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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]

Interval-valued fuzzy preference relations (IVFPRs) have been applied to many real-life decision-making problems. However, most definitions of consistency of IVFPRs do not satisfy invariability to compared objects' labels. To overcome this drawback, this paper mainly focuses on the multiplicative consistency analysis of interval-valued fuzzy preference relations (IVFPRs). Firstly, this paper proposes a new multiplicative consistency of complete IVFPRs. It is proved that this new multiplicative consistency is robust and invariable to compared objects' labels. Then, the definition of acceptable incomplete IVFPRs (In-IVFPRs) is presented. To make full use of all direct and indirect evaluations of decision-makers, an algorithm is devised to evaluate the missing elements of an acceptable incomplete In-IVFPR. To comprehensively describe the closeness between any two complete IVFPRs, the total deviation of two complete IVFPRs is defined based on the p -norm of a vector. By minimizing the total deviation of two complete IVFPRs, a programming model is built to determine an interval weight vector from a complete IVFPR. Subsequently, a novel decision-making method with an In-IVFPR is proposed. Lastly, three practical and numerical examples and simulation-based comparative analyses are provided to further validate the practicability and advantages of the proposed method. [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]

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]

Given a finite set of alternatives, the ranking problem statement builds a preference pre-order (partial or complete) on this set. In this paper, we are interested in multiple criteria ranking problems with a hierarchical structure of criteria; more precisely, we are interested in the existing hierarchical E lectre III method. This method requires eliciting several preference parameters (namely, the weights and the veto thresholds). A direct elicitation of such parameters can be cognitively very demanding; thus, it is adequate to define the parameters in a way that requires much less cognitive effort from the decision-maker. The model parameters can be indirectly elicited by using holistic information provided by the decision-maker; this information can be given in the form of a ranking on a set of reference alternatives and some additional preference information. This paper proposes an aggregation-disaggregation approach for inferring the model parameters of the hierarchical E lectre III based on an evolutionary algorithm. To verify the applicability and validity of the proposed preference disaggregation methodology, an illustrative example is addressed regarding the ranking of a set of universities. [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]

Three-way decision, an outstanding method to handle decision-making uncertainties, relies on essentially the loss functions derived from the Bayesian risk decision process. Actually, there are plentiful loss functions that depend on the subjective judgment of decision-makers under different decision scenarios, lacking uniform and objective measurement frameworks. This study pays attention to the real clinical diagnosis, and constructs a weighted probability kernel multi-granularity three-way decision method (WKMG-TWD) integrating gray relation analysis (GRA) over a multi-source heterogeneous decision information system (MHDIS). The method establishes a standardized data-driven calculation framework of loss functions. Foremost, the multi-kernel probabilistic similarity is defined and granularity's weights with knowledge consistency are explored. Subsequently, a weighted probability kernel multi-granularity rough set (WKMGRS) is constructed in this paper. Secondly, to introduce the three-way decision, this study proposes the cost-sensitive individual loss functions considering the correlation determined by GRA between decision objects and different decision classes. Ultimately, this study establishes and applies a three-way iterative classification model to hypertension diagnosis. The experimental results confirm the effectiveness and superiority of the model. The main contribution of this paper is twofold. One is to offer a uniform calculation framework for loss functions and granularity's weights. The other is to furnish invaluable guidance for solving complex medical decision-making problems. [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]

• To handle the uncertainty decision problems in incomplete hybrid data, a generalized three-way neighborhood decision model is proposed by distributing the interval-valued loss function to each object and averaging the interval-valued loss functions of all objects in the data-driven neighborhood class. • A matrix-based approach for representing three-way regions in the generalized three-way neighborhood decision model is presented by introducing the matrix forms of related concepts and the matrix operators. • An efficient framework for dynamically updating the three-way regions is provided when objects and attributes increase simultaneously. • An incremental algorithm based on matrix is designed for maintaining the three-way regions. • Experimental results demonstrate that the proposed incremental algorithm has an advantage in improving the computational performance. The theory of three-way decisions, as a powerful methodology of granular computing, has been widely used in making decision under uncertainty environments. Decision tasks in incomplete hybrid data including heterogeneous and missing features are of abundance in realistic situations. To deal with these tasks, some work based on three-way decisions has been investigated. However, the losses used for evaluating objects are precise real numbers, which makes these decision models have some limitations in applications when there exist missing values in incomplete hybrid data. Thus, this paper constructs a generalized three-way neighborhood decision model by assigning the interval-valued loss function to each object and further adopting an average strategy to integrate the interval-valued loss functions of objects in each data-driven neighborhood class. Moreover, considering that the objects and attributes of incomplete hybrid data will simultaneously change over time, this paper also provides an efficient framework to dynamically maintain three-way regions of the proposed model. An approach based on matrix to compute the three-way regions is first presented by introducing the matrix operations and the matrix forms of related concepts. Then, with the simultaneous variation of objects and attributes, the matrix-based incremental mechanism and algorithm are proposed for updating the three-way regions, respectively. Experimental results on nine datasets indicate that the proposed incremental algorithm can effectively improve the computational performance for evolving data in comparison with the static algorithm. [ABSTRACT FROM AUTHOR]

• To handle the uncertainty decision problems in incomplete hybrid data, a generalized three-way neighborhood decision model is proposed by distributing the interval-valued loss function to each object and averaging the interval-valued loss functions of all objects in the data-driven neighborhood class. • A matrix-based approach for representing three-way regions in the generalized three-way neighborhood decision model is presented by introducing the matrix forms of related concepts and the matrix operators. • An efficient framework for dynamically updating the three-way regions is provided when objects and attributes increase simultaneously. • An incremental algorithm based on matrix is designed for maintaining the three-way regions. • Experimental results demonstrate that the proposed incremental algorithm has an advantage in improving the computational performance. The theory of three-way decisions, as a powerful methodology of granular computing, has been widely used in making decision under uncertainty environments. Decision tasks in incomplete hybrid data including heterogeneous and missing features are of abundance in realistic situations. To deal with these tasks, some work based on three-way decisions has been investigated. However, the losses used for evaluating objects are precise real numbers, which makes these decision models have some limitations in applications when there exist missing values in incomplete hybrid data. Thus, this paper constructs a generalized three-way neighborhood decision model by assigning the interval-valued loss function to each object and further adopting an average strategy to integrate the interval-valued loss functions of objects in each data-driven neighborhood class. Moreover, considering that the objects and attributes of incomplete hybrid data will simultaneously change over time, this paper also provides an efficient framework to dynamically maintain three-way regions of the proposed model. An approach based on matrix to compute the three-way regions is first presented by introducing the matrix operations and the matrix forms of related concepts. Then, with the simultaneous variation of objects and attributes, the matrix-based incremental mechanism and algorithm are proposed for updating the three-way regions, respectively. Experimental results on nine datasets indicate that the proposed incremental algorithm can effectively improve the computational performance for evolving data in comparison with the static algorithm. [ABSTRACT FROM AUTHOR]

Currently, more and more researchers use the idea and strategy of three-way decision to guide scientific research. In this paper, we propose two comprehensive fuzzy concepts and apply them to construct a new three-way decision model. Firstly, with the TOPSIS method, this paper regards the optimal distance and the worst distance as the cost fuzzy concept and the benefit fuzzy concept, respectively. Then, based on the fuzzy concepts with opposite characteristics, two comprehensive fuzzy concepts (i.e., the comprehensive benefit fuzzy concept and the comprehensive cost fuzzy concept) are proposed, and the relationship between the decision-making regions corresponding to the two comprehensive fuzzy concepts is discussed. Further, four fuzzy neighborhood operators are used to describe the relationship between any two schemes and the relative loss function is used to compute the loss value of each scheme with different behaviors in different states. Afterwards, we introduce a new three-way decision model to solve the multi-criteria decision-making (MCDM) problem. Comparing analysis, Kendall analysis and Spearman analysis show that our method is feasible and stable. [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 outranking multi-criteria decision-making (MCDM) method focuses on the systematic comparison of alternatives and the non-compensation among criteria to conduct decision analysis. Z-numbers are powerful tools for characterizing decision-making information and identifying information reliability. This paper aims to explore Z-number outranking theories and the corresponding MCDM method on the basis of the idea of Elimination and Choice Translating Reality (ELECTRE) III, which is a very popular and capable outranking model. The concordance and discordance indices of Z-numbers are defined by processing their bimodal uncertainty fully. And an objective computation method is investigated to determine the values of thresholds in these indices. Further, three types of novel outranking relations, including dominance, support and opposition relations, for Z-numbers are presented by comparing these indices systematically. Then, an extended MCDM method with the distillation and flow ranking rules is proposed by detecting the outranking relations among alternatives under multiple criteria and carrying out the outranking aggregation and exploitation. To verify the applicability and effectivity of the proposed method, an illustrative example is provided, and a simulation test and a comparison discussion are conducted [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]

Z-numbers are efficient tools to represent uncertain information through restriction and reliability measurement. Z-numbers and their variants have been integrated with diverse decision-analysis methods to solve practical decision-making problems. To make researchers understand the research status and challenges in this area, this paper provides an overview of publications related to Z-number-based decision analysis methods and applications. Firstly, a bibliometric analysis is conducted to present the trends and hotspots in this research domain. To uncover theoretical developments of Z-numbers, concepts and operation rules of Z-numbers and their variants are then recalled. Furthermore, decision analysis methods regarding multiple criteria decision analysis, optimization, prediction, and reasoning within the context of Z-numbers are summarized. Applications of Z-number-based decision analysis methods are categorized into six different fields including business and financial management, industrial engineering and management, energy management, medical and healthcare management, environment and sustainable development, and others. Findings, challenges, and future research directions are further discussed. It is hoped that this paper can provide insights for scholars and practitioners in the fields of Z-number-based decision analysis and applications. [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]

The rapid development of online social networks (OSNs) has enabled seamless cyberbullying activities, which not only cause psychological harm to victims but also bring disharmony to society. From the perspective of OSN platform administrators, strategic decision making towards when/how to launch an anti-cyberbullying campaign is the key to mitigating its negative impact. Hence, this paper develops a dynamic anti-cyberbullying investment solution to mitigate the adverse impact of strategic cyberbullying phenomena cost-effectively. Specifically, this paper first quantifies the payoffs of the attacker/bullying instigator and the defender/platform administrator based on a newly proposed propagation model. Then, considering the budget-constrained factor for both sides, a differential game-theoretical model is proposed to simulate each party's optimal trade-off between cost and benefit. Next, by utilizing Pontryagin Maximum/Minimum Principle, a set of necessary conditions for a Nash equilibrium strategy profile have been proposed. Based on the forward-backward sweep method, an iterative algorithm (SCR optimization algorithm) is tailored to solve the conditions numerically. Through experiments conducted under Facebook, Youtube and Twitter sub-networks, the algorithm's performance has been evaluated by inspecting its convergence speed and payoff compared with randomized profiles. Consequently, the resulting strategies are verified to exhibit superior performance in dealing with cyberbullying spreading. [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]

• 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 the proposed IVIF-BWM, we build weight-determining models concerning expert's attitudes. • A bi-objective programming model is proposed to derive experts' dynamic weights. • Develop an IVIF-DBWM to determine the global weights of all criteria. • IVIF-SPA is proposed to evaluate the overall resumption risk of each alternative. Currently, China has achieved a remarkable achievement on the containment of COVID-19, which creates a favorable condition for the gradual resumption of normal life. However, COVID-19 infections continue to rise in many nations and some sporadic cases occur from time to time in China, which still poses some risks to the resumption. Hence, it is imperative to develop some reasonable techniques to assess the resumption risk. This paper aims to investigate an integrated interval-valued intuitionistic fuzzy (IVIF) technique to adroitly assess the resumption risk based on DEMATEL (decision making trial and evaluation laboratory), BWM (best-worst method) and SPA (set pair analysis). This integrated technique is called IVIF-DBWM-SPA, where the IVIF-DBWM (combined by the IVIF-DEMATEL and IVIF-BWM) is used to determine the global criteria weights and the IVIF-SPA is employed to generate the ranking order of the alternatives. The IVIF-DEMATEL and IVIF-BWM are used to determine the weights of dimensions and the weights of criteria under each dimension, respectively. In this IVIF-BWM, two bi-objective programming models are constructed by regarding experts' pessimistic and optimistic attitudes, respectively. Combined experts' intrapersonal and interpersonal uncertainties simultaneously, a bi-objective programming model is proposed to derive the dynamic weights of experts. Based on the determined weights of experts and criteria, an IVIF-SPA is developed to assess the risk levels of all alternatives. The validity of the proposed technique is demonstrated with a real case of college resumption risk assessment amid COVID-19. Some sensitivity and comparison analyses are provided to show the merits of the proposed technique. [ABSTRACT FROM AUTHOR]

Complex evidence theory, as a generation model of the Dempster-Shafer evidence theory, has the ability to express uncertainty and perform uncertainty reasoning. One of the key issues in complex evidence theory is the complex basic belief assignment (CBBA) generation method. But, how to model uncertainty information in complex evidence theory is still an open issue. In this paper, therefore, we propose a CBBA generation method by taking advantage of the triangular fuzzy number. Moreover, an algorithm for decision making is devised based on the proposed CBBA generation method. Finally, the decision making algorithm is applied in classification to verify its effectiveness. In summary, the proposed method can handle uncertainty modeling and reasoning both in the real number domain and the complex number domain, which provides a promising way in decision making theory. [ABSTRACT FROM AUTHOR]

A recent article by Liu et al. [8] devised measurement models to calculate additive consistency indices and weak transitivity indices for fuzzy preference relations (FPRs) with additive reciprocity breaking (ARB), and developed some decision models, such as the equivalency between FPRs with ARB and inconsistent FPRs with additive reciprocity, the optimization based weak transitivity improving model and priority vector derivation models. This paper utilizes six numerical illustrations to show that the measurement models are technically incorrect and sometimes the decision models are invalid or create contradictory results. New frameworks are proposed to define and measure additive consistency and weak transitivity for FPRs with ARB. Computational formulas are brought forward to acquire interval-valued or intuitionistic fuzzy priority vectors from additively consistent FPRs with ARB, and a linear programming model is built to ascertain interval-valued or intuitionistic fuzzy priority vectors from inconsistent FPRs with ARB. [ABSTRACT FROM AUTHOR]

Multistage group decision problems are characterized by a changeable decision-making environment and a complex group consensus process, which make it difficult to obtain decision-making results. However, few methods have considered the phenomenon of expert state transition between manageable subgroups in multistage problems. In this paper, we propose a multistage decision-making framework considering quantum-guided expert transition based on normal cloud models. First, a minimum cost consensus model considering individual compromise intervals and the cost function is established based on the normal cloud models to obtain consensual subgroup opinions. Second, an attribute weight optimization model is established based on adjustment satisfaction and fairness satisfaction to aggregate the subgroups. Third, we define the satisfaction determination method of experts in the transition process and then apply the quantum framework to update their state in the next stage. Finally, the feasibility and applicability of the proposed method are illustrated via a power grid emergency evaluation example by conducting analyses and comparisons of the decision results. [ABSTRACT FROM AUTHOR]

• The notion of heterogeneous diversified attribute multi-decision systems is presented. • A composite binary relation is defined based on attribute semantics. • Four kinds of variable precision multi-decision multi-granulation rough sets are established. • The established models are applied to medical diagnosis. • The feasibility, effectiveness, and superiority of the established models are verified. Rough set theory has become an effective tool to address uncertain decision-making problems. Nevertheless, existing rough set-based decision-making methods cannot effectively deal with the management decision-making problems with heterogeneity, multi-decision, and diversified attributes simultaneously. Given this, the purpose of this paper is to explore an effective classification solution for solving decision-making problems with the above-described characteristics from the perspective of granular computing. First, we present the notion of heterogeneous diversified attribute multi-decision systems. Because attribute semantics is crucial to multi-attribute decision analysis, we then divide an attribute set into nine subsets according to attribute semantics. Further, a composite binary relation that fits the realistic attribute features is constructed. Subsequently, considering different decision scenarios, we establish four kinds of variable precision multi-decision multi-granulation rough set models. Meanwhile, the related properties and relationships of these models are explored. We find that the established models are extensions of the existing classical rough sets. In the end, we apply the established models to an illustrative example of medical diagnosis. The results of the case and comparative analyses demonstrate the models' feasibility, effectiveness, and superiority. As a result, our work provides a kind of new decision thinking with reasonable semantic analysis for solving complex management decision-making problems in reality. [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]

• The new landscape in the longitudinal research of type-2 fuzzy sets (T2FS) domain are presented. • The multi-criteria decision making has gradually developed into moto theme. • The knowledge diffusion trajectory and thematic evolution of T2FS domain are presented. • The application of T2FSs in decision-making may the possible development directions. Nowadays, more scholars and practitioners are committed to improving and applying type-2 fuzzy sets (T2FSs) in various domains because of the stronger ability to handle the uncertainty of fuzzy complex systems. To explore the status and internal laws of development of this field, this paper presents the development overview based on the bibliometric analysis, then the dynamic evolution of main topics and the knowledge diffusion trajectory are also displayed on the basis of the strategy diagram and main path analysis (MPA). From 1997 to 2019, 1749 documents are retrieved from Web of Science (WoS) repository for the analysis. The results show that there are four stable collaborative communities existing in the countries/regions' collaborative network and the collaboration is affected by geographical factors to some degree. Three main evolution paths of hot topics are also presented in this paper and the multi-criteria decision-making (MCDM) has gradually developed into the moto theme. Furthermore, articles appearing on the main path mainly focus on the research of basic concept and framework, self-optimization and applications in various domains of T2FSs. In general, this paper provides a new landscape in the longitudinal research based on the development overview, thematic evolution and the knowledge diffusion trajectory. [ABSTRACT FROM AUTHOR]

Multi-attribute decision making (MADM) refers to a decision problem of choosing the best alternative or carrying out the ranking of alternatives under multiple attributes, and it is a key component of modern decision sciences. Three-way decisions (3WD) can effectively address MADM problems by reducing decision risks compared with traditional two-way decisions (2WD), and a decision model based on probabilistic dominance relations is presented in this paper. Particularly, we put forward a kind of 3WD-based MADM (3WD-MADM) with probabilistic dominance relations, where the two state sets are developed by virtue of probabilistic dominance classes. Afterwards, the independent innovation ability of high-tech enterprises is evaluated by using the proposed new method. At last, the newly proposed 3WD-MADM model in this paper is verified from different perspectives by comparative and experimental analyses. [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]

• New methodology to build predictive decision support models for campaign targeting. • Integration of statistical and economic objectives to improve business performance. • Comprehensive empirical analysis using 25 real-world marketing data sets. • Substantial improvements over challenging benchmarks in accuracy and profitability. Marketing messages are most effective if they reach the right customers. Deciding which customers to contact is an important task in campaign planning. The paper focuses on empirical targeting models. We argue that common practices to develop such models do not account sufficiently for business goals. To remedy this, we propose profit-conscious ensemble selection, a modeling framework that integrates statistical learning principles and business objectives in the form of campaign profit maximization. Studying the interplay between data-driven learning methods and their business value in real-world application contexts, the paper contributes to the emerging field of profit analytics and provides original insights how to implement profit analytics in marketing. The paper also estimates the degree to which profit-concious modeling adds to the bottom line. The results of a comprehensive empirical study confirm the business value of the proposed ensemble learning framework in that it recommends substantially more profitable target groups than several benchmarks. [ABSTRACT FROM AUTHOR]

Today's world needs new methods to deal with and analyze the ever-increasingly generated data streams. Two of the most challenging aspects of data streams are (i) concept drift, i.e. evolution of data stream over time, which requires the ability to make timely decisions against the high speed of receiving new data; (ii) limited memory storage and the impracticality of using memory due to the large amount of data. Clustering is one of the common methods to process data streams. In this paper, we propose a novel, fully-online, density-based method for clustering evolving data streams. In recent years, a number of methods have been proposed, which also have the ability to cluster data streams. The main limitation of these methods is the use of parameters based on knowledge-expert. This work is among the first works to address this issue. Constant False Clustering Probability, CFCP, has tried to choose the algorithm's parameters based on Statistics. The proposed method has also the ability to identify clusters with arbitrary shapes. It is robust to noise and offers high accuracy and efficiency in both low and high dimensions. In this method, we determine the value of the parameters by using statistical theories and do not require more information, taking advantage of expert-knowledge. The presented experimental results show that the method performs data clustering at high speeds without reducing the quality compared to the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• Obtaining the optimal discounting weights of BPAs is proposed using the BWM method by considering consistency ratio. • A new way to determine the best and worst BPA is presented based on the distance of evidences. • Partially decrease the computing cost of fusion system by decreasing the number of comparisons using the BWM method. • More reasonable results in decision making are obtained by the proposed methodology. Dempster-Shafer evidence theory (DST) could show its advantages during the process of data fusion. In DST, the determination of the weight of evidence in conflict management is attracting growing interest. Limited work has been done based on the discount model, the consistency of the weight is still virgin and may become a fascinating question. In this paper, a novel strategy about how to ascertain the optimal weight of basic probability assignment (BPA) using BWM method is proposed, which provides a promising way to ascertain the best BPA and the worst BPA. Then, a consistency ratio is utilized for BPA, which has the ability of inspecting the reliability of the comparisons and producing more rational results. Some numerical experiments and application examples are used to illustrate the effectiveness and practicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

• Investigating the effect of noises in multi-agent reinforcement learning. • Leveraging interactive interface to generate consensuses. • Training collaboration policy and behavior policy through a temporal abstraction mechanism. • Improving sampling by calculating sequence priority. Multi-agent reinforcement learning algorithms scarcely attend to noisy environments, in which agents are inhibited from achieving optimal policy training and making correct decisions. This work investigates the effect of noises in multi-agent environments and proposes a multi-agent actor-critic with collaboration (MACC) model. The model uses lightweight communication to overcome the interference from noises. There are two policies for each agent in MACC: collaboration policy and behavior policy. The behavior of an agent not only depends on its own state but also be influenced by each other agent through a scalar, collaboration value. The collaboration value is generated by the collaboration policy for each individual agent, and it ensures a succinct consensus about the environment. This paper elaborates on the training of the collaboration policy and specifies how it coordinates the behavior policy in a manner of temporal abstraction mechanism, while the observation sequence is considered for more accurate perception. Several experiments on multi-agent collaboration simulation platforms demonstrate that the MACC performs better than baselines in noisy environments, especially in partially observable environments. [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]

Decision models based on value function can help learn the preferences of decision makers using historical data. However, inconsistency of the preferences learned from data with the real preferences of decision makers may occur. Suppose decision data or scenarios in the target domain are insufficient to guarantee the consistency of learning preferences, and there exists one similar source domain with sufficient effective data. Then, knowledge from the source domain can help learn preferences in the target domain. Following this idea, this paper proposes a cross-domain decision making method using a parameter transfer strategy with homogeneous and heterogeneous criteria. A decision model based on the value function is constructed using a generalized additive model to ensure the interpretability of the model. The marginal value functions are adjusted using Sturm's theorem to keep the monotonicity of the learned marginal value functions on the criteria. Then, the parameter transfer strategy is adopted to transfer the obtained value functions to help learn the real preferences of the decision maker for the decision problem where preferences in historical data may not be consistent. The effectiveness of the proposed method is validated by solving the problem of diagnosing breast lesions in a hospital. [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]

Decision models based on value function can help learn the preferences of decision makers using historical data. However, inconsistency of the preferences learned from data with the real preferences of decision makers may occur. Suppose decision data or scenarios in the target domain are insufficient to guarantee the consistency of learning preferences, and there exists one similar source domain with sufficient effective data. Then, knowledge from the source domain can help learn preferences in the target domain. Following this idea, this paper proposes a cross-domain decision making method using a parameter transfer strategy with homogeneous and heterogeneous criteria. A decision model based on the value function is constructed using a generalized additive model to ensure the interpretability of the model. The marginal value functions are adjusted using Sturm's theorem to keep the monotonicity of the learned marginal value functions on the criteria. Then, the parameter transfer strategy is adopted to transfer the obtained value functions to help learn the real preferences of the decision maker for the decision problem where preferences in historical data may not be consistent. The effectiveness of the proposed method is validated by solving the problem of diagnosing breast lesions in a hospital. [ABSTRACT FROM AUTHOR]

Given a probability distribution, Shannon entropy can be used to measure its corresponding information volume. However, it is still an open issue to calculate the information volume of Z-number. In this paper, the information volume of the Z-number is presented using the proposed transformation of a Z-number into a mass function. In our proposed method, the mass function degenerates into probability distribution under the circumstance that the uncertainty of the Z-restriction is 0. In this case, the information volume degenerates into Shannon entropy. The information volume of a given Z-number increases approximately linearly with the unreliability of its Z-restriction. In addition, the information volume varies with the value of Z-restriction and fuzzy number A. Some illustrative examples are shown to demonstrate the properties of the proposed information volume of Z-number. A new Weighted Multiple Attribute Decision Making (WMADM) method is also proposed to illustrate the practical advantage of the proposed information volume. [ABSTRACT FROM AUTHOR]

• We generalize a two-layer social network model to describe the influence between different individuals and the linkage between their • opinions and actions. • A novel mechanism of manipulating collective opinions and actions is presented. • Detailed conditions for realizing the control of opinion and action are obtained. • We conclude that only manipulating opinion can also significantly alter action, as does the effect of action control on opinion change. This paper investigates a two-layer coevolution model of collective opinions and actions under two different control inputs. First, we introduce two control inputs, opinion regulator and impulsive stimulation, into this model. While changes in opinions tend to be gradual, changes in actions can instantly occur through external stimuli. These two inputs are control methods implemented on opinions and actions, respectively. Next, we conduct a series of investigations on how shifts of the collective opinions and actions are realized under the interventions brought by the control inputs. With only the opinion regulator, we explore conditions of the internal attributes of generic individuals. Assuming only the impulsive stimulation existed, we pay more attention to how to implement the intervention. These results provide valuable analytical references for guidance on public opinions and behaviors. Last, we show the validity of our theoretical results through numerical simulations. [ABSTRACT FROM AUTHOR]

Selecting the appropriate manufacturer is important in customized product development because a poor selection may delay the delivery schedule, increase costs, and even affect product quality. This selection task inherently involves ambiguous and imprecise information from decision-makers. The q-rung orthopair fuzzy (q-ROF) sets theory has been proven as a valuable instrument to model human uncertain expressions. However, the existing q-ROF score functions, an essential tool to rank q-ROF values, have some deficiencies, such as generating counterintuitive solutions and antilogarithm or division by zero problems. Furthermore, little research presented the modified best-worst methods (BWM) under q-ROF environments. Nevertheless, these models only generate crisp weights rather than q-ROF weights, which is against the original intention of the q-ROF BWM. To address these problems, this paper first introduces a novel q-ROF score function for measuring q-ROF values. A new q-ROF-BWM is then presented based on the q-ROF preference relations to determine the fuzzy criteria weights. Subsequently, an improved weighted aggregated sum product assessment (WASPAS) with q-ROF settings is presented. Based on them, an integrated q-ROF-BWM-WASPAS model is introduced to rank manufacturers. Additionally, a case study, sensitivity analysis, and several comparisons are conducted to illustrate and validate the usefulness of the developed model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs to conquer the drawbacks of the existing score functions of IVIFVs. Then, we construct the converted matrix based on the proposed score function of IVIFVs by calculating the score value of each IVIFV in the decision matrix (DM) offered by the decision maker (DMK). Then, we construct the NLP model via the obtained converted matrix and the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute given by the DMK. Then, we solve the NLP model to obtain the optimal weight for each attribute. Then, based on the obtained converted matrix and the obtained optimal weight of each attribute, we calculate the weighted score of each alternative. Finally, the alternatives are ranked on the basis of the obtained weighted scores of the alternatives. The larger the weighted score of an alternative, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. It offers us a very useful approach for MADM in IVIF settings. [ABSTRACT FROM AUTHOR]

• Development of a bi-level Bayesian control scheme for fault detection. • Multivariate hidden Markov model describes the deterioration process. • SMDP approach to formulate the control problem and to optimize the Bayesian policy. • Considerably better fault detection compared with published results. • Development of case studies and demonstration of the improved performance using multivariate data. Due to limitations of sensor techniques and system structures, the internal states of most complex devices are unobservable. Only partial observations can be monitored at discrete time epochs, which poses great challenges for fault detection and prediction. To facilitate the development of advanced approaches, this paper proposes a bi-level Bayesian control scheme for detecting faults of complex devices under partial observations. The deterioration of an operational system is modeled as a hidden three-state multivariate Markov process, in which the parameter estimates are obtained by an expectation maximization (EM) algorithm. Based on the multivariate Markov process, a bi-level Bayesian control scheme is presented to monitor the Bayesian posterior probability of the system in a warning state and uses two levels of sampling frequency to dynamically detect impending failures. The decision variables of the bi-level fault detection scheme are optimized and solved in a semi-Markov decision process (SMDP) framework. The particularity of this work is that two phases of system deterioration are considered into detection scheme design to avoid unnecessary false alarms. Using partially observed multivariate data from discrete monitoring, the proposed approach is validated to be capable of detecting the early fault occurrences. By comparing with other advanced methods, the superiority of the proposed model is demonstrated. [ABSTRACT FROM AUTHOR]

Traditional multi-criterion decision-making methods can help decision-makers decide whether to accept or reject an alternative, but they cannot ensure these results fully meet decision-makers' requirements. Three-way decision methods overcome this limitation by dividing alternatives into three regions. However, traditional three-way decision methods rarely considered the reliability of evaluation information and individual regrets under some criteria. Moreover, most weighting methods in three-way decisions ignored the influence of abnormal values. To fill the above gaps, this paper develops a linguistic Z-number-based sorting method combining the three-way decision with the gain and lost dominance score (GLDS) method that reflects individual regrets under some criteria. Firstly, to avoid individual regrets, we introduce the linguistic Z-number-based GLDS sorting (LZ-GLDS-Sort) method, which obtains two states of alternatives that will be used in the three-way decision. Linguistic Z-numbers can express linguistic evaluation and credibility. Two parameters are introduced in the LZ-GLDS-Sorting method to reflect the relative importance of evaluation information and credibility. Then, a three-way decision method is introduced to divide alternatives into three regions, in which the variation-coefficient weighting method is introduced to avoid the effect of abnormal values. Finally, the ecological function zoning as an example is provided to validate the applicability of this model. [ABSTRACT FROM AUTHOR]

The use of artificial intelligence for decision support and automation has shown tremendous potential in many areas. The ability to explain the decisions made by a machine learning algorithm is fundamental to facilitating the widespread use of this type of tool. There are many important real-world problems where the cost of the decisions depends on the characteristics of each example: these are called example-dependent cost (EDC) problems. For this type of classification problem, an appropriate formulation that takes into account the decision costs is fundamental both for the design of the classifier and for the explanation of its decisions. In this paper, we propose COCOA, an explanation method designed for EDC problems based on a Bayesian discriminant. The proposed method can provide counterfactual samples generated by considering decision costs. The COCOA method provides valid and plausible counterfactuals with a high success rate, which can be actionable, diverse, and sparse, achieving a remarkable improvement in terms of cost over five state-of-the-art methods on six real-world datasets. • COCOA provides actionable, plausible, sparse and diverse counterfactuals. • Decision costs are taken into account when generating counterfactuals. • The obtained counterfactuals improve cost savings. • The method is presented for MLPs, but other architectures can be used. [ABSTRACT FROM AUTHOR]

In the face of an emergency, regionally coordinated allocation is an important prerequisite for maintaining the normal order of production and living. Considering the complexity and uncertainty of the emergencies in local governments, this paper establishes a two-stage process for allocating medical resources. In the first stage, cooperative regions with incomplete weights and multidimensional uncertain information ranked via a novel decision-making method. The second stage is an optimal strategy which the optimization model is established to minimize the cost incurred by the local government considering two components of cost. The first stage is the reserve cost for the local government to prepare a certain amount of flexible procurement materials to respond to a public health emergency. The second is the scheduling cost when cooperative regions support medical resources. Theoretically, the optimal allocation of the reserve of different kinds of medical resources is deduced at the lowest cost. Through numerical simulation and sensitivity analysis, we explore the impacts of attribute weights, resource reserve capacity, unit costs, and the number of cooperative regions on the demand for different kinds of medical resources and the total costs incurred by local governments. This study provides a regional coordinated allocation framework and theoretical reference for government departments responding to the emergencies. [ABSTRACT FROM AUTHOR]

• We propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers. • We propose the concepts of fuzzy consistency index and fuzzy consistency ratio. • Four linear programming models are built to get optimal fuzzy weights, respectively. • We apply the proposed fuzzy BWM to deal with multi-criteria decision-making. • It gets a higher consistency than the ones of the existing fuzzy BWM and the BWM. In this paper, we propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers for multi-criteria decision-making (MCDM). Aimed at the Best-to-Others vector and the Others-to-Worst vector in the form of triangular fuzzy numbers, this paper regards consistency equations as fuzzy equations. The derivation of optimal fuzzy weights of criteria is formulated as a fuzzy decision-making problem, where a mathematical programming model is constructed to derive optimal fuzzy weights of criteria to build a normalized triangular fuzzy weight vector. Then, we propose four linear programming models based on the obtained mathematical programming model for the optimistic decision maker, the pessimistic decision maker and the neutral decision maker, respectively. Through a proper selection of the values of tolerance parameters, each of the linear programming models certainly has a unique global optimal solution. Moreover, this paper proposes the concept of fuzzy consistency index and the concept of fuzzy consistency ratio. Several application examples are used to validate the proposed fuzzy BWM. The proposed fuzzy BWM provides us with a very useful way for MCDM in fuzzy environments. [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]

In this paper, a novel approach to the self-organization of hierarchical prototype-based classifiers from data is proposed. The approach recursively partitions the data at multiple levels of granularity into shape-free clusters of different sizes, resembling Voronoi tessellation, and naturally aggregates the resulting cluster medoids into a multi-layered prototype-based structure according to their descriptive abilities. Different from conventional classification models, it is nonparametric and entirely data-driven, and the learned model can offer a high-level of transparency and interpretability thanks to the underlying prototype-based nature. The system identification process underpinning the approach is driven by the aim of separating data samples of different classes into nonoverlapping multi-granular clusters. Its associated decision-making process follows the "nearest prototype" principle and hence, the rationales of the subsequent decisions made can be explicitly explained. Experimental studies based on popular benchmark classification problems, as well as on a practical application to remote sensing image classification, demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Nowadays, with the increasing complexity of decision-making environment, more and more large-scale group decision making (LGDM) problems are faced. Due to the existence of social network relationships among experts, social network analysis (SNA) is proved to be an effective analysis method for LGDM problems. Meanwhile, it is crucial for LGDM issues to determine the weights of decision groups and to lessen the large-scale DMs' dimension, which will affect the result of decision making directly. This study proposes a clustering- and maximum consensus-based resolution framework with linguistic distribution (LD) for social network large-scale group decision making (SNLGDM) problems. In the consensus framework, independent sub-groups can be obtained by the division of large-scale DMs according to trust relationship using the proposed SNA-based trust network clustering model, and the LD assessments are used to represent the preference relation of sub-groups. Following this, by considering three dependable sources: consistency, similarity, and in-centrality degree, this paper devises a maximum consensus-based method, which can generate the sub-groups' comprehensive weight by maximizing the level of consensus between sub-groups and the collective matrix. Meanwhile, the final ranking of alternatives can be obtained based on collective preference relation. Conclusively, the availability and advantage of this research are verified through numerical example, coefficient analysis and comparative analysis. [ABSTRACT FROM AUTHOR]