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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]

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]

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]

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]

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy, accessibility, and cost-effectiveness. This paper investigates the potential applications of intuitionistic fuzzy sets (IFS) with rough sets in the context of sparse data. When it comes to capture uncertain information emanating from both upper and lower approximations, these intuitionistic fuzzy rough numbers (IFRNs) are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets, respectively. We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties. We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles. These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator (IFRWFA) and intuitionistic fuzzy rough ordered weighted fairly aggregation operator (IFRFOWA). These operators successfully adjust to membership and non-membership categories with fairness and subtlety. We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multi-attribute decision-making field. We use the intuitionistic fuzzy rough environment's architecture to create a novel strategy in situation involving several decision-makers and non-weighted data. Additionally, we developed a novel technique by combining the IFSs with quaternion numbers. We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers (IFQNs). With the help of this framework, we can simulate uncertainty in real-world situations and address a number of decision-making problems. Using the examples we have released, we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity of medical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology. [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 FROM AUTHOR]

In this paper rudiments of the theory will be outlined, and basic concepts of the theory will be illustrated by a simple tutorial example, concerning churn modeling in telecommunications. Real life applications require more advanced extensions of the theory but we will not discuss these extensions here. Rough set theory has an overlap with many other theories dealing with imperfect knowledge, e.g., evidence theory, fuzzy sets, Bayesian inference and others. Nevertheless, the theory can be regarded as an independent, complementary, not competing, discipline in its own rights. [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 mainly studies and proves the roughness bound of disturbation fuzzy sets. Firstly, based on the theory of determining self-increment and uncertain self-decrement operators, the problem that the execution subsets are not equal sets is effectively solved, which hinders the quantitative study of disturbed fuzzy sets and lays a foundation for the quantitative study of the related properties of disturbed fuzzy sets in the future. The boundary of roughness measure of disturbing fuzzy set is further studied and proved. The new territories proposed in this paper can effectively avoid the unnecessary calculation space outside the boundary in the calculation process, so as to improve the work efficiency. [ABSTRACT FROM AUTHOR]

Fuzzy rough set models are useful tools for dealing with fuzzy and real-valued data. They have been used in many real-world applications. In this paper, we investigate the fuzzy rough set model based on triangular norms and fuzzy implications. First, we extend some results in the published literature by removing the condition that is the continuity of triangular norms, and obtain more general conclusion about fuzzy upper approximation operators. Then, for the fuzzy neighborhood and the fuzzy lower approximation operator based on fuzzy implications, we investigate their characterization with each other. Finally, we establish the relationships between fuzzy rough sets and fuzzy topology. In this work, researches on the properties of fuzzy rough sets based on triangular norms which need not be continuous provide generalization results for fuzzy rough set theory from viewpoint of mathematics. [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]

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]

Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, the bipolar FS (BFS) theory can tackle the uncertainty and the bipolarity of the data in different circumstances. This article aims to introduce the idea of rough bipolar fuzzy ideals in semigroup (SG), which is a generalization of the concept of rough BFSs (RBFSs) in an SG. We also investigate the roughness in the bipolar fuzzy subsemigroup (BF-SSG) with the help of congruence relation (cng-R) defined on the SG and studied some relevant structural properties. Moreover, the idea is extended to the rough bipolar fuzzy left ideal, rough bipolar fuzzy right ideal, rough bipolar fuzzy two-sided ideal, rough bipolar fuzzy interior ideal, and rough bipolar fuzzy bi-ideal in SGs. Further, it is seen that cng-Rs and complete cng-Rs play vital roles in the construction of rough approximations of bipolar fuzzy ideals. Consequently, their associated properties are explored by using cng-Rs and complete cng-Rs. [ABSTRACT FROM AUTHOR]

Searching for quantitative scientific prediction models and methods under uncertain hybrid information environment is helpful to the scientific decision-making of practical management problems. In this paper, we discuss the uncertain decision making problem with hybrid attributes and fuzzy decision objects. Considering the characteristic of hybrid attribute information, we introduce kernel functions to abstract the similarities from different types of attributes. On this basis, the kernel-based upper and lower approximations of arbitrary fuzzy decision objects over hybrid attribute information system are given under a multi-granularity framework, i.e., kernelized multi-granulation fuzzy rough sets, called KMGFRS in this paper. Then, the attribute reduction on hybrid attribute decision system based on KMGFRS is discussed. In addition, we combine KMGFRS and fuzzy k-nearest neighbors (FkNN) to propose a new prediction method without prior information and apply it to stroke risk assessment and prediction in clinical decision-making. Finally, we use real clinical data and UCI datasets for experiment analysis, and the results verify the applicability and validity of the model. [ABSTRACT FROM AUTHOR]

The rough set (RS) and multi-granulation RS (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, the bipolar fuzzy sets (BFSs) are effective tools for handling bipolarity and fuzziness of the data. In this study, with the description of the background of risk decision-making problems in reality, we present (α β)-optimistic multi-granulation bipolar fuzzified preference rough sets ((α β)o-MG-BFPRSs) and (α β)-pessimistic multi-granulation bipolar fuzzified preference rough sets ((α β)p-MG-BFPRSs) using bipolar fuzzy preference relation (BFPR). Subsequently, the relevant properties and results of both (α β)o-MG-BFPRSs and (α β)p-MG-BFPRSs are investigated in detail. At the same time, a relationship among the (α β)-BFPRSs, (α β)o-MGBFPRSs and (α β)p-MG-BFPRSs is given. [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]

In fuzzy set theory, the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets. It is also to be noted that the intuitionistic fuzzy set is re ected as an extension of the fuzzy set accommodating both membership and non-membership functions together with a hesitation margin. In the intuitionistic fuzzy set theory, the sum of the membership function and the non-membership function is a value between 0 and 1. In recent times, intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory. Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in real-life problems and that is why many researchers paid more attention to this concept. Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties. In this paper, we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a set-theoretic approach. The proposed measure is able to give an exact result. In the application part, we consider a real-life problem for selecting a fair play award-winning team in a cricket tournament and describe the algorithm. [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]

The quantale module introduced by Abramsky and Vickers, engaged a large number of researchers. This research article focuses the combined behavior of rough set, soft set and an algebraic structure quantale module with the left action. In fact, the paper reflects the generalization of rough soft sets. This combined effect is totally dependent on soft binary relation including aftersets and foresets. Different soft substructures in quantale modules are defined. The characterizations of soft substructures in quantale modules based on soft binary relation are presented. Further, in quantale modules, we define soft compatible and soft complete relations in terms of aftersets and foresets. Furthermore, we use soft compatible and soft complete relations to approximate soft substructures of quantale modules and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough soft quantale modules. Additionally, we describe the algebraic relationships between the upper (lower) approximations of soft substructures of quantale modules and the upper (lower) approximations of their homomorphic images using the concept of soft quantale module homomorphism. [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]

The change in living standard made people to think on their physical health. Accordingly, healthcare organizations are concentrating more on physical health of people in terms of disease diagnosis and patient care. Digitization is a step towards this end. Nevertheless, digitization generates a voluminous of data every second. Besides, these data contain uncertainties and may be imprecise. Analyzing such uncertainties and impreciseness in an information system is a critical task. Computational intelligence techniques are developed to handle such cases. These techniques include fuzzy set, rough set, soft set, neutrosophic set, bio-inspired, nature-inspired, and evolutionary computing. This research paper presents an extensive review of healthcare that has been carried out by researchers using rough and bio-inspired computing. The purpose of this review is to provide an understanding of prevailing research and relevant information in disease diagnosis concerning rough set and bio-inspired computing. Besides, the application and future scope of research are also presented. [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]

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]

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]

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]

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]

Knowledge distance is used to measure the difference between granular spaces, which is an uncertainty measure with strong distinguishing ability in a rough set. However, the current knowledge distance failed to take the relative difference between granular spaces into account under the given perspective of uncertain concepts. To solve this problem, this paper studies the relative knowledge distance of intuitionistic fuzzy concept (IFC). Firstly, a micro-knowledge distance (md) based on information entropy is proposed to measure the difference between intuitionistic fuzzy information granules. Then, based on md, a macro-knowledge distance (MD) with strong distinguishing ability is further constructed, and it is revealed the rule that MD is monotonic with the granularity being finer in multi-granularity spaces. Furthermore, the relative MD is further proposed to analyze the relative differences between different granular spaces from multiple perspectives. Finally, the effectiveness of relative MD is verified by relevant experiments. According to these experiments, the relative MD has successfully measured the differences in granular space from multiple perspectives. Compared with other attribute reduction algorithms, the number of subsets after reduction by our algorithm is in the middle, and the mean-square error value is appropriate. [ABSTRACT FROM AUTHOR]

In the paper (Han et al. in IEEE Trans Fuzzy Syst 23:2358–2370, 2015), we proposed the bipolar-valued rough fuzzy set in one universe, which is an inevitable improvement by introducing inconsistentbipolarity to rough set. However, the bipolar-valued rough fuzzy set in one universe still has the limitations to complex practical problems. This motives us to propose the generalized concept of bipolar-valued fuzzy rough set in two universes, in which, inconsistentbipolarity is introduced into the crisp approximation space for the first time, and furthermore, two universes are considered to reflect the interrelations among different sources' inconsistentbipolarity information. Comparing with other existing fuzzy rough set models, in syntax, the new one generalizes the existing ones. And most importantly, in semantics, the new one firstly considering the inconsistentbipolarity information, which is important in practice. Based on the new concept, two methods to the decision-making problems with inconsistent fuzzy bipolarity information are proposed, together with their applications. The comparison study with other existing rough set related methods highlights the necessity of our study, which provides a new inconsistent fuzzy bipolarity perspective to rough set theory and related applications. [ABSTRACT FROM AUTHOR]

Recently, the notion of a three-way fuzzy set is presented, inspired by the basic ideas of three-way decision and various generalized fuzzy sets, including lattice-valued fuzzy sets, partial fuzzy sets, intuitionistic fuzzy sets, etc. As the new theory of uncertainty, it has been used in attribute reduction and as a new control method for the water level. However, as an extension of a three-way decision, this new theory has not been used in multi-criteria decision making (MCDM for short). Based on the previous work, in this paper, we present rough set models based on three-way fuzzy sets, which extend the existing fuzzy rough set models in both complete and incomplete information systems. Furthermore, the new models are used to solve the issue of MCDM. Firstly, three-way fuzzy relation rough set and three-way fuzzy covering rough set models are presented for complete and incomplete information systems. Because almost all existing fuzzy rough set models are proposed under complete information, the new proposed models can be seen as a supplement to these existing models. Then, a relationship between the three-way fuzzy relation rough set and the three-way fuzzy covering rough set is presented. Finally, a novel method for the issue of MCDM is presented under the novel three-way fuzzy rough set models, which is used in paper defect diagnosis. [ABSTRACT FROM AUTHOR]

Decision-making problem is a fundamental activity in human life every day. Regarding group decision-making, individuals have insufficient comprehension of the decision objects owing to the limited experience and knowledge and drawback the evaluation process. Therefore, the evaluation information is missing and the group cannot get the precise information for decision objects resulting in the generation of incomplete information systems. It is meaningful for individuals finding an approach to Leverage and tap into existing information. On the basis, the work presented in this paper focuses on group decision-making problems (GDM) with incomplete information. Under the framework of group decision-making, a GDM approach with an incomplete information system is presented combining the formal concept analysis and rough set theory. Firstly, we propose a concept called formal decision context and discuss the properties of the formal decision context, which could divide the incomplete information system into many cognitive units, and the definitions of cognitive units will be given. Then, the property and the relations of various cognitive units will be discussed. Additionally, the upper and lower approximation space under the formal decision context is founded considering the risk attitudes integrating fuzzy rough set and formal concept context. Considering the order relation of various cognitive units and decision objects, we introduce the dominance relation and the importance degree of each cognitive unit under the framework of formal decision context. Furthermore, a theoretical framework of the multi-criteria decision-making problem is presented and two models for the multi-criteria group decision-making problem are discussed combined with fuzzy rough set and formal decision context from two perspectives, including qualitative analysis and quantitative analysis. Finally, an illustrated example is applied to verify the validity and effectiveness of the proposed models. The contributions of this paper include two aspects. On the one hand, this paper provides a new perspective and paradigm considering MCGDM problems with the incomplete information system from the perspective of group consensus. On the other hand, this paper gives two approaches for group decision-making problems from sorting and set theory by the perspective of multi-granular rough set and group consensus. • A model of formal decision context with incomplete information to describe the cognitive situation. • An approach to MCDM problem combined rough set with formal decision context with incomplete information. • Two approaches to MCGDM problem from qualitative analysis and quantitative analysis. [ABSTRACT FROM AUTHOR]

As an extension of partition, fuzzy β -covering can provide a more realistic and accurate description of incomplete information. In this paper, we mainly integrate the idea of fuzzy β -covering with dual hesitant fuzzy (DHF) information and construct some novel three-way decision (3WD) models with DHF covering-based rough set. Firstly, we propose the notions of DHF β -covering, DHF β -minimal description and DHF β -maximal description, and then construct three types of DHF neighborhood operators. Meanwhile, we introduce DHF conditional probability by using DHF neighborhood operator. Secondly, in terms of DHF conditional probability, DHF covering-based probabilistic rough set, DHF covering-based decision-theoretic rough set and their 3WD models are established. In light of DHF neighborhood operator, we propose two pairs of optimistic and pessimistic DHF decision evaluation functions and build two 3WD models through them. Lastly, a numerical example is employed to elaborate the application of the above models, which is effective and credible to medicine screening for Alzheimer's disease. • Proposed neighborhood operators in dual hesitant fuzzy environment. • Three-way decision based on dual hesitant fuzzy probabilistic rough sets. • Three-way decision based on dual hesitant fuzzy decision-theoretic rough sets. • Three-way decision based on dual hesitant fuzzy decision evaluation functions. • Experiment on medication screening of Alzheimer's disease are given. [ABSTRACT FROM AUTHOR]

Datasets mainly consist of ambiguous objects, redundant and uncertain attribute values which increase complexity, time and cost in Knowledge Discovery in Databases (KDD) process. Rough set-based attribute reduction techniques deals with ambiguity but fails to handle uncertainty available in a real-valued dataset. Combining rough set with intuitionistic fuzzy set provides a great opportunity to the researchers working on attribute reduction of real-valued datasets as it provides better results when compared to the traditional fuzzy rough set theory. In this paper, we present a new intuitionistic fuzzy rough set model for attribute reduction to avoid misclassification and perturbation by handling hesitancy, ambiguity and uncertainty present in a dataset. We define an intuitionistic fuzzy tolerance relation between two objects along with lower and upper approximations based on that relation. Next, the concept of Degree of dependency is utilized to present attribute reduction by using model due to its better performing nature over other methods. The algorithm of the proposed technique is applied on benchmark datasets to perform a comparative study with recent approaches. We obtain the best result for the reduced Breast Cancer dataset by our proposed approach, with an accuracy of 98.96% along with 0.90 standard deviation by using SMO classifier. Finally, our proposed method is used to present a methodology to improve the prediction of umami peptides. Here, we record the best results with sensitivity, specificity, accuracy, AUC, and MCC of 96.8%, 93.6%, 97.7%, 0.988, and 0.899, respectively. From the experiments, it can be concluded that our method outperforms the existing methods. [ABSTRACT FROM AUTHOR]

Fuzzy sets are a major simplification and wing of classical sets. The extended concept of set theory is rough set (RS) theory. It is a formalistic theory based upon a foundational study of the logical features of the fundamental system. The RS theory provides a new mathematical method for insufficient understanding. It enables the creation of sets of verdict rules from data in a presentable manner. An RS boundary area can be created using the algebraic operators union and intersection, which is known as an approximation. In terms of data uncertainty, fuzzy set theory and RS theory are both applicable. In general, as a uniting theme that unites diverse areas of modern arithmetic, symmetry is immensely important and helpful. The goal of this article is to present the notion of rough fuzzy ideals (RFI) in the gamma ring structure. We introduce the basic concept of RFI, and the theorems are proven for their characteristic function. After that, we explain the operations on RFI, and related theorems are given. Additionally, we prove some theorems on rough fuzzy prime ideals. Furthermore, using the concept of rough gamma endomorphism, we propose some theorems on the morphism properties of RFI in the gamma ring. [ABSTRACT FROM AUTHOR]

Recently, the intelligent traffic control system and its uncertainty analysis are considered one of the hot spots for utilizing the available techniques. It became more essential when the automatic car, electric vehicle, and other smart cars have introduced the transportation. To control the traffic accident and smooth road services an intelligent traffic control system required. It will be also useful in decreasing the time, reaction time, and efficiency of traffic. However, the problem arises while characterization of true, false or uncertain regions of traffic flow and its future approximation. To deal with this issue some available mathematical technique for traffic flow using rough set, fuzzy rough set, and its extension with the neutrosophic set is discussed in this paper. Some of the papers related to graphical visualization of traffic flow is also discussed for further improvement. The rough set theory can be useful for dealing the uncertain, incomplete, and indeterminate data set. Hence, the hybridization of the neutrosophic set and rough can be considered one of the efficient tools for intelligent traffic control and its approximation via automatic red, green and yellow lights. This paper tried to provide an overview of each available technique to solve the traffic problem. It is hoped that the proposed study will be helpful for several researchers working on traffic flow, traffic accident diagnosis, and its hybridization as future research. [ABSTRACT FROM AUTHOR]

Some learners couldn't get ideal learning results from distance education, to find out the root of this problem, their learning behavior and initiative should be analyzed in real time. However, in existing research results, the collected distance learning behavior data of learners are not pertinent enough, the extraction methods of big data are not proper enough, and the analysis models of learning behavior are not scientific enough. For these reasons, this paper analyzed the autonomous learning behavior of learners during distance reading based on big data, and gave the analysis contents and methods. In the text, a sequence diagram transformation method that is selfadaptive to long and short sequences had been introduced to process the learning behavior data of learners, who were then classified according to the features of different autonomous learning behavior sequences. Then, an attribute reduction algorithm based on improved Bayesian fuzzy rough set was adopted for attribute reduction, and the behavior indexes that are closely related to the autonomous learning effect of learners were selected for correlation analysis. After that, this paper proposed a method for detecting nonautonomous learning behavior based on multiple time scales, combining shortterm autonomous learning pattern with long-term autonomous learning behavior and resource access behavior, this paper also analyzed the typical autonomous learning pattern of learners through the learning of hidden layer features. At last, experimental results proved the effectiveness of the proposed analysis method. [ABSTRACT FROM AUTHOR]

In real cases, missing values tend to contain meaningful information that should be acquired or should be analyzed before the incomplete dataset is used for machine learning tasks. In this work, two algorithms named jointly fuzzy C-Means and vaguely quantified nearest neighbor (VQNN) imputation (JFCM-VQNNI) and jointly fuzzy C-Means and fitted VQNN imputation (JFCM-FVQNNI) have been proposed by considering clustering conception and sufficient extraction of uncertain information. In the proposed JFCM-VQNNI and JFCM-FVQNNI algorithm, the missing value is regarded as a decision feature, and then, the prediction is generated for the objects that contain at least one missing value. Specially, as for JFCM-VQNNI algorithm, indistinguishable matrixes, tolerance relations, and fuzzy membership relations are adopted to identify the potential closest filled values based on corresponding similar objects and related clusters. On the basis of JFCM-VQNNI algorithm, JFCM-FVQNNI algorithm synthetic analyzes the fuzzy membership of the dependent features for instances with each cluster. In order to fill the missing values more accurately, JFCM-FVQNNI algorithm performs fuzzy decision membership adjustment in each object with respect to the related clusters by considering highly relevant decision attributes. The experiments have been carried out on five datasets. Based on the analysis of root-mean-square error, mean absolute error, comparison of imputation values with actual values, and classification accuracy results analysis, we can draw the conclusion that the proposed JFCM-FVQNNI and JFCM-VQNNI algorithms yields sufficient and reasonable imputation performance results by comparing with fuzzy C-Means parameter-based imputation algorithm and fuzzy C-Means rough parameter-based imputation algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we intend the concept of rough cubic Pythagorean fuzzy ideals in the semigroup. By using this notion, we discuss lower approximation and upper ap- proximation of cubic Pythagorean fuzzy left (right) ideals, bi-ideals, interior ideals, and study some of their related properties in detail. [ABSTRACT FROM AUTHOR]

This paper expose a study on rough interval valued pythagorean fuzzy sets in semigroups. We characterize rough interval valued pythagorean fuzzy sets by an exam- ple. Characterize composition of two interval valued pythagorean fuzzy sets. Introduce rough interval valued pythagorean fuzzy left(right, bi-, interior-,(1,2)-)ideals in semi- groups. Moreover we prove an interval valued pythagorean fuzzy set is an upper rough interval valued pythagorean fuzzy left(right) ideal of semigroup also we give an example for converse of this is not true. Lower and upper approximation of an interval valued pythagorean fuzzy ideal of semigroup is an interval valued pythagorean fuzzy ideal of semigroup. [ABSTRACT FROM AUTHOR]

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

The generalized rough set theory is based on the lower and upper approximation operators defined on the binary relation. The rough sets obtained from serial relations take an important place in topological applications. In this paper, we consider serial relation for texture spaces. A texturing U of a set U is a complete and completely distributive lattice of subset of the power set P(U) which satisfies some certain conditions. Serial relation is defined by using textural sections and presections under a direlation on a texturing. We give some properties of serial direlation and a discussion on rough set theory from the textural point of view under serial direlation. Further, the concept of serial direlation has been characterized in terms of lower and upper textural approximation operators.

Feature selection (FS) is defined as the process of selecting a criterion function for evaluating a feature subset and a search strategy for finding the best feature subset from a large number of feature subsets. Many strategies have been established to date, most of which are based on statistical theory; nevertheless, research is currently ongoing to find better solutions in terms of optimality and computing ease. In FS, where most other methods require supplemental knowledge, the rough set ideology of using only the available data and no further information offers several advantages. The key drawback is that the rough set-based feature selection does not function well on data that are real-valued or noisy (continuous datasets). To overcome this problem, we propose three algorithms based on particle swarm optimization with fuzzy rough fitness function for getting optimal feature subset from a feature set with a large number of features (i.e. continuous or discrete datasets). The suggested algorithms are compared against two classical feature selection methods, as well as three PSO and rough set-based feature selection approaches. Seven commonly used discrete datasets with a modest number of features and eight continuous datasets with a large number of features were utilized in the experiments. Two classification techniques (decision tree or DT and Naive Bays or NB) are used to evaluate the classification performance of selected feature subsets. The results show that using the proposed techniques, a small feature subset may be automatically selected with better classification accuracy than utilizing all features. In terms of classification accuracy and amount of features, the suggested algorithms beat the two traditional and three PSO and rough sets-based feature selection approaches. There is also a significant reduction in the number of features with higher weight on the rapid reduct of the fitness function, as well as improved classification accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid intelligent structure called "Double Bounded Rough Neutrosophic Sets" is defined, which is a combination of Neutrosophic sets theory and Rough sets theory. Further, the Attribute based Double Bounded Rough Neutrosophic Sets was implemented using this hybrid intelligent structure for Facial Expression Detection on real time data. Facial expression detection is becoming increasingly important to understand one's emotion automatically and efficiently and is rich in applications. This paper implements some of these applications of facial expression such as: differentiating between Genuine and Fake smiles, prediction of Depression, determining the Degree of Closeness to a particular Attribute/Expression and detection of fake expression during an examination. With the onset of COVID - 19 pandemic, majority of people are choosing to wear masks. A suitable method to detect Facial Expression with and without mask is also implemented. Double Bounded Rough Neutrosophic Sets proposed in this paper is found to yield better results as compared to that of individual structures (Neutrosophic sets theory or Rough sets theory). [ABSTRACT FROM AUTHOR]

The main aim of the proposed work is to develop the new technique based on decision‐theoretical rough sets (DTRSs) and their applications in three‐way decision‐making problems. This study first develop a fractional fuzzy set (FFS) and their operations, the FFS is a more generalized and accurate tool for describing uncertainty in real‐life data information. A new form of decision technique for dealing with the issue of choice based on DTRSs is included in the three‐way decisions. The loss function of DTRSs is being used in the proposed decision method model. Initially, the idea of fractional fuzzy α‐covering (FF α‐covering), fractional fuzzy α–neighborhood (FF α–neighborhood) was introduced. Under the fractional fuzzy state, we integrated the loss function of DTRSs with covering‐based fractional fuzzy rough sets. Furthermore, we proposed and established performance characteristics for a new fractional fuzzy α‐covering decision‐theoretical rough sets model (FFCDTRSs). Then, according to the level of fractional fuzzy numbers (FFN's) positive and negative membership and related three‐way decision‐making, four methods to solve the expected loss expressed in the form of (FFNs) are described. We have developed a multicriteria decision algorithm (MCDM) based on FFCDTRS. Then an example is used to prove the feasibility of the four methods to solve the MCDM problem. Finally, the results of four distinct decision procedures with various loss functions are compared. The proposed three‐way decision‐making models are more accurate as compared with particular fuzzy sets. [ABSTRACT FROM AUTHOR]

This paper aims to apply the concept of rough sets to Pythagorean fuzzy sets in UPalgebras. Then we introduce fifteen types of rough Pythagorean fuzzy sets in UP-algebras and study their generalization. In addition, we will also discuss t-level subsets of rough Pythagorean fuzzy sets in UP-algebras to study the relationships between rough Pythagorean fuzzy sets and rough sets in UP-algebras. [ABSTRACT FROM AUTHOR]

This paper deals with the rough approximations of spherical fuzzy sets. Also we study the applications of rough spherical fuzzy sets. Distance be- tween rough spherical fuzzy set, similarity measure between rough spherical fuzzy sets. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Real-world applications are now dealing with a huge amount of data, especially in the area of high-dimensional features. Trait reduction is one of the major steps in decision making problems. It refers to the determination of a minimum subset of attributes which preserves the final decision based on the entire set of attributes. Unfortunately, most of the current features are irrelevant or redundant, which makes these systems unreliable and imprecise. This paper proposes a new paradigm based on fuzzy soft relationship and level fuzzy soft relationship, called Union - Intersection decision making method. Using these new principles, the decision-making strategy is structured to choose a fuzzy set of optimal elements from the alternatives on the basis of a fuzzy soft set. Finally, we used our proposed method in medical application to make the decision to diagnose COVID-19. Moreover, we used MATLAB programming to obtain the results; this has coincided with the announcement by the World Health Organization and an accurate proposal was examined, which competes with that of the method of Zhao. [ABSTRACT FROM AUTHOR]