paper discussed two methods for determining accuracy: our method and Pawlak's qualitative data method. Both ideas show that because of the uncertainty and ambiguity of qualitative data, we get a lot of topologies based on one or two attributes. The new method was used to determine the accuracies. This method revealed the difference between one or two attributes. In fact, the most important factors affecting tooth decay have been identified. Furthermore, we are developing a new algorithm to treat dental caries problems. Tooth decay which includes the conclusions of some well-known results in the corresponding literature is highlighted and discussed. In addition, a comparative application that dwells on the generality of our obtained results is constructed. Our proposed approach is reasonable and effective. [ABSTRACT FROM AUTHOR]

A relation system, as an extension of information systems, is a significant form of representation and discovery of knowledge in rough set theory. Each relation system can induce a topological space. Topology is an invaluable tool for knowledge discovery in relation systems. In this paper, we use topological methods to study attribute reduction problems in relation systems. In the past studies, the topological reduction algorithm applied to arbitrary binary relations had not been proposed. To fill the gap, we propose the concept of topological reduction of relation systems based on binary relations without any other additional constraints. To identify all reductions, we define a discernibility matrix for this kind of reduction and develop its corresponding reduction algorithm. Finally, we conducted several experiments on five UCI datasets using six classification algorithms and two clustering algorithms to check our theoretical results. The experimental results show that our proposed algorithm is effective and practicable. [ABSTRACT FROM AUTHOR]

By a fuzzy preorder, it means a (0, 1]-binary relation on a nonempty set which is self-reflective and transitive. For a fuzzy preorder on a universe, this paper constructs a kind of fuzzy rough set model based on the multiplication and division of real numbers. The definable sets and the related fuzzy topology are studied. [ABSTRACT FROM AUTHOR]