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The ranking of decision makers (DMs)' preferences for feasible states in the graph model for conflict resolution (GMCR) is crucial for accurately determining stability results. This paper addresses the issue of subjective ranking methods lacking theoretical foundation and causing ambiguity when the number of feasible states is high by proposing the implementation of the multi-attribute decision-making (MADM) method in the GMCR. The paper utilizes the average level to choose evaluation based on distance from average solution (EDAS) method for determining the DM's preference ranking, which can effectively reduce the impact of anomalous evaluations. Further, the PUL-EDAS method based on probabilistic uncertainty linguistics (PUL) is developed, which overcomes the shortcomings of the traditional EDAS method, which only applies to the simple evaluation of information. The PUL aligns with DMs' daily evaluation practice by providing an interval for the quality of qualitative linguistic evaluations. Furthermore, it utilizes an objective aggregation method to calculate comprehensive evaluation information from all DMs. In addition, the four fundamental stability definitions, applicable solely under crisp preferences, are extended to the PUL context, providing related extended definitions. Finally, to ensure the scientific validity and practicality of the proposed theory, this paper selects digital rural governance as the research context for conflict calculus analysis, comparing it with other MADM methods in the preference ranking section. [ABSTRACT FROM AUTHOR]

In fuzzy large group decision making methods, an effective clustering method can greatly reduce the complexity of decision making, and it is an important ingredient for reaching a group consensus. In this paper, a novel fuzzy large group decision making method is established using three-way clustering and an adaptive exit-delegation mechanism. Traditional clustering approaches group together individuals (isolated points) that deviate from the whole. The individuals (edge points) may exist and wander in between two or more classes. Both circumstances can lead to unstable and unreasonable clustering results. To overcome both setbacks, we propose a three-way clustering method based on the k -means clustering algorithm. The method first applies k -means clustering to perform an initial division of the universe of decision-makers. Then, in the spirit of three-way clustering, the edge points and outliers are separated from the clustering results by resorting to the three-way relationships between individuals and classes. The final clustering stems from an adaptive exit-delegation mechanism, and a consensus measure-based model determines the intra-group individual weight and inter-individual trust weight. Finally, the feasibility and effectiveness of the methodology that arises from the model designed in this paper are verified by comparative analyses. [ABSTRACT FROM AUTHOR]

In this paper, the communication network associated with a linear heterogeneous clustered multi-agent system (CMAS) contains several clusters, each of which is modeled by a strongly connected digraph and contains a leader. Intra-cluster agents are in continuous communication with their intra-cluster neighbors during the communication period, whereas only the inter-cluster leaders can communicate with other leaders at a series of discrete moments, known as the reset time. Thus this paper presents a reduced-order observer-based reset output feedback controller that solves the output synchronization problem associated with the linear heterogeneous CMAS. Specifically, a reset internal model is built to solve the output synchronization for each agent, and a reset reduced-order observer is developed to estimate the unavailable states of each agent. Then an output feedback control strategy is developed using only the output information, internal model state, and observer state. Sufficient conditions are also obtained for ensuring the output synchronization of the CMAS. Finally, an illustrative example is provided to demonstrate the efficiency of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Heterogeneous multi-criteria group decision making (MCGDM) is a hot topic in the decision analysis field. This paper proposes a fairness-concern-based LINMAP (Linear Programming Technique for Multidimensional Analysis of Preference) method for heterogeneous MCGDM with hesitant fuzzy linguistic (HFL) truth degrees. Heterogeneous evaluation information includes crisp numbers, interval numbers, intuitionistic fuzzy values (IFVs), trapezoidal fuzzy numbers (TrFNs) and hesitant fuzzy sets (HFSs). This paper introduces the fairness concern to calculate the HFL consistency and the HFL inconsistency indices. Based on the framework of LINMAP, a bi-objective HFL programming model is built to derive the criteria weights, the positive ideal fairness vector (PIFV) and the negative ideal fairness vector (NIFV) for each decision maker (DM) simultaneously. Based on the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), a multi-objective programming model is built to obtain DMs' weights. The alternatives ranking is derived by comprehensive collective relative closeness degrees. Finally, a real example is applied to verify effectiveness and superiority of this heterogeneous MCGDM method. The proposed heterogeneous MCGDM method provides a very useful approach for MCGDM with heterogeneous information. [ABSTRACT FROM AUTHOR]

Topological index of a graph is a numerical representation linked to the graph or the molecular structure associated with the graph, shedding light on its topological and structural properties. Different topological indices showcase unique attributes rooted in their degree, spectrum, and distance characteristics. Among these, the first and second K Banhatti indices, introduced by Kulli, involving both vertex and edge degrees, have garnered significant scholarly interest, prompting extensive discussions in graph theory. Within this research paper, a thorough exploration delves into the attributes surrounding the fuzzified first and second K Banhatti indices. This exploration is directed towards several bounds of the index and index of various structures like cycles, complete fuzzy graphs, complete bipartite graphs and stars. Relation between a fuzzy graph and its partial subgraphs, fuzzy graph and its complement graph in connection with the indices is also found. Additionally, the research paper investigates the first and second K Banhatti indices concerning graph operations such as the corona product and coalescence. Additionally, the paper outlines an algorithm designed to accurately compute the first and second K Banhatti indices and proposes an application in decision-making. [ABSTRACT FROM AUTHOR]

The paper is concerned with the recursive state estimation problem for a class of two-dimensional systems over decode-and-forward relay channels subject to packet dropouts. Taking into account the sensor's limited transmission ability, a decode-and-forward relay is deployed between the sensor and the remote estimator to enlarge the propagation distance and improve the communication quality. The packet dropout phenomenon is described by two sequences of mutually uncorrelated random variables that obey Bernoulli distributions. The main objective of this paper is to design a recursive state estimator for the underlying system with guaranteed estimation performance. An upper bound on the estimation error variance is firstly derived by resorting to some coupled difference equations, and then such an upper bound is locally optimized at each iteration through proper design of the estimator gain. Furthermore, the impacts of the packet dropouts and the decode-and-forward relay on the estimation performance are evaluated with rigorously theoretical analysis. Finally, an illustrative example is presented to validate the effectiveness of the proposed estimation scheme. [ABSTRACT FROM AUTHOR]

In real life, multiple issues may have different weights in leading to conflicts. Some of the existing conflict analysis literature related to weight does not involve an explicit weight method, and some use common methods such as entropy weight method. This paper aims to design a reasonable weighting method for the inherent characteristics of conflict analysis. The main motivation is that the issues getting vast majority of support (or opposition) are assumed to be more likely to cause intense conflicts. Firstly, a novel weighting method using N -bounded symmetric concave reciprocal function is brought in. Some properties of the method such as duality, objectivity and symmetry are discussed. Then, by embedding the weights into the existing distance function a weighted three-way conflict analysis model is proposed. Next the thresholds of conflict, alliance and neutrality relations are given by decision-theoretic rough set theory. In addition, as a main characteristic of the model, the conflict distance between any two agents is determined by the overall conflict table rather than their own. Finally, the model of this paper is compared with the existing conflict analysis weight model. At the same time, a comparative simulation experiment was carried out on the weight change and the number of maximal coalitions. The new weighted conflict model proposed in this paper can effectively compensate for the limitations of existing weighted models, especially in three-valued information systems and multi-valued information systems. It can also theoretically expand the field of three-way conflict analysis. [ABSTRACT FROM AUTHOR]

In this paper, we develop an improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (ILIVAIFWA) aggregation operator (AO) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs). The ILIVAIFWA AO of LIVAIFNs presented in this paper can conquer the drawbacks of the linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (LIVAIFWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy ordered weighted averaging (LIVAIFOWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy weighted geometric (LIVAIFWG) AO and the linguistic interval-valued Atanassov intuitionistic fuzzy ordered weighted geometric (LIVAIFOWG) AO of LIVAIFNs. We also develop a novel group decision making (GDM) method on the basis of the proposed ILIVAIFWA AO of LIVAIFNs. The GDM method presented in this paper can oconquer the drawbacks of the existing GDM methods in the context of LIVAIFNs. [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]

Regarding the defects of Ruspini partition-based clustering in revealing the intrinsic correlation between classes, this paper proposes a series of generalized multiplicative fuzzy possibilistic product partition clustering algorithms. First, based on the existing concept of generalized multiplicative intuitionistic fuzzy sets, this paper introduces a new concept of generalized multiplicative fuzzy sets and further defines the corresponding multiplicative fuzzy partition. Then, based on the concept of multiplicative fuzzy partition, a novel generalized multiplicative fuzzy possibilistic product partition C-means (GMFPCM) clustering algorithm is presented, and its local convergence is strictly proved using Zangwill's theorem. Meanwhile, a robust Gaussian-base radial kernel based on the M-estimator is introduced into the GMFPCM algorithm to improve its robustness against noise and outliers in numerical data. Additionally, a multiplicative fuzzy possibilistic local information factor is constructed and embedded into the GMFPCM algorithm to strengthen its ability to suppress noise in images. Finally, the comparison with existing fuzzy possibilistic clustering algorithms in the literature confirms the competitiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

With the rapid development of e-commerce, more and more people are willing to post their reviews and opinions about the products they buy online. Therefore, the use of online review data for decision-making appears to be more practical and universal, and how to effectively use this kind of data to support large-scale group decision-making (LSGDM) is a worthy research direction. In this paper, we firstly use sentiment analysis to analyze online review data to derive the decision maker's (DM's) sentiment value, and apply the sentiment value to construct a social network based on a dual trust relationship, which considers both familiarity-based trust and similarity-based trust. Secondly, a directed Louvain clustering algorithm in light of dual trust relationships and a method for solving the DM's intra-group weights and the group's weights are proposed based on this network. A two-stage clustering based consensus model in light of dual trust relationships is then proposed, in which the DMs in the agreement cluster can communicate with other DMs outside of such a cluster and dynamically update the grouping using the clustering algorithm. Finally, the practicality and effectiveness of the LSGDM method proposed in this paper are verified through a real case. [ABSTRACT FROM AUTHOR]

This paper proposes a new intuitionistic fuzzy best-worst method (IFBWM) for group decision making (GDM) with intuitionistic fuzzy (IF) preference relations (IFPRs). IF values (IFVs) are used to express reference comparisons of criteria. Based on the additive consistency of IFPRs, this paper proposes the definition of additive consistency of IF reference comparisons (IFRCs). Based on the deviation minimization, a linear goal programming model is established to calculate the optimal IF priority weights. By the additive consistency, the consistency index in the closed form is computed by the score function of IFVs. A new approach is devised to enhance the additive consistency of IFRCs. Thus, an IFBWM with the additive consistency of IFRCs is proposed. For GDM with IFPRs, the best criterion and the worst criterion are identified for each decision maker by constructing the score matrix of the IFPR. The individual ranking order of the criteria is obtained by using the proposed IFBWM. Then, the collective ranking order of the criteria is obtained via building a 0–1 integer programming model. Therefore, a GDM method based on the developed IFBWM with IFPRs is proposed. Four examples are analyzed to demonstrate the effectiveness and the advantages of the proposed IFBWM for GDM. [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]

• In this article, we present a three-phased framework to aid the multi-criteria decision analysis of portfolios in an online and interactive fashion. • This approach is based on the idea of enriching a classical mathematical technique (e.g. goal programming, ?-constraint, or compromise programming) by incorporating some concepts based on fuzzy relations taken from the European School of MCDA (Multi-Criteria Decision Analysis). • Experimental evidence on synthetic and real-world instances shows that our model computes quickly enough to be interactive and it is even capable of improving high quality solutions. • The contribution of this paper is in providing a guideline to build compromise programming models that follow the principles of ELECTRE III to prevent incomparability during the analysis. It aids the DM in identifying strictly preferred solutions. • In practical terms, the chief contribution of this approach is the level of confidence that the DM can feel in the final prescription. This paper introduces an interactive approach to support multi-criteria decision analysis of project portfolios. In high-scale strategic decision domains, scientific studies suggest that the Decision Maker (DM) can find help by using many-objective optimisation methods, which are supposed to provide values in the decision variables that generate high-quality solutions. Even so, DMs usually wish to explore the possibility of reaching some levels of benefits in some objectives. Consequently, they should repeatedly run the optimisation method. However, this approach cannot perform well – in an interactive way – for large instances under the presence of many objective functions. We present a mathematical model that is based on compromise programming and fuzzy outranking to aid DMs in analysing multi-criteria project portfolios on the fly. This approach allows relaxing the problem of rapidly optimising portfolios while preserving the beneficial properties of the DM's preferences expressed by outranking relations. Our model supports the decision analysis on two instance benchmarks: for the first one, a better compromise solution was generated 84% of the runs; for the second one, this ranged from 93% to 97%. Our model was also applied to a real-world problem involving social projects, obtaining satisfactory results. [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]

In this paper, the cluster synchronization problem of a heterogeneous second-order leader-following multi-agent system with nonlinear dynamics, actuator faults, and integral quadratic constraints (IQCs) under a directed topology with a directed spanning tree is investigated. Based on the local topology information, two adaptive fault-tolerant pinning control strategies with fixed and adaptive pinning gains are proposed to guarantee cluster synchronization in finite time. An adaptive input compensation is developed to attenuate the adverse effects of actuator faults. It is worth mentioning that just one parameter needs to be estimated for each agent in this compensation, which implies that the strategies designed in this paper can effectively reduce the computational cost. Furthermore, the use of the pinning control method instead of the fully equipped control method makes the strategies more cost-effective for large-scale multi-agent systems. Finally, numerical simulation examples are introduced to demonstrate the effectiveness and advantages of the proposed strategies. [ABSTRACT FROM AUTHOR]

Ensemble learning is a widely used methodology to build powerful predictors from multiple individual weaker ones. However, the vast majority of ensemble learning models are designed for offline application scenarios, the use of evolving fuzzy systems in ensemble learning for online learning from data streams has not been sufficiently explored, yet. In this paper, a novel self-adaptive fuzzy learning ensemble system is introduced for data stream prediction. The proposed ensemble system employs the very sparse random projection technique to compress the consequent parts of the learned fuzzy rules by individual base models to a more compressed form, thereby reducing redundant information and improving computational efficiency. To improve the overall prediction performance, a dynamical base model pruning scheme is introduced to the proposed ensemble system together with a novel inferencing scheme, such that less accurate base models will be removed from the ensemble structure at each learning cycle automatically and only these more accurate ones will be involved in joint decision-making. Numerical examples based on a wide range of benchmark datasets demonstrate the stronger prediction performance of the proposed ensemble system over the state-of-the-art alternatives. [ABSTRACT FROM AUTHOR]

• Establish formulas to compute spread and indeterminacy indices of fuzzy judgments. • Develop a novel trapezoidal fuzzy extension of Saaty's consistency. • Propose a new framework to normalize trapezoidal fuzzy utility vectors. • Build a linear program to acquire trapezoidal fuzzy utility vectors from TFRPMs. • Find an analytical solution for optimal fuzzy utility vectors of consistent TFRPMs. Fuzzy extensions of Saaty's consistency play an important role in developing fuzzy analytic hierarchy process based decision-making methods. This paper proposes formulas to calculate ratio-based increasing and decreasing spread indices and to obtain ratio-based indeterminacy indices of modal and support intervals for fuzzy judgments of trapezoidal fuzzy reciprocal preference matrices (TFRPMs). A transitivity equation with parametric fuzzy elements is introduced and combined with the existence of parameter values to define consistency of TFRPMs. To cope with the challenge of identifying the existence, computational formulas are developed to directly obtain values of parameters from the fuzzy judgments in a TFRPM, and an equivalent consistency concept is proposed for TFRPMs. Properties of consistent TFRPMs are presented and a logarithmic deviation based formula is provided to compute consistency indices of TFRPMs. A new framework of normalized vectors with trapezoidal fuzzy elements is introduced. A logarithmic goal programming model is established and transformed into a linear program for acquiring normalized trapezoidal fuzzy utility vectors from TFRPMs. An analytical solution is found for optimized trapezoidal fuzzy utility vectors of consistent TFRPMs. The developed models are validated by three numerical illustrations possessing comparative studies. [ABSTRACT FROM AUTHOR]

This paper aims to develop a new axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making (HMCGDM) problems with linguistic fuzzy truth degrees (LFTDs). The main contributions of this paper are summarized in five aspects: (1) The information content definitions for six types of fuzzy numbers are initially provided according to axiomatic design. (2) Considering the authority of experts on different criteria and group consensus, a bi-objective programming model is constructed to derive experts' weights by maximizing individual deviation and minimizing group discordance. (3) Each alternative is assessed on the basis of its information content to a fuzzy positive ideal solution. Information content is firstly used to define the linguistic fuzzy consistency and inconsistency indices. (4) A bi-objective linguistic fuzzy mathematic programming model is built to determine the criteria weights, which considers consistency and inconsistency indices simultaneously. This model can be dexterously transformed into a crisp linear programming model for resolution by the linguistic scale function. (5) The group information content of each alternative to fuzzy positive ideal solution is calculated to determine the ranking order of alternatives. Finally, an example of blockchain service provider selection is given to validate the proposed method. [ABSTRACT FROM AUTHOR]

• Group decision making with fuzzy information. • Multi-person decision making with the theory of expertons. • A new computer software for multi-person decision making. • Weighted averages in multi-expert analysis. Experton theory, a generalization of probabilistic set theory, that is of great usefulness to group decision analysis, was first proposed as a means of improving the processing and analysis of opinions issued by experts. This theory produces an information-fusion mathematical object, the experton, which can be used in predictive problems to justify decisions based on well-constructed reasoning. The aim of this paper is to present an aggregative method of several expertons, with the idea that some of the groups of experts involved in producing these expertons may have more influence than others in the decision-making process. In this article, we carry out an aggregation analysis of expertons, not experts, which culminates in the creation of a new mathematical object. This object, which is called the weighted average multiexperton, is coherent with an experton-type object created from a weighting of the initial data provided by all experts. Since the aggregation method presented has been devised to represent the decision-maker's attitude regarding the importance of different groups of experts, this approach represents a new tool for dealing with group decision-making problems. Additionally, the study presents some properties of the new object. Finally, the paper ends with an application for business decision-making. [ABSTRACT FROM AUTHOR]

To address the challenge of facilitating overall problem solving and improving the overall efficiency of intelligent systems efforts through group decision making (GDM) by experts at all stages of the systems, this paper proposes an approach that focuses on improving consistency and enhancing local consensus. The proposed approach specifically considers the probabilistic linguistic preference relations (PLPRs) and incorporates personalized individual semantics (PISs) of decision makers (DMs). For the consistency procedure, we construct an expectation-additive consistency-driven semantic model to acquire PISs of different DMs. Secondly, the preference relation (PR) which does not satisfy the consistency is improved based on a minimum adjustment model. In particular, according to the expected value with PISs this paper, DMs offer PLPRs can be transformed into fuzzy preference relations (FPRs) correspondently for making decisions. For the FPRs, a virtue consensus measure is explored for the consensus reaching process (CRP) from two levels to combine the average value and variance of pair similarities, which effectively improves the accuracy of the consensus measurement. Next, a collective consensus level is calculated to replace the consensus threshold objectively, and then the DMs and alternative pairs that do not reach consensus are identified locally from two levels. Subsequently, an optimisation model that combines the two objectives is developed to improve the consensus level while ensuring consistency. Finally, our method is applied to a publicly available air quality dataset, and the consensus and ranking results are discussed in comparison with other advanced methods to confirm the superiority of the established method. [ABSTRACT FROM AUTHOR]

Multiattribute group decision-making (MAGDM) is a decision analysis method used to address decision-making problems that have multiple attributes and multiple decision alternatives. It is generally believed that multigranulation rough sets (MGRSs) are a twofold scheme to solve MAGDM problems. Thus, in this paper, we aim to generalize MGRSs and decision-theoretic rough sets (DTRSs) to intuitionistic fuzzy β -covering (IF β C) information systems and propose a novel MAGDM method to handle decision-making problems, which not only deepens the cognition of the three-way decision (3WD) model but also expands its application in decision-making problems. The paper first introduces a novel conditional probability using the ideal positive degree of intuitionistic fuzzy numbers (IFNs) and then investigates its properties. Second, in the IF β C environment, we utilize the proposed conditional probabilities to construct two types of multigranulation decision-theoretic rough set (MGDTRS) models, an optimistic strategy and a pessimistic strategy, discuss their theoretical properties and explore the relationship between the two strategies. Third, a novel MAGDM method for multi-intuitionistic β -neighborhoods is established in accordance with the proposed MGDTRS model. We also establish an algorithm for the proposed MAGDM method. Fourth, we apply the proposed method to address several MAGDM problems. By conducting comparative analysis with existing methods, we demonstrate the effectiveness of the proposed method and discuss the advantages and limitations of the proposed method. Furthermore, we conduct extensive parameter experimentation analysis on the proposed method from different perspectives. The experimental results demonstrate the stability and effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

As information continues to expand and uncertainty intensifies, traditional three-way decision methods in multi-criteria environments often appear inadequate when dealing with ranking problems. Most traditional three-way decision methods usually rely on subjective concepts or require decision-makers to specify probability parameters when constructing scheme descriptions, which leads to high subjectivity of the methods. Based on this background, this paper proposes an optimization-based three-way decision model for multi-criteria ranking strategy considering intuitionistic fuzzy concept, with the aim of mitigating the excessive subjectivity observed in most of the three-way decision methods. Firstly, a scheme-oriented intuitionistic fuzzy concept is defined to represent the decision-maker's fuzzy perception and selection of the scheme. Then, using the scheme-oriented intuitionistic fuzzy concept and the classic description of candidate schemes obtained through intuitionistic fuzzy c -means clustering algorithm, this paper provides a new method for estimating the conditional probability of the schemes that is not limited by parameter settings. Secondly, combining the scheme-oriented intuitionistic fuzzy concept and intuitionistic fuzzy information table, a new risk loss function is proposed, which is suitable for decision problems under intuitionistic fuzzy environment. Then, based on three-way decision model formulated using an optimization-based approach, an objective new ranking strategy is constructed. In addition, numerical analysis, comparative analysis, and parameter analysis are used to validate the rationality and feasibility of the presented ranking strategy. Finally, through quantitative analysis of multiple datasets and qualitative analysis of several ranking models, the operability of the new ranking strategy is verified. [ABSTRACT FROM AUTHOR]

Consensus reaching process (CRP) is very important for multi-criteria group decision making (MCGDM). Recently, social network driven CRP methods have been deeply investigated. However, these methods rarely considered knowledge levels of DMs. In fact, knowledge levels of DMs can decide the correctness of final decision result which play an important role in CRP. Therefore, this paper proposes knowledge degree to measure knowledge level of DM and develops a new social network driven CRP method for probabilistic linguistic MCGDM problems. Based on the similarity degree and knowledge degree, similarity degree-based social network (SDSN) and trust relationship-based social network (TRSN) are constructed successively. According to the constructed SDSN and TRSN, the proposed CRP method consists of two stages. In the first stage, pair-wise DMs in complementary social network adjust their evaluations. In the second stage, the evaluations of DMs who contribute less to group consensus are modified. To ensure that the group consensus index (GCI) is non-decreasing in the above two stages, the constructed programming models not only improve similarity degrees between DMs-to-adjust and reference DMs but also consider similarity degrees between DMs-to-adjust and other DMs. Finally, an investment selection example and comparison analyses demonstrate the applicability and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

• An adaptive consensus model based on feedback mechanism and social interaction is proposed to improve the consensus efficiency. • The stubbornness of decision makers to the initial opinions is considered in the consensus model. • The evolution of weights and self-confidence degrees of decision makers is integrated into the consensus model. • Social interaction may have a double-sided impact on the consensus reaching. Many consensus models in social network group decision making (SNGDM) have been reported to obtain a collective solution despite the initial opinions of decision makers (DMs) may be different. However, these models ignore the obstinacy of DMs to their initial opinions, which violates the sociological research results. Aiming at the consensus reaching of SNGDM where DMs are stubborn to their initial opinions, this paper proposes a novel consensus model based on the passive adjustment based on feedback mechanism (PA-FM) and active adjustment based on social interaction (AA-SI), which adaptively adopts AA-SI or PA-FM in each round according to the opinion distribution of DMs. Specially, the proposed consensus model assimilates the advantage of PA-FM and AA-SI, where adjustment intensity of DMs affects the consensus level of PA-FM, and stubbornness degree of DMs affects that of AA-SI. To elucidate the performance and advantages of the proposed consensus model, a hypothetical application and three simulation analyses are constructed. The results show that (1) In the decision-making group that is stubborn to the initial opinions, social interaction has a beneficial or harmful effect on the consensus reaching, depending on the stubbornness degree and opinion distribution of DMs; and (2) Given any stubbornness degree and adjustment intensity, the proposed consensus model outperforms existing consensus methods in consensus efficiency and success rate. [ABSTRACT FROM AUTHOR]

Witnessing the growth of inaccurate data with uncertainty and ambiguity, the belief rule base system is attracting increasing research interest because of its usage in decision-making problems as a disjunctive paradigm particularly when there is incomplete information. In this paper, we devise a novel method that employs fuzzy association rules to optimize disjunctive belief rule base (DBRB) systems regarding incomplete information in decision-making and achieve a significant performance improvement compared to the existing ones. First, we devise a method for constructing a fuzzy representation base from history data by using the triangular membership functions to blur history information. Then, a method is proposed to construct association rules based on the fuzzy representation base, in which the association rules are found regarding the missing input information by carrying out reasoning to complete the data and then making decisions on the data filled with DBRB system. Lastly, we evaluate the effectiveness of our proposed method against the public test data set, demonstrating that our method outperforms other baselines for decision-making with incomplete information. [ABSTRACT FROM AUTHOR]

For complex decision-making problems, the joint evaluation of multiple experts is indispensable for efficiently addressing them. Therefore, multi-attribute group decision-making (MAGDM) problems have become popular in recent decades, however the development of MAGDM problems in the environment of probabilistic linguistic term sets (PLTSs) is not mature. To this end, the paper aims to study group consensus under PLTSs. Specifically, since some existing distance measures do not meet the basic principle of distance measures, and some ones can not measure the distance between PLTSs of different lengths, a new distance measure is defined to eliminate these two drawbacks. In the consensus reaching process, most of common orientation rules choose to change all evaluation information of experts, which is actually hard in reality. For the sake of guaranteeing the original information as much as possible with consensus reaching, the attribute discriminant value is proposed via using the idea of sequential three-way decision (STWD). Then, an STWD -based group consensus method is constructed under PLTSs , namely PLTS-STWD. Meanwhile, dynamic modification parameters are developed associated with attribute discriminant values. Afterwards, the regret-rejoice function is employed to rank all alternatives. Finally, the constructed method is applied to a realistic case and compared with other consensus methods to verify its effectiveness and feasibility. [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]

This paper proposes a new group decision making (GDM) approach in the environments of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs, where the proposed score function of IVIFVs can overcome the drawbacks of the existing score function of IVIFVs. The properties of the proposed score function of IVIFVs are also presented. Then, we propose the advanced interval-valued intuitionist fuzzy averaging (AIVIFA) aggregation operator of IVIFVs. We also provide the proofs of the properties of the proposed AIVIFA aggregation operator. Then, we propose the advanced interval-valued intuitionist fuzzy weighted averaging (AIVIFWA) aggregation operator of IVIFVs. Then, we propose a new GDM approach based on the proposed AIVIFWA aggregation operator of IVIFVs and the proposed score function of IVIFVs. Finally, we apply the proposed GDM approach to deal with a real-world application of cloud service selection. The proposed GDM approach can overcome the drawbacks of the existing GDM approach, which is unable to distinguish the ranking orders of alternatives in some situations. The proposed GDM approach gives us a very useful way to deal with GDM problems in the environments of IVIFVs. [ABSTRACT FROM AUTHOR]

• An advanced anomaly detection method via granular computing is proposed; • Granular data descriptors are used to construct anomaly detectors; • A fuzzy rule-based modeling method is applied for anomaly data detection (ADD); • The constructed granular ADD detectors are low-cost and effective; It is meaningful for data-driven studies to detect and remove the anomaly data from a given raw dataset. Considering the existing anomaly data detection (ADD) methods have some drawbacks, e.g. confidence and uncertainty in anomaly description, computation cost of kernel learning and deep learning in ADD, therefore this paper proposes an advanced approach for constructing low-cost and effective ADD detectors. Firstly, making use of the good data description ability of information granules, granular data descriptors are constructed for anomaly and normal data description. Then, based on these data descriptors, reconstruction-based strategy is applied to model anomaly detection. Subsequently, with consideration of anomaly data's uncertainty, fuzzy rules are formed and used to realize the final anomaly data detection. In this study, both synthetic and publicly available datasets are considered in experimental analysis. Numerical results illustrate the proposed method has a superiority ranging from 8.60% to 32.58% to conventional models on ADD performance, verifying the feasibility and effectiveness the proposed methods via granular data descriptors. Moreover, through the discussion on computation complexity, the proposed method is also demonstrated efficient on detecting anomalies. [ABSTRACT FROM AUTHOR]

In this paper, we propose a series of novel aggregation techniques based on overlap and grouping functions for group decision-making (GDM) issues in the Z -number environment. Firstly, we introduce an optimization model to determine the underlying distribution for Z -numbers, meanwhile, the mean function of Z -numbers is revised to better reflect the three-dimensional structure of the Z -numbers. And then, a series of operations for Z -numbers using overlap and grouping function are defined, and their properties are also investigated. Subsequently, we construct the overlap function-based Z -number weighted Bonferroni mean (OZWBM) operator to integrate the information in the Z -number environment. Furthermore, to verify the efficiency of novel aggregation techniques, a new energy investment selection issue is addressed. Besides giving the rankings of alternatives, by analyzing the calculation results, we can also derive the degree of preference from investment experts in scoring each investment object. Finally, by comparing the existing methodologies, we confirm that the new approach is effective and reasonable for the multi-criteria group decision-making (MCGDM). [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]

• Logic AND operation in FNNs did not depict the uncertainty of pixels in images well. • A new fuzzy rule is proposed for the uncertainty using the similarity between pixels. • A novel SR method is proposed by combining fuzzy set theory and deep learning. • Some deep learning modules are designed to extract more effective image features. • The proposed method has better performance in SR medical image reconstruction. The clarity of medical images is crucial for doctors to identify and diagnose different diseases. High-resolution images have more detailed information and clearer content than low-resolution images. It is well known that medical images can frequently have some blurred object boundaries, and that traditional deep learning models cannot adequately describe the uncertainty of these blurred boundaries. This paper proposes a new fuzzy metric to characterize the uncertainty of pixels and designs a fuzzy hierarchical fusion attention neural network based on multiscale guided learning. Specifically, a fuzzy neural information-processing block is proposed, which converts an input image into a fuzzy domain using fuzzy membership functions. The uncertainty of the pixels is processed using the proposed fuzzy rules, and then the output of the fuzzy rule layer is fused with the result of the convolution in the neural network. Simultaneously, a multiscale guided-learning dense residual block and pyramidal hierarchical attention module are designed to extract more effective hierarchical image information. Finally, a recurrent memory module with a residual structure is used to process the output features of the hierarchical attention modules. A recursive sub-pixel reconstruction module is used at the tail of the network to reconstruct the images. Compared with existing super-resolution methods using the public COVID-CT dataset, the proposed method demonstrated superior performance in high-resolution medical image reconstruction and reduced the number of parameters and analysis time of the models. [ABSTRACT FROM AUTHOR]

• Design a sentiment analysis-based expert comment extraction and conversion method. • Propose a core-periphery structure detection method to cluster numerous experts. • Measure expert reliability by investigating consistency level and social influence. • Construct a novel two-stage consensus reaching model based on prospect theory. • A case study is provided to show the effectiveness and superiority of the method. The development of big data and social media has driven large-scale group decision making (LSGDM) to merge with social networks and focus on individual behavioral factors. Following this trend, this paper develops a novel LSGDM consensus model that explores and manages the meso -scale structure among experts using free texts to express their opinions under social network settings. In the proposed approach, firstly the sentiment analysis is adopted to extract preferences over alternatives provided by experts and the preferences are further converted into distributed linguistic preference relation matrices. Then a core-periphery detection method for the social network constructed based on the newly defined distance measure for linguistic distribution assessments is proposed. After that, expert weights are derived by an optimization model that maximizes the expert reliability based on consistency and node centrality. Moreover, considering reference dependence and bounded rationality features of members among the detected network, a prospect theory-based two-stage consensus model is developed to improve group consensus systematically and gradually. Finally, a case study regarding life science investments is provided to illustrate the usefulness of our proposal. The convergence of the proposed model is proven by theoretical and simulation analysis. Comparative analysis reveals the features and advantages of our model. [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]

Formation control of multi-agent systems has a wide range of applications, but it has not been paid much attention in Takagi–Sugeno (T-S) fuzzy systems. In this paper, an event-triggered sampling strategy is designed for the formation control of T-S fuzzy systems, which allows the fuzzy controller and the fuzzy model not to share the same membership functions. The control strategy reduces the transmission frequency of sampling states by setting event conditions for information transmission. By means of Lyapunov stability theory, a set of formation conditions based on LMI is established. Less conservative and more efficient conditions are also obtained based on the properties of membership functions. Numerical examples show the validity of the proposed formation conditions, and the conservatism of the two criteria is compared. [ABSTRACT FROM AUTHOR]

• The minimum cost consensus model is proposed to coordinate the opinions of experts. • A new method of LSGDM clustering is proposed to improve CRP efficiency. • A consensus index CI reflecting the harmony degree between experts is devised. • A robust counterpart of robust optimization consensus is implemented. Recently, large-scale group decision making (LSGDM) in social network comes into being. In the practical consensus of LSGDM, the unit adjustment cost of experts is difficult to obtain and may be uncertain. Therefore, the purpose of this paper is to propose a consensus model based on robust optimization. This paper focuses on LSGDM, considering the social relationship between experts. In the presented model, an expert clustering method, combining trust degree and relationship strength, is used to classify experts with similar opinions into subgroups. A consensus index, reflecting the harmony degree between experts, is devised to measure the consensus level among experts. Then, a minimum cost model based on robust optimization is proposed to solve the robust optimization consensus problem. Subsequently, a detailed consensus feedback adjustment is presented. Finally, a case study and comparative analysis are provided to verify the validity and advantage of the proposed method. [ABSTRACT FROM AUTHOR]

Uncertain group decision making (UGDM) has been a hot research direction over the years. In this paper, according to VOS viewer and CiteSpace, we make a comprehensive bibliometric analysis of UGDM during the last four decades, namely from 1980 to 2019. After data preprocessing, 4,887 publications related to UGDM are obtained from the Web of Science (WoS). Considering numbers, citations and cooperation of publications, general analysis is explored on the basis of bibliometric indicators at the levels of countries/regions, institutions and authors. In order to investigate the development of UGDM, we present cooperation network in the whole period of time and the dynamic networks during the four sub-periods. After that, some deep researches are conducted by bibliometric analysis, such as burst detection analysis, co-occurrence analysis, timeline view analysis and bibliographic coupling analysis. Based on which, further discussions are provided, including current challenges and possible directions. Finally, some main findings are summarized from three aspects, and the advantages and disadvantages of methods in this paper are concluded. This paper explores the hot topics and development trends of UGDM, which offers an important reference for future research. [ABSTRACT FROM AUTHOR]

• The definition of dissipativity for 2-D positive systems is given for the first time. • Controllers are designed to guarantee the dissipativity of the closed-loop systems. • The minimum dwell time method and M-P inverse are utilized in this paper. • Dissipative characteristics of the feedback interconnected system are presented. This paper addresses the dissipativity analysis and controller design for a class of T-S fuzzy positive systems which are described by the Roesser model. First, sufficient conditions obtained by utilizing the minimum dwell time method and co-positive Lyapunov function approach are given to guarantee the considered system is 2-D (ζ , η)- α -dissipative. Then via the state feedback fuzzy controller and the static output feedback fuzzy controller, criteria are also presented under which the resulting closed-loop systems are positive and 2-D (ζ , η)- α -dissipative. Moreover, the explicit design schemes for the desired controller parameters are also presented in the form of linear programming. Finally, a simple illustrative example is provided to show the validity of the approach outlined in this article. [ABSTRACT FROM AUTHOR]

• Show flaws of existing multiplicative transitivity models of interval-valued fuzzy preference relations (IVFPRs). • Develop an and-like-uninorm-based functional transitivity equation for IVFPRs. • Find a closed-form solution for the optimal interval-valued fuzzy weights of IVFPRs. • Formulate geometric consistency indices of IVFPRs and propose a new acceptability checking model. • Devise an and-like-uninorm-based method to aggregate local interval-valued fuzzy weights. The framework of interval-valued fuzzy preference relations (IVFPRs) is adequate and effective to model human preference evaluations under indeterminacy. This paper analyzes three recently presented multiplicative transitivity models of IVFPRs and exposes their drawbacks. An and-like-uninorm-based functional transitivity equation is developed to introduce a multiplicative consistency notion for IVFPRs. Based on the transitivity logarithmic equation, a geometric-consistency index is further proposed to compute the inconsistency level of an IVFPR. The paper builds a logarithmic least squares model with row indeterminacy constraints and equivalently transforms it into a quadratic programming model for finding a closed-form solution of the normalized interval-valued fuzzy weights of IVFPRs. A novel method is subsequently presented to check the acceptability of an IVFPR by examining its acceptable consistency and acceptable indeterminacy. An approach including an and-like-uninorm-based maximization model is introduced to aggregate local interval-valued fuzzy weights and an interval fuzzy analytic hierarchy process is designed step-by-step. An illustrative example and a comparison study are utilized to demonstrate the performance and merits of the presented models. Meanwhile, an outstanding undergraduate student selection problem in international exchange is provided to show the application of the proposed decision method. [ABSTRACT FROM AUTHOR]

The comprehensive logistics distribution center location selection (CLDCLS) problem is a multiattribute group decision-making (MAGDM) problem in which multiple commodity preference weights are considered. To better describe the preference information and expert evaluation information, this paper utilizes 2-dimensional linguistic (2DL) information to express the preference information of various commodities and the expert evaluation, which can represent not only the evaluation information of experts but also the reliability of the evaluation information. Additionally, for solving the CLDCLS problem, this paper puts forward improved operational rules a score function, a distance formula and a correlation coefficient measure. Based on the 2DL information and the improved operational rules, we propose a 2-dimensional linguistic similarity-degree-based clustering analysis method, the 2-dimensional linguistic partitioned Maclaurin symmetric mean (2DLPMSM) operator, and the 2-dimensional linguistic weighted partitioned Maclaurin symmetric mean (2DLWPMSM) operator. The corresponding properties and special cases are demonstrated. By using these proposed methods, this paper constructs a MAGDM solution framework for the CLDCLS problem. A practical case of the CLDCLS problem is presented to demonstrate the effectiveness, rationality, robustness and superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel multiple attribute decision making (MADM) method using the improved intuitionistic fuzzy weighted geometric (IIFWG) operator of intuitionistic fuzzy values (IFVs) proposed in this paper. First, we develop the IIFWG operator of IFVs to conquer the weak points of the existing operators of IFVs, where they have the drawbacks that their aggregated values are indeterminate in some situations. Based on the proposed IIFWG operator of IFVs, we present a MADM method to overcome the weak points of the existing MADM methods, which have the shortcomings that they obtain unreasonable ranking orders (ROs) of alternatives or they cannot discriminate the ROs of alternatives in some circumstances. [ABSTRACT FROM AUTHOR]

• A partial sampled-data control scheme is proposed to cut down the updating rate and shorten the operating time of the controllers. • Using the discrete-time Lyapunov approach, a new lemma is established to simplify the analysis process for partial sampled-data control systems. • Two interval-dependent functionals are developed to enlarge the allowable data loss ratio. This paper is concerned with the synchronization problem of chaotic Lur'e systems by using partial sampled-data information. First, a useful lemma is established on the basis of discrete-time Lyapunov theory and interval estimate methods, which contributes to the stability of partial sampled-data control (PSC) systems. According to the features of the designed control scheme, a single-interval-dependent functional and a double-intervals-dependent functional are constructed by utilizing the corresponding interval information, respectively. Unlike the previous Lyapunov functional methods, the proposed functionals are essentially continuous and then some additional constraint conditions are removed. Then, based on several inequality methods, two sufficient criteria dependent on the controller gain, sampling period, and allowable data loss ratio (ADLR), are respectively developed to guarantee the global synchronization of Lur'e systems. Additionally, the quantitative analysis about the ADLR is discussed. Compared with the existing results, the developed interval-dependent functional techniques are beneficial to enlarging the ADLR. Finally, illustrative examples and an application to image encryption are given to demonstrate the advantages and effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Recently, some researchers have explored three-way decision models in the fuzzy multi-criteria environments from the perspective of criterion fuzzy concept. The main characteristics of these models include the subjective preference of decision-maker for criteria and the evaluation value information system provided by decision-maker. However, the criterion fuzzy concept only considers the decision-maker's membership preference to each criterion, and ignores the decision-maker's non-membership preference to each criterion. In view of this, this paper further proposes a new criterion fuzzy concept, namely the intuitionistic fuzzy concept, to express decision-maker's preference for each criterion. At the same time, we build an intuitionistic fuzzy concept-oriented three-way decision model to solve the ranking and classification problem in the intuitionistic fuzzy multi-criteria environments with decision-maker's preference. Firstly, based on the defined intuitionistic fuzzy concept, we construct a new intuitionistic fuzzy loss function model. Meanwhile, using intuitionistic fuzzy similarity, we propose a new conditional probability calculation method to express the correlation degree between the intuitionistic fuzzy concept and alternative's evaluation values. Secondly, we introduce three decision-making perspectives from the membership degree and non-membership degree of expected loss to obtain the final three-way classification scheme. Moreover, by combining the thresholds of the positive and negative perspectives, we obtain the comprehensive thresholds of the comprehensive perspective, which can be used to rank all alternatives. Finally, a supplier selection problem is used to verify the feasibility and superiority of the model, and six data sets are used to verify the applicability of the model. [ABSTRACT FROM AUTHOR]

• Propose an interval biform game model to handle both strategy choice and coalition formation. • Develop an interval weighted equal contribution division method to solve cooperative games. • Identify existence and necessary conditions of pure strategy Nash equilibriums. • Numerical examples are presented to illustrate the proposed method. This paper develops an interval noncooperative-cooperative biform game (referred to as the interval biform game in short hereafter) model that accounts for both strategy choice and coalition formation while also addressing profit allocation with interval coalition characteristic values. This interval biform game consists of four elements: a finite set of players, their strategy choices, coalitions, and interval coalition characteristic functions, and contains both noncooperative and cooperative parts. The payoffs of different strategies are not directly given a priori in the noncooperative part but obtained by solving interval cooperative games in the cooperative part. To solve the interval cooperative game, we extend a real-valued weighted equal contribution division (WECD) approach to an interval-valued version. Subsequently, an interval acceptability degree comparison method is introduced to compare the interval payoff values. We then establish existence and necessary conditions of pure strategy Nash equilibriums and derive a condition for a Nash equilibrium to be efficient in an interval biform game. Finally, numerical examples are furnished to illustrate the validity and applicability of the proposed framework. [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]

This paper investigates global fuzzy leader-follower consensus problem of mixed-order nonlinear multi-agent systems (MAS) with partially unknown direction control. The follower system is described by a first-order or second-order unknown nonlinear system model with partially unknown direction control and the leader system is described by a second-order time-varying nonlinear system model. Leader can share its position or velocity information with some followers. Due to the different distribution of agents in the network topology, a new hybrid distributed adaptive control protocol is presented in this study. Compared with the asymptotic consensus bounded result, this paper obtains the asymptotic consensus result. The global consensus result is obtained in the paper, which adopts the design method that the fuzzy logic systems (FLSs) acts as a feedforward compensator to approximate the unknown nonlinear dynamics. In the end, a simulation example is given to show the effectiveness of the proposed consensus control protocol. [ABSTRACT FROM AUTHOR]

• The novel transformation and comparison methods for MGPLZNs are developed. • DEA is employed to solve the normalized priority weight vectors for MGPLZNPRs. • Expert credibility that reflects the certainty, ambivalence, and hesitancy of experts is defined. • The subjectively determined expert weights are adjusted according to the expert credibility. • Two case examples are used to illustrate the validity of the proposed method. Multi-granularity probabilistic linguistic Z-number (PLZN) is an effective and flexible tool for expressing expert opinions. For group decision-making (GDM) problems with multi-granularity PLZN preference relations (PLZNPRs), this paper proposes a GDM method based on data envelopment analysis cross-evaluation (DEA-CE) model and expert credibility. First, as the foundation for solving GDM problems with multi-granularity PLZNPRs, this paper reveals the inadequacies of existing methods on transformation and comparison between multi-granularity PLZNs through arithmetic examples. After analyzing these inadequacies, this paper proposes the novel transformation and comparison methods with better performances. Second, to obtain the priorities of multi-granularity PLZNPRs more efficiently, DEA-CE model is introduced and the effectiveness of introducing DEA-CE model is demonstrated. The superiority of introducing DEA-CE model is that it requires no further adjustment of preference relations at any consistency level, which helps to maximize the retention of original information. Third, the subjective expert weights determined based on realistic situations are objectively adjusted using the expert credibility calculated according to the information quality, making the results more reasonable. Finally, this paper illustrates by two case examples that the proposed model can be well adapted to GDM problems with all sizes, regardless of the numbers of decision variables and experts. [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]

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]