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Fuzzy rough set theory can tackle feature redundancy in data and select more informative features for machine learning tasks. Gaussian kernel is often coupled with fuzzy rough set theory to measure fuzzy relation between data instances. However, Gaussian kernel has a serious long-tail phenomenon, which would perform poorly in modeling the fuzzy relation for high-dimensional data. Moreover, a robust feature evaluation function is also nontrivial in a fuzzy rough set model because a naive model may select those non-optimal feature subsets due to the perturbations from redundant features. This paper delves into Student- t kernel and fuzzy divergence to address these challenges for fuzzy rough feature selection. This paper proposes a new Student- t Kernelized Fuzzy Rough Set (SKFRS) model. The new model uses fuzzy divergence to evaluate uncertain information in the data. It also explores a newly-defined feature evaluation function on the biases of the dynamic relation between the relevance and indispensability of features in feature selection process. A novel forward greedy search algorithm is then presented to solve the final objective function. The selected features are subsequently evaluated on downstream classification tasks. Experimental results using real-world datasets demonstrate the effectiveness of the proposed model and its superiority against the baseline methods. [ABSTRACT FROM AUTHOR]

Fuzzy rough set theory can tackle feature redundancy in data and select more informative features for machine learning tasks. Gaussian kernel is often coupled with fuzzy rough set theory to measure fuzzy relation between data instances. However, Gaussian kernel has a serious long-tail phenomenon, which would perform poorly in modeling the fuzzy relation for high-dimensional data. Moreover, a robust feature evaluation function is also nontrivial in a fuzzy rough set model because a naive model may select those non-optimal feature subsets due to the perturbations from redundant features. This paper delves into Student- t kernel and fuzzy divergence to address these challenges for fuzzy rough feature selection. This paper proposes a new Student- t Kernelized Fuzzy Rough Set (SKFRS) model. The new model uses fuzzy divergence to evaluate uncertain information in the data. It also explores a newly-defined feature evaluation function on the biases of the dynamic relation between the relevance and indispensability of features in feature selection process. A novel forward greedy search algorithm is then presented to solve the final objective function. The selected features are subsequently evaluated on downstream classification tasks. Experimental results using real-world datasets demonstrate the effectiveness of the proposed model and its superiority against the baseline methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel multiattribute decision making (MADM) approach based on Fermatean hesitant fuzzy sets (FHFSs) and the modified VIKOR method. Firstly, we propose the definition of distance measures of FHFSs and present its properties. Further, taking the effectiveness of FHFSs for dealing with ambiguous and imprecise data in MADM problems, this paper proposes the remoteness index-based Fermatean hesitant fuzzy-VIKOR (FHF-VIKOR) MADM method. The generalized distance measure for FHFSs is subsequently employed to establish the notions of remoteness indices with the positive ideal and the negative ideal remoteness indices. The objective weighting procedure is developed using the maximum deviation principle and the generalized distance measure to obtain the attributes' weights. Some examples are discussed to reveal the performance of the proposed MADM method. Finally, the advantages of the proposed MADM method in terms of the robustness and the flexibility are shown by a comparative study. The proposed MADM method based on FHFSs and the modified VIKOR method can overcome the drawbacks of the existing MADM methods. [ABSTRACT FROM AUTHOR]

• Research about the intuitionistic fuzzy set theory is analyzed systematically with quantitative analysis. • The evolution of hot topics and knowledge diffusion path are investigated. • The self-citations phenomenon is deeply discussed when performing main path analysis. • The application of the intuitionistic fuzzy set in the domain of decision making is becoming more and more dominant. Since the intuitionistic fuzzy set theory was proposed, it has received widespread attention. To get a deeper understand of this field, this paper analyzes a total of 2913 papers downloaded from the Web of Science (WoS) from 1984 to 2019 from different perspectives. On the one hand, this research identifies important themes and their interrelationships, showing the thematic evolution of this field vividly. On the other hand, this research digs out the knowledge diffusion paths of this domain with the help of global and key-route main paths. From the perspective of the thematic evolution, five thematic area are detected including Intuitionistic fuzzy relation , IVIFS-Similarity , MCDM/MADM-GDM , Aggregation operator and Extensions of IFS. Among them, MCDM/MADM-GDM has evolved from an emerging theme to a motor theme being the most important topic and GDM integrating themes MADM 、 MCDM and Aggregation operator shows continuous growth. From the perspective of knowledge diffusion paths, research topic has gradually translated from theorical construction to practical application, and several factors such as self-citation, indirect citation, hierarchy and references that may influence the result of the main path are discussed. In general, this research systematically provides scholars with the development process in this domain, which is conductive to them to fully grasp the state-of-the-art research. [ABSTRACT FROM AUTHOR]

In the subjective evaluation process, the hesitant fuzzy set (HFS), as a convenient and robust presentation tool, cannot only suitably address the decision makers' (DMs') or experts' hesitant and uncertain issues but also can arise the dimension curse puzzle. Furthermore, the decision-making result is just derived according to the given objective and subjective information, without considering the DM's subjective evaluation and the environment's dynamic influence. Unlike the previous studies, this paper tries to address them from the deep learning viewpoint. To this end, we first define the non-equidimensional HFS (NHFS) and then introduce the equidimensional and classification characters into the NHFS to further develop the equidimensional HFS (EHFS) and the EHFS with the optimal classification result. Then, the equidimensional hesitant fuzzy-generative adversarial network (EHF-GAN) model is proposed to transform the hesitant fuzzy information from the non-equidimensional to the equidimensional form. The generalization and the convergence of the new model are proven to show the models' reasonability. In addition, the double-learning algorithm of the EHF-GAN model is designed, which can fuse the DMs' dynamic judgments and derive the optimal decision-making results. Lastly, this paper applies the proposed model and algorithm to an illustrative example of the new smart city enterprises and then shows their feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

The first step of implementing computing with words using a perceptual computer is to establish an encoder to transform words into interval type-2 fuzzy sets. In this paper, a novel approach named the retained region approach is introduced for encoding words into interval type-2 fuzzy sets. In the retained region approach, the data part is redesigned relative to the existing approaches, and a new fuzzy set part is established in accordance with the principle of justifiable granularity. The different means and standard deviations of the embedded type-1 fuzzy sets associated with a word are recognized as the origins of its inter-uncertainty, and the relations between them are taken into account in the construction of interval type-2 fuzzy sets. Importantly, the retained region approach is a versatile approach that does not impose redundant constraints on the selection of embedded type-1 fuzzy sets, and the capacity of the retained region can be flexibly adjusted along the two dimensions of the mean and the standard deviation. Finally, the performance of the retained region approach is illustrated by several simulations and comparisons with existing approaches. [ABSTRACT FROM AUTHOR]

Inconsistency in classification and regression problems occurs when instances that relate in a certain way on the condition attributes, do not follow the same relation on the decision attribute. It typically appears as a result of perturbation in data caused by incomplete knowledge (missing attributes) or by random effects that occur during data generation (instability in the assessment of decision attribute values). Inconsistencies with respect to a crisp preorder relation (expressing either dominance or indiscernibility between instances) can be handled with set-theoretic approaches like rough sets and by using statistical/machine learning approaches that involve optimization methods. In particular, the Kotłowski-Słowiński (KS) approach relabels the objects from a dataset such that inconsistencies are removed, and such that the new class labels are as close as possible to the original ones in terms of a given loss function. In this paper, we generalize the KS approach to handle inconsistency determined by a fuzzy preorder relation rather than a crisp one. The method produces a consistent fuzzy relabeling of the instances and may be used as a preprocessing tool with algorithms for binary classification and regression. As the obtained fuzzy sets can be represented as unions of meaningful simple fuzzy sets or granules, we call them granular approximations. We provide statistical foundations for our method, develop appropriate optimization procedures, provide didactic examples, and prove several important properties. • Proposing the definition of granular approximations; a novel way of integrating machine learning, fuzzy sets, and rough sets. • Inconsistencies in data, defined according to the rough set framework, are removed with optimization methods. • The new method generalizes Kotłowski and Słowiński's approach defined for crisp relations. • The fuzzy rough set lower and upper approximations are extreme cases of the granular approximation. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for predicting and explaining instances of Information Disorder. The paper reports two significant findings: i) the use of structures of opposition to describe relationships between instances of Information Disorder, and ii) the development of an explainable prediction method that combines Fuzzy Rough Sets and TOPSIS with these structures. The findings have the potential to assist analysts and decision-makers in gaining a deeper understanding of the phenomenon of Information Disorder. The results are based on real data and demonstrate promising applications for future research. [ABSTRACT FROM AUTHOR]

This paper shows that a bipolar-valued fuzzy set and a special interval-valued fuzzy set, whose cut-off point of left and right ends of the interval-valued membership is λ (0 < λ < 1) , are identical from a mathematical point of view. All results on bipolar-valued fuzzy sets can be obtained by corresponding results of interval-valued fuzzy sets or fuzzy sets. This paper does not completely reject bipolar-valued fuzzy sets, but points the way for such research. [ABSTRACT FROM AUTHOR]

The concept of bipolar-valued fuzzy set was introduced by Zhang. Can we discuss three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces? In response to this problem, firstly, the paper discusses partially orders on truth values of bipolar-valued fuzzy sets and three-way decision spaces on this basis. Secondly, this paper presents construction method of decision evaluation functions based on bipolar-valued fuzzy sets over three-way decision spaces. Thirdly, this paper makes three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces and uses an example on an evaluation problem of credit card applicants to illustrate some notions of the (semi-, quasi-)three-way decision spaces and benefits of constructing methods from semi-(quasi-)decision evaluation functions to decision evaluation functions. Finally, the conclusions are summed up. [ABSTRACT FROM AUTHOR]

The paper explores a novel way to solve the multi-attribute decision-making issues under the hesitant fuzzy environment (HF-MADM) with three-way decision (3WD) theory. Firstly, according to the nature of the relative loss function (RLF), the RLF under the hesitant fuzzy (HF) environment is defined. Then, according to the practical significance of the loss function, this paper establishes the relationship between the loss function and the evaluation value. At the same time, considering that the HF-MADM has multiple attributes and multiple evaluation values, we provide an aggregated loss function via the hesitant fuzzy weight average (HFWA) operator to reflect the overall loss of the alternative. We establish the mixed information table (HF-MADMRLF) based on the overall loss function. Secondly, based on an outranking function and a distance from the positive ideal (PI) solution, this paper defines an estimation on the conditional probability method. Finally, we utilize the presented method to solve actual medical diagnosis of pneumonia (MDP) issue, and prove the validity and applicability of the method through comparison with several representative methods and experimental evaluations. [ABSTRACT FROM AUTHOR]

Non-singleton fuzzification is used in rule-based fuzzy systems when the measurements that activate them are imperfect or uncertain or when their inputs are words. It models such measurements or words as fuzzy numbers or more general fuzzy sets so that, regardless of the cause of a measurement's or word's imperfections or uncertainties, they are treated within the framework of fuzzy sets and systems. Since 2011, there has been a resurgence of interest in both type-1 and interval type-2 non-singleton fuzzy systems. This paper removes a computational bottleneck associated with computing the firing level or firing interval for such fuzzy systems, by providing closed-form formulas for them when the involved fuzzy sets are trapezoidal or triangular, which are widely used fuzzy sets. This is done for both the minimum and product t-norms. It is also demonstrated that a non-singleton fuzzy system that uses the product t-norm has the potential to outperform a non-singleton fuzzy system that uses the minimum t-norm. The results in this paper greatly simplify non-singleton fuzzy systems, which should make them much more popular. [ABSTRACT FROM AUTHOR]

Overlap functions, as a class of not necessarily associative novel aggregation functions, have played an important role in the relevant theory and applications involving fuzzy sets and systems. Recently, extension study has become a hot topic in the theoretical research of overlap functions, especially for the so-called quasi-overlap functions. In this paper, we investigate the set-based extended quasi-overlap functions, which are one kind of set-based extended aggregation functions proposed by Mesiar et al. lately. Specifically, after introducing the definition of set-based extended quasi-overlap functions, we study some of their elementary properties. Furthermore, we give two equivalent characterizations of set-based extended quasi-overlap functions by means of mappings from the set composed by all finite subsets of unit closed interval with no repetition of elements to unit closed interval and 0,1-aggregation functions recently proposed by the author, respectively. In particular, it is shown that the family of set-based extended quasi-overlap functions is closed to convex combination and that the repetition of values in the input vectors to be aggregated and adding any value between its minimum and maximum values have no effect on the output value under the aggregation of set-based extended quasi-overlap functions. The obtained results afford theoretical basis for more potential applications of quasi-overlap functions in real problems, especially when there are more than two classes or objects in fuzzy context or fuzzy sets for which we need to measure the degree of overlapping or generate overlap indices. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new entropy measure of Pythagorean fuzzy sets (PFSs). The proposed entropy measure of PFSs can conquer the shortcomings of the existing entropy measure of PFSs. We also propose the Pythagorean fuzzy weighted arithmetic mean (PFWAM) aggregation operator (AO) of Pythagorean fuzzy numbers (PFNs). The proposed PFWAM AO of PFNs can conquer the shortcomings of the existing sine trignometry Pythagorean fuzzy weighted averaging (ST-PFWA) AO and the existing sine trignometry Pythagorean fuzzy weighted geometric (ST-PFWG) AO of PFNs. Based on the proposed entropy measure of PFSs and the proposed PFWAM AO of PFNs, we propose a new group decision making (GDM) approach in the environment of PFNs. The proposed GDM approach can conquer the shortcomings of existing GDM approaches, where they cannot distinguish the ranking orders (ROs) of alternatives in some conditions. It offers us a very useful approach to deal with GDM problems in the environment of PFNs. [ABSTRACT FROM AUTHOR]

A common approach to constructing fuzzy rough sets (FRSs) is using t-norms. Furthermore, establishing multi-granulation fuzzy rough sets (MGFRSs) is also usually undertaken by means of t-norms. However, most of these sets cannot satisfy the property that upper approximations contain lower approximations under fuzzy binary relations, which is imperative for rough set models. The overlap function is a type of aggregate function that is widely used in multi-attribute decision-making (MADM), image processing and other fields. In this paper, two novel types of MGFRS models under n -dimensional overlap functions are established to overcome the shortcomings of existing models, which are then applied to the multi-attribute group decision-making (MAGDM) problem. First, idempotent n -dimensional overlap functions are used to establish optimistic and pessimistic MGFRSs. These new models fully preserve the important properties of the traditional MGFRS model. Second, through the theoretical analysis of MGFRS based on overlap functions (OMGFRS) and in combination with the TOPSIS method, a solution mechanism for the MAGDM method is proposed. Finally, to fully illustrate this decision-making method, an effective example is developed. A comparison with available methods indicates that this approach is more suitable and has wider adaptability, and that is can be used to handle decision-making problems. [ABSTRACT FROM AUTHOR]

In the real word, due to the existence of uncertainty in decision-making information, it is often difficult to accurately evaluate utility values of alternatives. Recently, a series of discrete choice models based on fuzzy subjective utility have been proposed. Specifically, utility evaluation of each alternative has been expressed by fuzzy membership grades. However, traditional fuzzy membership function has only considered supporting degree, but has not considered the degrees of opposition and indeterminacy involved in decision makers' evaluations. In this paper, a series of novel discrete choice models based on Atanassov-type intuitionistic fuzzy set are proposed, in which membership degrees, non-membership degrees, and hesitation degrees are simultaneously taken into account to jointly express the utility evaluations. Moreover, the attitudinal character of decision makers and relative weights of attributes are also considered to further extend the proposed models. Compared with existing discrete choice models, these new models are more flexible and general, which increase the applicability of discrete choice models for decision-making under an uncertain and imprecise environment. Two real-world case studies are given to illustrate the effectiveness and rationality of the new models. [ABSTRACT FROM AUTHOR]

A common approach to constructing fuzzy rough sets (FRSs) is using t-norms. Furthermore, establishing multi-granulation fuzzy rough sets (MGFRSs) is also usually undertaken by means of t-norms. However, most of these sets cannot satisfy the property that upper approximations contain lower approximations under fuzzy binary relations, which is imperative for rough set models. The overlap function is a type of aggregate function that is widely used in multi-attribute decision-making (MADM), image processing and other fields. In this paper, two novel types of MGFRS models under n -dimensional overlap functions are established to overcome the shortcomings of existing models, which are then applied to the multi-attribute group decision-making (MAGDM) problem. First, idempotent n -dimensional overlap functions are used to establish optimistic and pessimistic MGFRSs. These new models fully preserve the important properties of the traditional MGFRS model. Second, through the theoretical analysis of MGFRS based on overlap functions (OMGFRS) and in combination with the TOPSIS method, a solution mechanism for the MAGDM method is proposed. Finally, to fully illustrate this decision-making method, an effective example is developed. A comparison with available methods indicates that this approach is more suitable and has wider adaptability, and that is can be used to handle decision-making problems. [ABSTRACT FROM AUTHOR]

In the real word, due to the existence of uncertainty in decision-making information, it is often difficult to accurately evaluate utility values of alternatives. Recently, a series of discrete choice models based on fuzzy subjective utility have been proposed. Specifically, utility evaluation of each alternative has been expressed by fuzzy membership grades. However, traditional fuzzy membership function has only considered supporting degree, but has not considered the degrees of opposition and indeterminacy involved in decision makers' evaluations. In this paper, a series of novel discrete choice models based on Atanassov-type intuitionistic fuzzy set are proposed, in which membership degrees, non-membership degrees, and hesitation degrees are simultaneously taken into account to jointly express the utility evaluations. Moreover, the attitudinal character of decision makers and relative weights of attributes are also considered to further extend the proposed models. Compared with existing discrete choice models, these new models are more flexible and general, which increase the applicability of discrete choice models for decision-making under an uncertain and imprecise environment. Two real-world case studies are given to illustrate the effectiveness and rationality of the new models. [ABSTRACT FROM AUTHOR]

Fuzzy rough set (FRS) has a great effect on data mining processes and the fuzzy logical operators play a key role in the development of FRS theory. In order to generalize the FRS theory to more complicated data environments, we firstly propose four types of fuzzy neighborhood operators based on fuzzy covering by overlap functions and their implicators in this paper. Meanwhile, the derived fuzzy coverings from an original fuzzy covering are defined and the equalities among overlap function-based fuzzy neighborhood operators on a finite fuzzy covering are also investigated. Secondly, we prove that new operators can be divided into seventeen groups according to equivalence relations, and the partial order relations among these seventeen classes of operators are discussed, as well. And then, two types of neighborhood-related fuzzy covering-based rough set models are proposed via the overlap function-based fuzzy neighborhood operators and the t -norm-based fuzzy neighborhood operators. Furthermore, the groups and partially order relations are also discussed. Finally, a novel fuzzy TOPSIS methodology is put forward to solve a biosynthetic nanomaterials select issue, and the rationality and enforceability of our new approach is verified by comparing its results with nine different methods. [ABSTRACT FROM AUTHOR]

The concept of hesitant set was introduced by Hu, which purpose is to unify hesitant fuzzy sets, interval-valued hesitant fuzzy sets, shadowed sets etc. This paper discusses the construction of decision evaluation functions and three-way decisions based on hesitant sets over three-way decision spaces. First, this paper presents the construction methods of decision evaluation functions based on hesitant sets over semi-three-way decision spaces and quasi-three-way decision spaces. Second, this paper presents some transformation methods of decision evaluation functions based on hesitant sets from semi-three-way decision spaces and quasi-three-way decision spaces to three-way decision spaces. Third, this paper presents three-way decisions based on hesitant sets. Numerous examples are given to support this paper's argument on the existence of semi-(quasi-)decision evaluation functions and significance of the transformation methods. [ABSTRACT FROM AUTHOR]

• The aim of this paper is to develop a model to analyze the interdependence between the indicators and compute the KPIs under the large group. The major contributions include five points. First, the hesitant 2-TUPLE linguistic is utilized to deal with the fuzzy assessment information regarding the interrelationships of indicators. Second, the experts are clustered based on the similar degree method. Third, this paper determines the weight of clustering with evaluation information based on the minimized variance method. Fourth, an extended DEMATEL method is used to analyze the relationship among indicators and calculate KPIs to improve the internationalization of higher education system. Finally, the proposed model effectively achieves the analysis and evaluation, KPIs are provided for the improvement of the internationalization of higher education. The internationalization of higher education has become an important means for countries worldwide to develop and enhance their strengths, in which performance measurement plays a vital role. However, current performance measurement usually involves many indicators, and it is impossible to improve them all due to resource constraints. Therefore, a suitable performance measurement system can enhance the international influence and competitiveness of higher education institutions. In response, based on the matrix decision, this study develops a large group evaluation approach using a hesitant 2-tuple linguistic model. The decision-making trial and evaluation laboratory (DEMATEL) method is used, and key performance indicators (KPIs) are determined for higher education internationalization. In the method, the KPIs are focused on by constructing the correlation matrix between indicators using the hesitant 2-tuple linguistic model, which can then be determined by the extended DEMATEL method based on the cause-and-effect relationships between the performance indicators. In the case study, the effectiveness and applicability of the proposed hesitant 2-tuple linguistic DEMATEL method are verified. The results show that the proposed model can help higher education institutions focus on a limited number of key indicators and systematically manage higher education internationalization. [ABSTRACT FROM AUTHOR]

• Introduced some solid mathematical concepts named Bipolar Complex picture fuzzy and soft sets. • Introduced novel, effective ideas can be used to manage complex, unreliable data in real-world applications. • Presents modeling methodologies based on BCPFSSs. • Conducted a comparative study of existing techniques. The goal of this paper is to present novel concepts and effective theories for the ability to accurately represent difficult and ambiguous information in real-life problems. In order to accomplish this goal, this paper investigated the original idea of bipolar complex picture fuzzy soft set (BCPFSS), which combination of two distinct theories known as the bipolar complex picture fuzzy set (BCPFS) and the soft set (SS). The capabilities of this new model are to achieve a larger range with the aid of the membership degree (MD), non-membership (NMD), and abstinence degree (AD) with complex integers. The BCPFSS represented two different degrees, known as positive degrees examine positive aspects of the problem and negative degrees examine negative aspects of the problem. Moreover, human–computer interaction (HCI) is an effective human–computer interface that presents a realistic world. HCI is a field that recognizes the significant role of educational applications and platforms in visualizing content, providing students with easy access to education in their homes, and paving the way for the development of alternative and advanced methods for implementing the concept of e-learning. With the technological advancements of HCI, it has become a fundamental tool in every area of activity, revolutionizing work environments and expanding their scope. In order to resolve the challenge of analyzing complex and unreliable data in real-world contexts, we proposed the idea of bipolar complex picture fuzzy soft sets (BCPFSSs). The innovative concept of BCPFSS defines many operations such as complement, extended intersection, and restricted intersection. The idea of BCPFSSs possesses a broad structure as they explore all values of MD, AD, and NMD with both positive (+ve) and negative (−ve) perspectives, making them adept at handling multivariable challenges. In this paper, modeling approaches based on BCPFSSs are proposed for choosing the HCI for effective implementation by formulating and analyzing score functions. Finally, a comparative analysis section illuminates a comprehensive and organized comparison of recent works to the earlier work. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiple attribute decision making (MADM) approach based on the multi-attribute ideal-real comparative assessment (MAIRCA) method, the standard deviation-based method, and Pythagorean fuzzy sets. We also propose a weight-determining method to determine the weights of attributes using a standard deviation-based approach with Pythagorean fuzzy information. The drawbacks of the existing MADM methods in Pythagorean fuzzy environments are that they cannot distinguish the preference orders of alternatives in some situations. The proposed MADM approach can overcome the drawbacks of the existing MADM approaches in the Pythagorean fuzzy context. The main contributions of this paper include: (1) It proposes a weight-determining method to derive attributes' weights based on the standard deviation-based method with Pythagorean fuzzy information, (2) It proposes a new MADM methodology based on the MAIRCA method, the standard deviation-based method, and PFSs for MADM in the Pythagorean fuzzy setting, and (3) The proposed MADM method can overcome the shortcomings of the existing MADM methods in the Pythagorean fuzzy context. It provides us a flexible and effective method for MADM in Pythagorean fuzzy environments. [ABSTRACT FROM AUTHOR]

The paper proposes a novel approach to address the challenges of clustering datasets and identifying outliers by utilizing the Atanassov intuitionistic fuzzy sets (AIFS) environment. The approach provides a more flexible and nuanced solution by incorporating a new function called the typicality function for outlier detection and tuning the parameters used in defining it to improve clustering. To optimize the parameter tuning process and reduce time complexity, the paper introduces a global error search approach (k -GESA) within a finite space. The paper also presents a new clustering algorithm, called Global Intuitionistic Fuzzy Weighted C -Ordered Means (Global-IFWCOM), which utilizes k -GESA to improve the clustering results. The proposed approach is evaluated against various C -ordered means algorithms, including Fuzzy C -ordered means (FCOM), Intuitionistic fuzzy C -ordered means (IFCOM), Intuitionistic fuzzy weighted C -ordered means (IFWCOM), Fuzzy weighted C -ordered means (FWCOM), and Hesitant-FWCOM, on a two-dimensional synthetic dataset with outliers. Furthermore, the effectiveness of Global-IFWCOM is demonstrated using a six-dimensional synthetic dataset with noise and outliers compared to FWCOM. • Global error search approach (k-GESA) is proposed. • Developed a novel Weighted C-means clustering algorithm. • Performance evaluation with state-of-the art is done. • Two and six dimensional synthetic datasets are taken to demonstrate. [ABSTRACT FROM AUTHOR]

Fuzzy rough sets (FRSs) can be served as a useful technique to cope with inconsistent data by providing a pair of lower and upper fuzzy rough approximations of a fuzzy concept. Diversified FRS models have been proposed over the years. Meanwhile, t-norms and t-conorms, as two binary aggregation operators, play a critical part in the construction of fuzzy rough approximation operators. Nevertheless, one of common properties of t-norms and t-conorms is that they all fulfill associativity. Additionally, the associativity plays an important role in discussing properties of FRSs. Therefore, if the binary aggregation function does not satisfy associativity, how to define FRS models and discuss the relevant properties is a topic worthy of further investigation. Overlap functions, as a new kind of not necessary associative binary aggregation operator, have been continuously investigated by many scholars in theory and practical applications. Therefore, based on the advantages of overlap functions, and as the extension models for FRSs, we propose two new types of FRSs via overlap functions and their residual implications (or called I O -implications) in this paper. More specifically, we first give the definition of the 1 st type of FRSs and study some essential properties. Subsequently, the definition of the 2 nd type of FRSs is presented and the relevant properties are also investigated. Furthermore, the relationship between the 1 st type of FRSs and the 2 nd type of FRSs is described. That is, in a fuzzy approximation space, the 2 nd type of lower approximation is contained in the 1 st type of lower approximation, while the 1 st type of upper approximation is included in the 2 nd type of upper approximation when the overlap function has 1 as the identity element. At the end, a novel three-way decision (3WD) method is presented on an information table by using the new type of FRSs, and its practicality and superiority are verified via a numerical example and a series of experimental analyses. [ABSTRACT FROM AUTHOR]

Frequent pattern mining (FM) has a wide range of applications in the real world. But FM sometimes discovers many uninteresting patterns at the same time. Constraint-based FM, especially periodic constraint FM, becomes of interest, and it reduces redundant patterns. Most of the state-of-the-art algorithms for mining periodic frequent patterns (PFPs) are designed to find PFPs only in binary temporal databases. However, vast information in real situations is more suitable to be modelized as quantitative databases, in which most existing methods are inapplicable. Patterns obtained by those methods may change due to a tiny perturbation in the database, which is not expected in many situations. In this paper, we propose an algorithm (FP2M) to mine fuzzy-driven periodic frequent patterns and an algorithm (SFP2M) to find stable fuzzy-driven periodic frequent patterns in quantitative temporal databases. Fuzzy sets are used in our algorithms to deal with quantitative data since they provide a relaxed interval segmentation and are easy to implement. Novel pruning strategies and a new structure called Estimated Period Co-occurrence Structure (EPCS) are designed to speed up the mining process and improve efficiency. An improved method (SFP2M) is also presented by using the lability measurement to find stable patterns. Experimental evaluations on both real and synthetic datasets show good performance of the designed algorithms. [ABSTRACT FROM AUTHOR]

• Bibliometric techniques identify the productivity and influence on research. • Fuzzy systems are an area of study with potential for further research. • Zadeh is known as the most influential author in fuzzy research in North American. • The United States is the most productive and influential country in fuzzy research. The objective of this paper is to apply bibliometric techniques to analyze the evolution of fuzzy systems research (FSR) in the United States of America and Canada. The aim is to visualize the progression of FSR since Zadeh's first publication of fuzzy sets and the regional impact that these ideas have in the scientific community. This work obtains data retrieved from the Web of Science (WoS) scientific database. Using a hybrid methodology designed to maximize the obtention of representative results, we analyze 20,317 documents published between 1965 and 2020. The main findings show that Zadeh is the most influential author and that Pedrycz is the most productive author at FSR. Journals such as Fuzzy Sets and Systems (FSS) and IEEE Transactions on Fuzzy Systems (TFS) publish most of the FSR articles. The results show a greater contribution by the United States of America compared to Canada in FSR. This analysis contributes to visualization and evolution in the field of study of FSR in diverse regions. [ABSTRACT FROM AUTHOR]

The generalized three-way decision (G3WD) theory is featured by a trisecting-acting-outcome paradigm. Experiments in psychology and economics have indicated that risky decision-making problems should take into account the psychological characteristic of agents. Moreover, the loss of information acts as a serious challenge in G3WD. Thus, exploring valid G3WD approaches that consider the mental state of decision-makers in incomplete information systems (IISs) is imperative. This paper explores a new three-way decision (3WD) approach that combines the prospect theory with the regret theory for IISs with the support of fuzzy set pair dominance degrees. First, the notion of fuzzy set pair dominance degrees to process evaluation information in IISs is put forward. Then, an approach that obtains objective reference points and determines the weighting function in the prospect theory is given by combining 3WD with the behavioral decision theory. In light of the prospect theory, a prospect value function is obtained, which is introduced into the regret theory to obtain two utility perception functions. As a consequence, a G3WD approach based on fuzzy set pair dominance degrees and the behavioral decision theory is constructed for IISs. By using two medical cases in the KEEL and UCI datasets, the superiority, effectiveness and stability of the constructed approach are verified via corresponding comparative and experimental analyses. [ABSTRACT FROM AUTHOR]

Label distribution learning (LDL) is a novel framework for handling label ambiguity problems and has been used widely in practice. However, dealing with high-dimensional data or data with redundant features in the LDL context is still an open problem. Existing feature selection algorithms cannot be directly applied to LDL due to the unique challenges caused by the label uncertainty nature. In this paper, we propose a novel LDL feature selection algorithm based on neighborhood rough sets. Specifically, we first introduce dual-similarity that is used to measure sample similarity in both the feature and the label spaces. Second, we invent a novel neighborhood fuzzy entropy as a feature evaluation metric, with which neighborhood rough sets can be applied to deal with LDL problems. Lastly, we complete a feature selection model that inherits the spirit of neighborhood rough sets and neighborhood fuzzy entropy. Extensive experiments have been conducted on twelve real-world LDL datasets, and the results demonstrate the superiority of our proposed model against to other six state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Decision making is undertaken by individuals whose perceptions for the objectives are vague due to the dynamics of decision-making objectives, the complexity of decision-making situation and the limitations of individuals' education backgrounds, experiences, etc. Therefore, decision making which uses fuzzy set (FS) and its variants to describe the individuals' vague perceptions has become more and more popular. Furthermore, in real-life decision-making situations, individuals are always bounded rationality, which is clearly described by prospect theory (PT). Thus, PT has been integrated into fuzzy decision making (FDM). Since then, FDM with PT have been rapidly developed. In this paper, we systematically analyze the existing FDM with prospect framework. Firstly, a detailed analysis about the existing research on this topic is given separately, including how to determine the reference point, how to express the value function and weighting function in PT under vague conditions. With this in mind, the applications and challenges of the existing methods are described and some possible directions for future research are provided. According to our review, it is worth mentioning that the FDM with psychological factors of decision makers will surely receive much more attention from researchers and practitioners in the future. [ABSTRACT FROM AUTHOR]

Linguistic intuitionistic fuzzy numbers (LIFNs) are useful to express the uncertainty of qualitative aspects of information, which have received many attentions in recent years. In this paper, we propose the distance measure of linguistic intuitionistic fuzzy sets (LIFSs), where the membership grade and the non-membership grade of each element in the universe of discourse belonging to a LIFS are represented by LIFNs. We also provide the proofs of the validity and some desirable properties of the proposed distance measure of LIFSs. Moreover, we also propose the weighted distance measure of LIFSs. Based on the proposed weighted distance measure of LIFSs and the "Technique for Order Preference by Similarity to Ideal Solution" (TOPSIS) method, we propose a new group decision making (GDM) approach in the environments of LIFNs. We also use some examples to illustrate the practicability and the feasibility of the proposed GDM approach. The proposed GDM approach can overcome the drawbacks of the existing GDM approaches, where they have the drawbacks that they cannot distinguish the ranking orders of the alternatives in some situations. It provides us a very useful method for dealing with GDM problems in the environments of LIFNs. [ABSTRACT FROM AUTHOR]

[Display omitted] • Generalized preference information is used to reduce subjective randomness. • Imputation of missing values occurs systematically under different scenarios. • Weights of experts and criteria are systematically determined. • Waste treatment options are ranked rationally. • Practicality is validated by using a case study from Tamil Nadu. A generalized orthopair fuzzy set can express uncertain information easier than most other processes, which gives us more space for decision-making. In recent times, the selection of healthcare waste treatment (HCWT) technology can be considered as multi-criteria decision-making (MCDM) problem due to the involvement of multiple conflicting criteria. To reduce the unhealthy impact on the ecosystem and promote sustainable disposal, researchers have investigated MCDM problems to select apt HCWTs. In a bid to the minimize negative environmental impact of healthcare waste, researchers adopted MCDM, and faced challenges such as: (i) handling uncertainty/subjective randomness; (ii) imputation of missing values; and (iii) consideration to experts' attitude and interdependencies during MCDM process. To remedy these, this paper has attempted to establish a novel decision model with generalized orthopair fuzzy information (GOFI). Initially, missing values are systematically imputed. Experts' preferences were fused to obtain an aggregated matrix by considering the interdependencies among experts. Also, criteria weights were computed utilizing attitude-based entropy measures, and HCWTs were ranked using the GOFI-evaluation based on distance from average solution (GOFI-EDAS) approach. Lastly, the methodology's superiority was validated using an illustrative example, followed by a comparison with extant models. The results confirm that the developed framework is more efficient than and consistent with earlier methods under uncertainty. [ABSTRACT FROM AUTHOR]

[Display omitted] • Generalized preference information is used to reduce subjective randomness. • Imputation of missing values occurs systematically under different scenarios. • Weights of experts and criteria are systematically determined. • Waste treatment options are ranked rationally. • Practicality is validated by using a case study from Tamil Nadu. A generalized orthopair fuzzy set can express uncertain information easier than most other processes, which gives us more space for decision-making. In recent times, the selection of healthcare waste treatment (HCWT) technology can be considered as multi-criteria decision-making (MCDM) problem due to the involvement of multiple conflicting criteria. To reduce the unhealthy impact on the ecosystem and promote sustainable disposal, researchers have investigated MCDM problems to select apt HCWTs. In a bid to the minimize negative environmental impact of healthcare waste, researchers adopted MCDM, and faced challenges such as: (i) handling uncertainty/subjective randomness; (ii) imputation of missing values; and (iii) consideration to experts' attitude and interdependencies during MCDM process. To remedy these, this paper has attempted to establish a novel decision model with generalized orthopair fuzzy information (GOFI). Initially, missing values are systematically imputed. Experts' preferences were fused to obtain an aggregated matrix by considering the interdependencies among experts. Also, criteria weights were computed utilizing attitude-based entropy measures, and HCWTs were ranked using the GOFI-evaluation based on distance from average solution (GOFI-EDAS) approach. Lastly, the methodology's superiority was validated using an illustrative example, followed by a comparison with extant models. The results confirm that the developed framework is more efficient than and consistent with earlier methods under uncertainty. [ABSTRACT FROM AUTHOR]

In the paper, we describe the new measure of matching two intuitionistic fuzzy sets. The operations known in the intuitionistic fuzzy set theory are used, and the perturbation of one intuitionistic fuzzy set by another intuitionistic fuzzy set is understood as an impact of one intuitionistic fuzzy set on another intuitionistic fuzzy set. The opposite case can also be considered wherein the second intuitionistic fuzzy set is perturbed by the first one. The introduced measure of the perturbation of one intuitionistic fuzzy set by another intuitionistic fuzzy set is considered instead of commonly used distance between two intuitionistic fuzzy sets. In general, the new measure can be asymmetric and therefore can provide more information compare to a distance between intuitionistic fuzzy sets. The values of such measures of intuitionistic fuzzy sets' perturbation are ranged between 0 and 1. In this paper specific mathematical properties of the measure of intuitionistic fuzzy sets' perturbation are studied. The presented methodology is explained by several illustrative examples. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method, referred to as ParGenFS, for finding a most specific generalization of a query set represented by a fuzzy set of topics assigned to leaves of the rooted tree of a taxonomy. The query set is generalized by "lifting" it to one or more "head subjects" in the higher ranks of the taxonomy. The head subjects should cover the query set, with the possible addition of some "gaps", taxonomy nodes covered by the head subject but irrelevant to the query set. To decrease the numbers of gaps, we admit some "offshoots", nodes belonging to the query set but not covered by a head subject. The method globally minimizes the total number of head subjects, gaps and offshoots, each suitably weighted. Our algorithm is applied to the structural analysis and description of a collection of 17,685 abstracts of research papers published in 17 Springer journals related to Data Science for the 20-year period 1998–2017. Our taxonomy of Data Science (TDS) is extracted from the Association for Computing Machinery Computing Classification System 2012 (ACM-CCS), a six-level hierarchical taxonomy manually developed by a team of ACM experts. The TDS also includes a number of additional leaves that we added to cater for recent developments not represented in the ACM-CCS taxonomy. We find fuzzy clusters of leaf topics over the text collection, using specially developed machinery. Three of the clusters are indeed thematic, relating to the Data Science sub-areas of (a) learning, (b) information retrieval, and (c) clustering. These three clusters are then lifted in the TDS using ParGenFS, which allows us to draw some conclusions about tendencies in developments in these areas. [ABSTRACT FROM AUTHOR]

Recently, Hu proposed the notion of three-way decision spaces based on partially ordered sets with involutive negations by the axiomatic definition. However, involutive negation is so strong that imposes restrictions on the use of the theory of three-way decision spaces from theoretical point of view. Therefore, this paper attempts to extend the concept of three-way decision spaces from partially ordered sets with involutive negations to partially ordered sets with negations. At first, we generalize three-way decision spaces and three-way decisions based on general partially ordered sets with negations such that the existing three-way decisions are the specific cases of generalized three-way decision spaces discussed in this paper. And then, we give some new decision evaluation functions in generalized three-way decision spaces (e.g., decision evaluation functions based on fuzzy sets, interval-valued fuzzy sets, fuzzy relations, shadowed sets and hesitant fuzzy sets), which enriched the class of decision evaluation functions. In particular, they provide more choices for decision-makers in realistic decision-making problems. Finally, in order to illustrate the practical applications of the results presented in this paper, we analyse a practical example of an evaluation problem of credit card applicants. [ABSTRACT FROM AUTHOR]

This paper proposes a novel top-down approach to rule-based fuzzy systems, one that begins with the product—an equation—and then addresses the unique features of the product, without requiring the reader to know anything about fuzzy sets and systems. The "products" are adaptive variable-structure basis function expansions , where "adaptive variable-structure" means that different subsets of its basis functions are active (non-zero) in different regions of the state space, something that occurs automatically by virtue of the structure of the basis functions, so that the products can be said to "adapt" to locations in the state space. These products are novel candidates for machine learning. Unique features of all products are: (1) Number of basis functions is no longer a variable and is established locally through type-1 or type-2 uncertainty partitioning of each variable; (2) Both coarse and fine sculpting of the state space are achieved, and are described in terms of first- and second-order partitions of the state space, respectively; and (3) Linguistic interpretability is obtained, which may be of value to an end-user. Learning about rule-based fuzzy systems can be greatly compressed by using the top-down approach that is described in this paper. [ABSTRACT FROM AUTHOR]

Since Torra introduced the concept of hesitant fuzzy sets, it has seen wide applications in decision-making problems, cluster analysis, medical diagnosis, personnel appraisal, information retrieval and so on. And, nowadays, there arise many discussions related to hesitant fuzzy sets. In particular, recently, Hu extends the truth values set of hesitant fuzzy sets and hesitant fuzzy relations from the family of subsets of unit interval to the family of nonempty subsets of any linearly ordered set with an involutive negator and calls them hesitant sets and hesitant relations, respectively. This paper continues to consider this topic and mainly intends to give a systematical discussion to hesitant relations on their properties and potential applications in three-way decisions. First, this paper shows some novel properties of the operations on linearly ordered set with an involutive negator. Second, this paper investigates some vital properties of hesitant relations, especially for the compositions, projections, reflexivity, symmetry, *-transitivity and so on. Third, this paper proposes various types of ordered hesitant relations. Finally, this paper discusses some applications of hesitant relations in the constructions of decision evaluation functions in three-way decision spaces. [ABSTRACT FROM AUTHOR]

Multi-attribute decision making (MADM) plays an important role in decision analysis. Based on a new fuzzy rough set theory (FRS), this paper presents a multi-attribute prediction analysis model in fuzzy information systems (FISs). In this prediction model, the proposed FRS is based on an attribute-oriented fuzzy similarity relation; the cosine deviation of a candidate to optimistic decision and pessimistic decision is proposed to construct a trend function, for further predicting the development trend of the candidate. It deals with MADM problems from the perspective of multi-attribute predictive analysis, and is a valuable continuation of fuzzy decision making research. To evaluate the validity and feasibility of the proposed prediction model, experiments with real data sets and comparative experimental analysis are conducted. The experimental results prove that the prediction performance of the proposed model is well-pleasing in terms of both prediction accuracy and AUC results. [ABSTRACT FROM AUTHOR]

In this paper we show a methodology for designing operators on spaces of lattice-valued mappings. More precisely, from a family of operators on a bounded lattice L and mappings from a set X to itself, we may construct an operator, that we call the induced operator, on the lattice of set mappings from X to L. Furthermore, if X is also a bounded lattice, under suitable conditions preserving the orders on L and X , the induced operator belongs to the lattice of monotone mappings from X to L. The procedure is quite simple, versatile and allows to obtain plenty of different examples in a wide range of lattices. In particular, by appropriate choices of X and L , it can be applied to the most important types of fuzzy sets. The relation with some properties associated to popular types of operators is studied. Hence, we show that, under certain conditions, aggregation operators, implications, negations, overlap functions and others are preserved by the induction process. [ABSTRACT FROM AUTHOR]

Shadowed set divides a fuzzy set into three regions through fuzzy-rough transformation to denote acceptance, rejection and uncertain decision. Based on the tri-partition property, shadowed sets are utilized to implement the machine learning methods for uncertain data analysis. The extant uncertain machine learning methods with shadowed sets include the unsupervised clustering on only unlabeled data and the supervised classification on only labeled data. However, for the partial labeled data containing both labeled and unlabeled data instances, the studies of uncertain learning methods with shadowed sets are very limited. Aiming at the requirement, in this paper, we propose a novel semi-supervised shadowed set on partial labeled data and thereby construct semi-supervised shadowed neighborhoods to implement the three-way classification of uncertain data. To construct the semi-supervised shadowed set, we reformulate the objective function of shadowed sets, in which the membership loss in fuzzy-rough transformation is weighted by labeled and unlabeled data. We also analyze the influence of labeled data to the shadowed set construction. Experiments validate that the proposed three-way classification method with semi-supervised shadowed sets is effective to utilize partial labeled data to achieve low-risk uncertain data classification. [ABSTRACT FROM AUTHOR]

Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on finding solutions and solvability criteria for such systems. The situation is quite different with the so-called weakly linear systems, in which an unknown fuzzy relation is on both sides of the equation or inequality. Precisely, the scholars have only given the characterization of the set of exact solutions to such systems. This paper describes the set of fuzzy relations that solve weakly linear systems to a certain degree and provides ways to compute them. We pay special attention to developing the algorithms for computing fuzzy preorders and fuzzy equivalences that are solutions to some extent to weakly linear systems. We establish additional properties for the set of such approximate solutions over some particular types of complete residuated lattices. We demonstrate the advantage of this approach via many examples that arise from the problem of aggregation of fuzzy networks. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs) become a useful tool to describe the complex cognition of decision makers (DMs). In this paper, Pythagorean fuzzy preference relations (PFPRs) whose elements are PFSs are used for group decision making (GDM). First, a novel multiplicative consistency of PFPRs is proposed. Then, a programming model is constructed to derive the priority weight vector of PFPRs. Then, an inconsistency-repairing method of PFPRs is designed. Moreover, a group consensus index to calculate the degrees of similarity among PFPRs is proposed and an iterative consensus reaching procedure with PFPRs is developed. By maximizing the group consensus level of PFPRs, a model is built to determine DMs' weights. Furthermore, a new GDM method based on PFPRs is proposed. Finally, we offer an example to illustrate the proposed GDM method and complete a comparative analysis. The proposed GDM method outperforms the existing GDM methods for GDM in Pythagorean fuzzy environments. [ABSTRACT FROM AUTHOR]

• 14 new IT2FPID controllers are proposed using multiple fuzzy sets and 1D input space. • The validity of the controllers is examined, and their properties are studied. • Effects of the FOUs on the structures of the proposed controllers are investigated. • Applicability of the controllers is demonstrated in simulation and real-time. • Effectiveness of the controllers is depicted through system performance comparison. Interval Type-2 Fuzzy PID (IT2FPID) controllers use Interval Type-2 Fuzzy Sets (IT2FSs). The difference between Type-1 Fuzzy PID (T1FPID) controllers and IT2FPID controllers is the Footprint of Uncertainty (FOU) which occurs due to the use of IT2FSs. FOU gives an extra degree of freedom to the controller structure, which is capable of handling uncertainty in the plant. However, the effect of FOU on the analytical structures of the IT2FPID controllers is not yet explored when uniformly/non-uniformly distributed multiple IT2FSs are used on the input side and uniformly/non-uniformly distributed multiple singleton fuzzy sets are considered on the output side of the controller. In this paper, controllers with three different types of FOUs and two different defuzzification methods are considered, and their analytical structures are derived. The suitability of the controllers is examined, and the properties of the suitable controllers are explored. Effects of FOU on the nonlinearity, gain, and computational aspects of the suitable controllers are studied. The applicability of proposed IT2FPID controllers is shown through simulation and real-time studies. The effectiveness of the proposed controllers is depicted by comparing their performances with that of the recently developed Integer Order Fuzzy PID (IOFPID) and Fractional Order Fuzzy PID (FOFPID) controllers. [ABSTRACT FROM AUTHOR]

This paper proposes a variable-type hierarchical fuzzy system (VTHFS) with high accuracy and strong interpretability. An improved rear-part direct-connected structure is used in the VTHFS, which eliminates the intermediate variables of the hierarchical fuzzy system (HFS). A new feature sorting method is proposed to find suitable input variables for each layer of subsystems of VTHFS. Under the proposed topology structure, layer by layer training of VTHFS can be achieved by changing the expected output of each layer, thereby reducing residual errors layer by layer and improving the prediction accuracy of VTHFS. Three fuzzy set distribution constraints are used in parameter optimization of VTHFS to improve the interpretability, including integrity, distinguishability, and footprint of uncertainty. The type of fuzzy set is automatically adjusted according to the uncertainty characteristics of input data measured by fuzziness, which further enhances the semantic interpretability of the VTHFS and solves the problem of requiring prior knowledge to define the fuzzy set type in existing research. Finally, the proposed VTHFS is tested on the regression data sets in the real world. Experimental results demonstrate the effectiveness of the feature sorting method and the fuzzy set type adjustment method. Through a large number of quantitative indicators, it can be confirmed that VTHFS has stronger interpretability and higher prediction accuracy compared to other fuzzy systems. [ABSTRACT FROM AUTHOR]

A rule-based system is a widely used artificial intelligence system that employs a set of rules to make decisions. The belief rule-based (BRB) classification system is an extension of fuzzy rule-based (FRB) system that handles uncertainty and imprecision in classification tasks by incorporating Dempster-Shafer evidence theory and fuzzy set theory. However, the BRB classification system suffers from the combinatorial explosion and high time complexity problems. To solve these issues, the fuzzy unordered rule induction algorithm (FURIA) is introduced into the BRB classification systems to design a novel BRB classification system in this paper. FURIA is computationally less complex and has superior classification performance. The proposed system outperforms BRB classification systems in terms of classification performance and significantly reduces the number of rules and conditions. Furthermore, the proposed system offers a more effective solution than FURIA. To evaluate the validity and superiority of the proposed system, we conduct two classification experiments, comparing it with five traditional classifiers and seven rule-based systems, respectively, in terms of classification performance and interpretability. [ABSTRACT FROM AUTHOR]

Overlap functions, which can be characterized as a type of non-associative binary aggregation operators, have emerged as one of the most extensively utilized aggregation operators in numerous applications, including image processing, information fusion, and classification problems. At the same time, fuzzy rough sets have also been widely used in these fields due to their excellent ability to handle continuous and uncertain information. However, the variable precision fuzzy rough set model based on overlap functions and its applications have not been fully studied. For instance, some basic properties are invalid and there is a lack of practical applications. In this paper, both overlap functions and precision parameters are introduced into the fuzzy rough sets, namely the overlap function-based variable precision fuzzy rough set (OVPFRS), which is then used in the practical problem of tumor classification. First, considering the existing overlap function-based rough set models, the OVPFRS model is established, and some underlying properties of this model are explored. Second, on the basis of the proposed model, a method for attribute reduction is developed. Finally, the new method is applied to the classification of tumor data from the real world. Through experimentation and comparison with other attribute reduction methods, it has been demonstrated that our model is flexible and the algorithm is viable and effective. [ABSTRACT FROM AUTHOR]

As one of the most promising classification approaches, association classification (AC) integrates data classification and association discovery techniques for generating a compact set of classification association rules. Recently, the fuzzy set and evidence theories are successively applied into AC in order to improve the classification performance in terms of accuracy and interpretability. However, from the perspectives of applicability and universality, there still exists two important issues in the current AC framework. On one hand, several key parameters, such as the number of fused rules in classification and the minimum support threshold in association discovery, are difficult to be accurately predefined in practice. On the other hand, the fixed grid-based fuzzy partition is not benefit to adapt for those datasets with large number of features. In this paper, an association rule-based adaptive fuzzy-evidential classification framework (AR-AFEC) is developed for overcoming the above limitations. To do so, an optimal rule fusion strategy and a dynamic minimum support threshold setting scheme are proposed for adaptively learning the parameters during classification and association mining respectively. In addition, an entropy-based trapezoidal fuzzy partition technique is proposed to adaptively obtain the fuzzy sets defined on each continuous feature domain. Experiments on 26 benchmark datasets and a human activity recognition application demonstrate that the proposal can achieve better accuracy than some state-of-the-art rule-based classification approaches, using less rules with more general structure. [ABSTRACT FROM AUTHOR]

Deep learning-based recommendations have demonstrated impressive performance in improving recommendation accuracy. However, such approaches mainly utilize implicit feedback to predict user preferences and neglect the adverse impact of explicit preference noise, which affects the robustness and reliability of model training. To consider the reliability of both rating input and output, we propose a novel joint deep neural recommendation framework that incorporates rating reliability derived solely from ratings to provide reliable recommendations for active users. Firstly, we introduce a noise detection method based on intuitionistic fuzzy sets to identify incorrect ratings from the perspective of fuzzy preferences and label them to generate a binary rating reliability matrix. Subsequently, we propose a joint deep neural framework that integrates rating reliability to simultaneously capture the high-order features of users and items, yielding predictions with their corresponding reliability probabilities. Finally, to achieve a balance between accuracy and reliability for recommendations, we design a reliability threshold selection strategy based on K-means clustering to find an appropriate threshold. Experimental results on three widely used datasets show that our model achieves an average improvement of 9.4% and 8.0% in the metrics Recall and NDCG, respectively, compared with the closest competitor. This paper provides new insights for integrating rating reliability into a deep neural network to enhance the performance of recommender systems. [ABSTRACT FROM AUTHOR]

Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if..., then..." rules, which form the backbone of rough set rule induction. Alternatively, this property of granular representability can be defined as being free from inconsistencies, i.e. there are no elements within the set that are indiscernible to elements outside the set. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. Additionally, we provide counterexamples for the granular representability of other FQFRS models, and show that despite this, these approaches still demonstrate effectiveness in mitigating inconsistencies in real-life datasets. This observation highlights the potential of these models for resolving data inconsistencies and managing noise. [ABSTRACT FROM AUTHOR]