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• 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, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming methodology, the Euclidean distance between interval-valued intuitionistic fuzzy values (IVIFVs), and the proposed score function of IVIFVs. Firstly, a new score function of IVIFVs is proposed to overcome the shortcomings of the existing score functions of IVIFVs. Then, we construct the score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, a nonlinear programming model is proposed based on the Euclidean distance between IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we solve the proposed nonlinear programming model to obtain the optimal weights of the attributes. Then, the weighted score of each alternative is calculated based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores of the alternatives. The MADM method proposed in this paper can conquer the shortcomings of the existing MADM methods in the environments of IVIFVs. [ABSTRACT FROM AUTHOR]

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

In this paper, the problem of dynamic event-based finite-horizon H ∞ fault estimation is studied for a class of discrete-time complex networks with fading channels. In the communication from sensor to estimator, the channel fading phenomenon is considered, which is a dynamic process and reflects the actual situation. Moreover, the dynamic event-triggered mechanism is implemented to schedule the signal transmissions. This paper plans to design a fault estimator to meet the predetermined H ∞ performance requirements. First, sufficient conditions are established to ensure the existence of the desired H ∞ fault estimator. Then, the gain of the H ∞ fault estimator is derived in terms of the solution to a set of recursive matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of our developed fault estimation approach. [ABSTRACT FROM AUTHOR]

• Design and evaluation of three methods for generation of counterfactual explanations. • Linguistic fuzzy counterfactual explanations embrace imprecise information. • Perceived explanation complexity can be automatically measured from data. • Explanation complexity correlates with informativeness, relevance, and readability. • Human evaluation should focus on explanation issues uncorrelated with complexity. The explanatory capacity of interpretable fuzzy rule-based classifiers is usually limited to offering explanations for the predicted class only. A lack of potentially useful explanations for non-predicted alternatives can be overcome by designing methods for the so-called counterfactual reasoning. Nevertheless, state-of-the-art methods for counterfactual explanation generation require special attention to human evaluation aspects, as the final decision upon the classification under consideration is left for the end user. In this paper, we first introduce novel methods for qualitative and quantitative counterfactual explanation generation. Then, we carry out a comparative analysis of qualitative explanation generation methods operating on (combinations of) linguistic terms as well as a quantitative method suggesting precise changes in feature values. Then, we propose a new metric for assessing the perceived complexity of the generated explanations. Further, we design and carry out two human evaluation experiments to assess the explanatory power of the aforementioned methods. As a major result, we show that the estimated explanation complexity correlates well with the informativeness, relevance, and readability of explanations perceived by the targeted study participants. This fact opens the door to using the new automatic complexity metric for guiding multi-objective evolutionary explainable fuzzy modeling in the near future. [ABSTRACT FROM AUTHOR]

As decision-making problems become increasingly complicated nowadays, a growing number of decision-makers are likely to use probabilistic linguistic term sets (PLTSs) rather than precise numbers. Three-way decision (TWD), as an effective way of dealing with multi-attribute decision-making (MADM) problems, aims to minimize expected losses, and the choice of delayed decisions in the presence of insufficient evaluation information can significantly reduce expected losses. In light of the combination of PLTSs with TWD, a TWD method under PLTSs is put forward in this paper, i.e., the TWD-PLTS method. First, two conversion operators are designed to ensure that both real-valued and linguistic data can be converted to PLTSs. By using the difference in terms of information entropies between linguistic term sets (LTSs) and corresponding PLTSs, attribute weights can be derived. Next, a dominance set is constructed based on the probabilistic linguistic TODIM (PL-TODIM) method, which can in turn calculate conditional probabilities. Then, a relative loss function matrix is constructed with PLTSs, and the TWD-PLTS method is presented in this way. Finally, the TWD-PLTS method is applied to address a realistic case and compare it with other decision-making methods for verifying the feasibility and validity of the presented method. [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 problem is formulated in a general setting investigating pairwise comparisons matrices. • Innovative concepts of consistency, intensity and coherence of FPCMs are introduced. • New algorithm for calculating the priority vector is proposed. • Two illustrating examples of the proposed algorithm are presented and discussed. Applying the Analytic Hierarchy Process (AHP) in a decision making (DM) problem, fuzzy elements are appropriate whenever the decision maker is uncertain about the value of his/her evaluation of the relative importance of the elements in question, i.e., criteria and/or alternatives. The method, often called the fuzzy AHP, is also used when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. In this paper, the DM problem is formulated in a general setting using pairwise comparisons matrices with elements from an Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive, or fuzzy approaches. Here, we propose some desirable properties (consistency, coherency, and intensity) of priority vectors, and derive sufficient conditions for the existence of priority vectors with those properties. In general, the most popular methods for deriving the priority vector – the Eigenvector Method and the Geometric Mean Method – do not always provide priority vectors having these desirable properties. Here, we formulate a new solution algorithm for deriving the priority vector based on a specific optimization problem satisfying the desirable properties under appropriate assumptions. Two illustrating examples of the algorithm are presented and discussed. [ABSTRACT FROM AUTHOR]

Trust relationship is an effective basis for reducing the dimensionality of decision makers (DMs) for group decision making (GDM) problems in the context of social networks, and have received extensive attention in the past few years. However, most existing studies describe the trust relationship only from the single perspective of the interpersonal relationships between DMs, which easily leads to inaccurate decision-making results. In this paper, we propose a dynamic consensus method using a dual-trust relationship-based social network (DTRSN) to solve large group emergency decision-making (LGEDM) problems. First, to more accurately reflect the trust relationship among DMs, a DTRSN based on familiarity-based trust and similarity-based trust is developed, which can comprehensively model the interpersonal relationships and opinion similarity between DMs simultaneously. Next, a DTRSN-based clustering method that considers dual-trust relationships is introduced to divide the large-group DMs into several clusters. Subsequently, to improve the efficiency of LGEDM, the exit-delegation mechanism is modified and introduced into our study, which can speed up consensus by excluding some subgroups whose opinions differ greatly from other subgroups and reserve their influence. Subsequently, a dynamic consensus method based on the modified exit-delegation mechanism is proposed to help DMs reach an agreement quickly. Finally, a case study regarding emergency alternative selection to deal with heavy rainstorms in Zhengzhou, China, is conducted to verify the efficiency of our study, and several comparison and simulation analyses are also conducted to demonstrate the feasibility and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a distributed algorithm based on the alternating direction method of multipliers is proposed to solve an unconstrained consensus optimization problem. The network topology among the agents is assumed to be connected and self-loops of each agent are considered. This algorithm takes less time than sequential algorithms because the optimization variables of the agents can be updated synchronously. In addition, it is shown that the algorithm is actually a Jacobi-proximal ADMM algorithm and the requirement of the proximal matrix is relaxed. A convergence analysis of the algorithm is provided, and its convergence rate is found to be O (1 / k). Finally, the characteristics of the proposed algorithm are illustrated by numerical experiments, and comparisons are made with other ADMM algorithms in solving a least-squares problem. [ABSTRACT FROM AUTHOR]

• We proposed a social influence diffusion (SID) module to model the social networks by graph neural networks to enhance the representation learning of individual users. • We proposed an interest evolution learning (IEL) module to learn users' dynamic and evolving preferences. This is the first group recommender system that learns users' interest evolution to the best of our knowledge. • A novel group recommendation framework, called DASIIE, is designed to dynamically aggregate SID and IEL through a two-way attention mechanism (TWA), considering both group members' roles and expertise simultaneously. • We conduct extensive experiments on two real-world datasets, and the results show the better performance of our model compared to the state-of-the-art baseline models. The rapid development of social networks has made group activities part of people's daily lives. It is in high demand to recommend items for a group of users that meet their common preferences, known as group recommendations (GRs). Recently, some studies have focused on GRs and adopted deep neural networks to model the process of group decision-making. These approaches can be further divided into two phases: the individual preference learning phase and the group decision phase, both of which face several challenges although recent research has some achievements. In the first individual preference learning phase, the challenges are how to effectively incorporate social networks to overcome the sparsity issue of user interaction data and how to capture the dynamic evolutions of users' preferences over time. The challenge for the second group decision phase is how to adjust group members' preference weights dynamically since each group member may carry different deciding power in different situations, depending on their roles in the group and domain expertise. In this paper, to address these challenges, we propose a novel group recommendation framework that d ynamically a ggregates the s ocial i nfluence diffusion and i nterest e volution (DASIIE). Specifically, DASIIE is composed of three main modules: 1) a social influence diffusion (SID) module which stacks multi-layer graph neural networks to simulate the influence propagation in social networks; 2) an interest evolution learning (IEL) component which learns individuals' interest evolutions over time from their behavior sequences; 3) a two-way attention (TWA) module which learns group members' role weights and expertise weights during the decision-making process simultaneously. We conduct extensive experiments on two real-world datasets, and the results show the better performance of our model compared to the state-of-the-art baseline models. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fixed-time problem for a class of nonlinear systems with actuator faults, unknown nonlinear functions as well as limited communication, where an event-triggered mechanism is considered to decrease the computing and communication burthen. A smooth function and an adaptive method are employed to solve the difficulty of the event-triggered mechanism and actuator faults that exist simultaneously in the control scheme design process. Based on the adding one power integrator technique and the backstepping method, an event-triggered adaptive fixed-time fuzzy fault-tolerant control strategy is designed, in which the unknown time-varying actuator faults are allowed. It is proved that the practical fixed-time stability of the resulting closed-loop systems can be ensured under the proposed event-triggered adaptive fixed-time fuzzy control strategy and no Zeno phenomenon occurs. Finally, the effectiveness of the proposed strategy is shown by illustrative examples. [ABSTRACT FROM AUTHOR]

• Propose a dynamic weight determination model with PLTSs. • Propose a comprehensive hierarchical clustering method with PLTSs. • Propose the extended power aggregation operators with PLTSs. • Propose a dynamic decision-making method based on PROMETHEE. • Propose a DLMAGDM method for PLTSs and verify its validity. Dynamic large-scale multiple attribute group decision making (DLMAGDM) is ubiquitous in many areas of the real world. It is composed of large numbers of decision makers, several continuous periods, alternative set and attribute set changed with time. Given the characteristics implicited in decision-making elements and the advantages of probabilistic linguistic term sets (PLTSs) in modelling uncertainty and complexity of decision makers' subjective opinions, this paper constructs a probabilistic linguistic DLMAGDM method. First of all, a dynamic weight determination model based on trust relationships and evidential conflicts between decision makers is proposed to obtain current dynamic weights of decision makers. Then, a comprehensive hierarchical clustering method that divides large numbers of decision makers into several subgroups is constructed based on three clustering constrains. Moreover, some probabilistic linguistic extended evidential power aggregation operators are proposed to aggregate PLTSs. These operators can appropriately handle the extreme PLTSs and fully consider the role of incomplete probabilistic distributions in PLTSs. In addition, a dynamic decision-making method based on PROMETHEE is developed to determine the final priority order of alternatives according to preferences between alternatives over several periods. Lastly, a case study for supply chain finance risk assessment for several firms in Chinese household appliance industry is utilized to illustrate the practicality and effectiveness of the probabilistic linguistic DLMAGDM method. Furthermore, the comparative analysis with some other existing methods and the sensitivity analysis are made to verify its advantages. [ABSTRACT FROM AUTHOR]

Multiobjective optimization problems (MOPs) are the optimization problem with multiple conflicting objectives. Generally, an optimization algorithm can find a large number of optimal solutions for MOPs, which easily overwhelm decision makers (DMs) and make it difficult for decision-making. Preference-based evolutionary multiobjective optimization (EMO) aims to find the partial optima in the regions preferred by the DM. Although it narrows the scope of the optimal solutions, it usually still returns a population of optimal solutions (typically 100 or larger in EMO) with a small distance between adjacent optima. Top-K, which is a well-established research subject in many fields to find the best K solutions, may be a direction to reduce the number of optimal solutions. In this paper, first, we introduce the top-K notion into preference-based EMO and propose the top-K model to obtain the best K individuals of multiobjective optimization problems (MOPs). Then, with the top-K model, we propose NSGA-II-TopK and SPEA2-TopK to search for the top-K preferred solutions for preference-based continuous and combinatorial MOPs, respectively. Finally, the proposed algorithms with several representative preference-based EMO algorithms are compared in different preference situations for MOPs. Experimental results show the proposed algorithms have strong performances against the compared algorithms. [ABSTRACT FROM AUTHOR]

In order to improve diversity services and boost diagnostic accuracy, more and more emerging technologies are applied to assist medical treatment. The medical emerging technology service provider selection is a noteworthy problem for hospital risk management. Thus, we develop a heterogeneous group AHPSort (GAHPsort) to provide the recommendation for hospitals and explore the consensus of GAHPSort to avoid the conflict. Specifically, by considering the difference of decision makers' evaluation standard, we design a group sorting consensus of GAHPSort from the angle of sorting result via pairwise comparison of decision makers. Meanwhile, we construct asymmetrical classification error cost function to describe classification error costs of different decision makers' preferences. Further, a minimum adjustment model based on sorting consensus index with classification error is established. Considering that the results of technology providers in the same class are close, this paper develops the distinction between the inter-class and the between-class distances to depict the weak opinion consensus and extend the minimum adjustment model. Besides, in order to avoid the unexplainable evaluation, we design the semantic tolerance and further improve the minimum adjustment model. Finally, we utilize two cases to validate our proposed method via comparison analysis. [ABSTRACT FROM AUTHOR]

As the field of intelligent decision making continues to evolve, research on multi-attribute group decision making (MAGDM) is advancing at a steady pace. Nevertheless, existing research seldom addresses the aggregated solution of self-confidence and consensus in decision making information with diverse possibilities, despite its relevance to uncertain decision making environments. Consequently, this paper presents an approach to self-confidence and consensus-based group decision making. Firstly, the method provides a way for transforming three-parameter interval grey numbers into randomized decision making information. This establishes the foundation for the computation of possibility decision making information for uncertain decisions. Then, a method based on self-confidence and consensus is developed to determine the decision makers (DMs) weights, which is derived from the randomized decision making information. Next, a novel self-confidence index (SCI) for computing self-confidence and a new group consensus index (GCI) for computing consensus are demonstrated, and a reliability index (REI) method for randomized decision making information is given, which is used to identify high self-confidence and high consensus decision making information to improve the quality of decisions. Subsequently, a possibility ranking method is constructed based on pairwise comparisons of alternatives, taking into account density preferences, in order to obtain final possibility ranking conclusions. Finally, an illustrative example is provided to illustrate the concrete implementation process of the methods employed in this research. The efficacy of the proposed method is also demonstrated through a comparative analysis with the other methods. [ABSTRACT FROM AUTHOR]

Pedrycz shadowed sets are three-way approximations of fuzzy sets by transforming the infinite levels of fuzzy set membership grades in the unit interval [ 0 , 1 ] into three levels. The three levels represent qualitatively the sets of the white, grey, and black members of a shadowed set. In this paper, we generalize the notion of shadowed sets to the case of L-fuzzy sets by making three new contributions. First, we consider two representations of a shadowed set. One is a three-valued L-fuzzy set and the other is three pairwise disjoint sets. Second, we introduce two methods for constructing a shadowed set. One divides a finite lattice based on the notion of a pair of a set of designated core membership grades and a set of designated null membership grades. The other uses a pair of threshold sets, which generalizes the method that uses a pair of thresholds. We study formal properties of the two methods and show that they are equivalent. Finally, based on a distance function on a lattice, we present a simple method to build the sets of designated core and null membership grades. [ABSTRACT FROM AUTHOR]

The multilevel nature of social networks and the multiple identities of decision makers (DMs) have led to the co-existence of overlapping and non-overlapping subgroups in social network group decision-making. This paper focuses on three issues in an intuitionistic fuzzy environment in this situation. Firstly, some unknown trust relationships exist between DMs belonging to different subgroups. Secondly, interactions between DMs and subgroups affect the final consensus result. Thirdly, opinions of DMs belonging to multiple subgroups simultaneously (i.e., key DMs) affect the opinions of these overlapping subgroups to varying degrees. To address the first issue, a trust propagation operator considering trust influence and trust decay is proposed to estimate the trust values between DMs belonging to different subgroups. To solve the second issue, we describe interactions within and between subgroups by factors such as trust value and overlapping level. To manage the third issue, we introduce the Choquet integral to gather opinions and construct an interactive behavior-driven hierarchical consensus model to obtain the group opinion for the non-additive interactions between DMs and subgroups. Finally, the effectiveness and applicability of the method are verified through illustrative examples and comparisons. • The missing indirect trust values between DMs in different subgroups are estimated. • The indirect trust values take into account trust influence and trust decay. • The interaction behavior is considered in the consensus reaching process. • A hierarchical consensus model is constructed to obtain the final group solution. [ABSTRACT FROM AUTHOR]

• Propose a rough integrated asymmetric cloud (RIAC) model. • Put forward a new AC score function, distance, and similarity. • Expert weights are measured from the perspective of cooperative game. • Establish a trust propagation model through the social network and RIAC. • Comparison analysis is performed to validate the superiority of our approach. Large group decision-making often contains strong uncertainty and randomness due to the complexity of decision-making problems. Moreover, existing methods about large group decision-making usually assume that the relationships among decision-makers are mutually independent, which will neglect the relevance of decision information to some extent. To address these limitations, this paper proposes a novel rough integrated asymmetric cloud model to tackle large group decision-making under multi-granularity linguistic environment. This model can not only flexibly portray decision-makers' preferences, but also objectively handle the uncertainty and randomness in large group decision-making through the relevance of preferences. Firstly, a trust propagation model based on rough integrated asymmetric cloud is raised to consider the impact of uncertainty and randomness in the trust propagation on large group decision-making. Secondly, a new asymmetric cloud distance and similarity are proposed to overcome some defects of existing methods. Thirdly, a decision-maker weight calculation method based on the Shapley function is advanced to enhance the decision-making reasonableness. Next, an investment problem is solved by the proposed method. Finally, the effectiveness and superiority of the proposed method are demonstrated by the sensitivity and comparison analyses. [ABSTRACT FROM AUTHOR]

This paper introduces a relative utility function-based consensus method for three-way group decision (TWGD) in a social network scenario where overlapping subgroups and non-overlapping subgroups co-exist. Firstly, we construct a three-way decision (TWD) model rooted in utility theory, which proposes a novel objective calculation method for the relative utility functions based on evaluation values. The relative utility matrices of decision makers (DMs) are derived on this basis. Secondly, a utility and trust-driven overlapping clustering algorithm is designed to maximize the overall trust level and the difference between subgroup clustering centers, aiming to divide the group into several manageable subgroups. In addition, we identify contrarian DMs, triggering a delegation-exit mechanism, and determine the weights of subgroups and DMs. Thirdly, a three-way group consensus decision model is formulated to provide targeted adjustment strategies for different types of DMs. To improve group consensus, we address the influence of key DMs on the opinions of overlapping subgroups with a minimum adjustment consensus model. Finally, we demonstrate the feasibility and scientificity of the proposed method through the illustrative example, sensitivity analysis, and comparative analysis. • The utility-three-way decision model is further developed for IFVs. • An objective calculation method for determining the relative utility is proposed. • Consider trust and utility information in the overlapping clustering algorithm. • The TWGD consensus model is established considering decision makers' types. [ABSTRACT FROM AUTHOR]

Multi-task optimization problems in the real world often contain constraints. When dealing with these problems, it is necessary to consider multiple tasks and their respective constraints simultaneously. However, most of existing research on multi-task optimization neglects the influence of constraints, which leads to slow convergence speed and susceptibility to local optima. To address the aforementioned issues, this paper proposes a reinforcement learning assisted constrained multi-task evolutionary algorithm. First, to meet the different requirements of different tasks and constraints, an adaptive operator selection strategy based on reinforcement learning is proposed. Second, to enhance population diversity, a multi-population method with different constraint handling techniques is introduced. This method assigns two independent populations to each task. The main population aims to find feasible solutions, while the auxiliary population focuses on exploring the entire search space. Finally, considering the individual differences between tasks, a dimension-based knowledge transfer is employed to facilitate positive information exchange. Compared with other state-of-the-art constrained evolutionary algorithms, the experimental results on constrained multi-task benchmark suite demonstrate the superiority of the proposed algorithm. The source code can be obtained from https://github.com/yufeiyng/RL-CMTEA. • A reinforcement learning-based evolutionary algorithm designed for constrained multi-task optimization. • A multi-population method is employed to facilitate populations traversal through infeasible regions. • An adaptive operator selection strategy based on Q-Learning with upper confidence bound. • An dimension-based knowledge transfer is employed for constrained multi-task optimization. • Comprehensive experiments confirming the effectiveness and superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Related to many applications in different fields, such as game theory, information fusion, data mining, and decision making, we have introduced in one our previous paper so called generalized Choquet-type integral for a real-valued function concerning a set-function and a σ -additive measure. The present study further generalizes the generalized Choquet-type integral in terms of a double set-function Choquet integral for a real-valued function based on a set-function and fuzzy measure. Several of its properties and convergence theorems are obtained, and a novel type of Jensen's inequality is proved. The stability of the proposed system formed by a double set-function Choquet integral concerning multiple inputs and one output is indicated. An effective application in decision making is shown through numerical examples. [ABSTRACT FROM AUTHOR]

As the generalization of fuzzy covering, fuzzy β covering can effectively deal with uncertain information in hybrid data. Swarm intelligence algorithm has unique advantages in feature selection. This paper proposes a novel cooperative swarm intelligence feature selection method for hybrid data based on fuzzy β covering and fuzzy self-information. First, the parameterized fuzzy β neighborhood and fuzzy decision in a fuzzy β covering decision information system are defined, and the lower and upper fuzzy approximations are further studied. Fuzzy rough set model exclusively focuses on the information derived from the lower fuzzy approximation within a decision. In actual circumstances, the uncertainty of fuzzy information is linked to not only the lower fuzzy approximation but also the upper fuzzy approximation. Then, by incorporating the lower and upper fuzzy approximations of a decision, fuzzy self-information and relative fuzzy self-information are introduced as two evaluation indicators of feature selection. Next, a forward feature selection algorithm based on heuristic search strategy is designed by means of these two evaluation indicators. Moreover, in order to effectively explore feature subsets to a greater extent, a cooperative swarm intelligent feature selection algorithm based on random search strategy is also designed by combining particle swarm optimization algorithm and cuckoo search algorithm. Finally, an array of experiments is executed to compare two designed algorithms with five other existing feature selection algorithms. Experimental results show that these two designed algorithms achieve a high feature selection rate while improving the classification accuracy of the raw data. [ABSTRACT FROM AUTHOR]

• Criteria system construction for selecting GRID suppliers. • Introduction of novel fuzzy sets (SVZs, SVZPRs) combining Z-numbers and CST. • Improved efficiency of S-BWM through SVZPR extension. • Development of TOPSIS with SVZs combining TOPSIS and CST. • Enhancement of decision reliability through PageRank integration in SMCDM. Firms need a reliable decision-making framework to select suppliers who are Green, Resilient, and embrace Inclusive Development (GRID). However, GRID supplier selection is challenged by events that are uncertain and often dependent. Such events affect supplier rankings in a fuzzy decision environment. This paper builds a GRID-based criteria system and applies an enhanced Best Worst Method (BWM) and Technique for Order Preferencing using the Similarity to the Ideal Solution (TOPSIS), with Scenario-Varying Z-numbers (SVZs) and reversed PageRank. The decision criteria are extracted from the literature and confirmed by expert judgement. The SVZs and SVZ Preference Relations (SVZPRs) are developed by combining the Concept of Stratification Theory (CST) with Z-numbers, to reflect the impact of Dependent Uncertain Events (DUEs). Reverse PageRank is then used to find the occurrence probability of the scenarios due to DUEs. BWM is applied in an SVZPR environment to obtain the weights of the decision criteria. TOPSIS, incorporating SVZs, is used to rank the suppliers. An example is used to highlight the enhanced BWM-TOPSIS, to find the priority ranking of the GRID weights. Comparative and sensitivity analyses are conducted to validate the proposed method. [ABSTRACT FROM AUTHOR]

In addressing complex and dynamic meteorological disaster decision-making environment, the traditional multi-attribute group decision-making domain model is often unable to effectively deal with the correlation between attributes and the mutual influence of group opinions. To overcome this challenge, this paper proposes a novel quantum framework for group decision-making, which is used to deal with the emergency situation of meteorological disaster. The model initially characterizes attribute correlations using 2-additive Choquet integrals and employs Dempster-Shafer evidence theory to both integrate information and ascertain attribute weights, and decision makers' weights are calculated based on grey relative correlation. On this basis, a quantum-like Bayesian network is developed to capture the interference among decision-makers' opinions. The alternatives are ranked by quantum probabilities computed based on Bayesian principle. Finally, a case study on meteorological disaster emergency scenario assessment is conducted to validate the proposed model's effectiveness and superiority. Additionally, its stability and practicality are confirmed through sensitivity analysis and comparative analysis. • Propose an innovative multi-attribute quantum group decision-making model, reflecting the mutual influence of group opinions. • Adopt a 2-additive Choquet integral based on Mobius transformation to handle the correlation between attributes. • Apply grey relative correlation analysis to determine decision makers' weights. • Employ D-S evidence theory to reconcile conflicting evidence to determine attributes' wrights. [ABSTRACT FROM AUTHOR]

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

Consensus building is crucial in multi-criteria group decision making (MCGDM) because a consensual decision outcome is beneficial for implementing the result. However, expert credibility and its dynamic variation are rarely considered in the consensus reaching process (CRP) for MCGDM problems. In reality, experts are not completely reliable, and their credibility changes dynamically during the CRP. Therefore, this paper proposes a novel CRP method based on dynamic expert credibility for GDM under Dempster-Shafer theory (DST). First, expert credibility is defined by measuring the extrinsic discrepancy and intrinsic ambiguity of decision information to quantify experts' abilities to provide high-quality evaluations. Then, a novel consensus measure is proposed based on the inverse-square law to check whether the current consensus level satisfies the designated threshold. If not, a new feedback mechanism considering dynamic expert credibility is activated to promote group consensus. Furthermore, the attribute weights are comprehensively determined from both objective and subjective perspectives. Finally, an illustrative example and comparative analysis are presented to validate the proposed method. [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]

Fusion functions and their most important subclass, aggregation functions, have been successfully applied in fuzzy modeling. However, there are practical problems, such as classification via Convolutional Neural Networks (CNNs), where the data to be aggregated are not modeling membership degrees in the unit interval. In this scenario, systems could benefit from the application of operators defined in domains different from [ 0 , 1 ] , although, presenting similar behavior of some aggregation functions whose subclasses are currently defined only in the fuzzy context (e.g., overlap functions and t-norms). So, the main objective of this paper is to present a general framework to characterize classes of fusion functions with floating domains, called (a , b) -fusion functions, defined on any closed real interval [ a , b ] , based on classes of core fusion functions defined on [ 0 , 1 ]. The fundamental aspect of this framework is that the properties of a core fusion function are preserved in the context of the analogous (a , b) -fusion function. Construction methods are presented, and some properties are studied. We also introduce a framework to define fusion functions in which the inputs come from an interval [ a , b ] but the output is mapped on a possibly different interval [ c , d ]. Finally, we present an illustrative example in image classification via CNNs. [ABSTRACT FROM AUTHOR]

The 6-DOF attitude-orbit fast synchronous control problem in the space circumnavigation mission is investigated in this paper with dynamics coupling, uncertainties and disturbances, input constraints, and rough dynamical information feedbacks. The orbital-information-based desired angular acceleration information is dynamically compensated via a set of hierarchical fuzzy systems to avoid the derivation operation of orbital states amplifying measurement noise. Since the adaptive laws for updating fuzzy weights are developed based on hyperbolic tangent function, estimation results are updated slowly, even if the initial tracking errors are large. A novel nonsingular practical terminal sliding-mode (PTSM) reduced-order system is proposed for drive tracking errors fast converge with high precision. Benefiting from the absence of information coupling in the derivative of the PTSM function, an observation-based super-twisting algorithm (STA) is employed to establish the PTSM manifold with weakened chattering. Adaptive laws estimate the maximum uncertainty, and an auxiliary system compensates for the input constraints. Simulation results verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

• A consensus model based on endo-confidence is constructed. • Double hierarchical clustering is introduced in the consensus reaching process. Firstly, the experts are classified according to their evaluations (the numerical evaluations given by experts) as the first hierarchical cluster, and then according to their endo-confidence levels in each first hierarchical cluster as the subcluster. • Three types of experts who need to adjust their evaluations are defined. Furthermore, an automatic adjustment mechanism considering endo-confidence levels is given. With the development of novel technological and societal paradigms, consensus in multi-attribute large-scale group decision making is of great significance. The confidence derived by evaluation is considered in this paper and it is named as endo-confidence. Then, a novel adaptive consensus model to manage endo-confident behavior is proposed. First, the experts are classified by their evaluations as the first cluster, and then by their endo-confidence levels in each cluster named as sub-cluster. Furthermore, the new method considering endo-confidence level is introduced to determine the weights. To better manage consensus reaching process, we further discuss three types of experts in the non-consensus cluster to adjust their evaluations, including i) experts who are lack of endo-confidence, ii) experts who are over endo-confidence, and iii) experts whose evaluations greatly deviate from the overall level. Next, an automatic feedback mechanism which considers both evaluations and endo-confidence levels of experts is proposed for the non-consensus experts. Finally, a case study is carried out to demonstrate the feasibility of the proposed model, and a series of comparative analyses are used to show its stability. [ABSTRACT FROM AUTHOR]

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

• Propose spread-based indices to measure vagueness of judgments in TFARPRs. • Develop an actual triangular fuzzy extension of Tanino's additive consistency. • Devise a method to generate consistent TFARPRs from fuzzy utility vectors. • Build a linear program to derive normalized fuzzy utility vectors from TFARPRs. • Obtain an analytical solution of normalized utility vectors for consistent TFARPRs. This paper focuses on extending Tanino's additive consistency to triangular fuzzy additive reciprocal preference relations (TFARPRs) and deriving normalized optimal fuzzy utility vectors from TFARPRs. Spread based indices are introduced to measure vagueness of [0, 1]-valued triangular fuzzy judgments and TFARPRs. A transitivity equation with parameters is devised to define additive consistency of TFARPRs. Values of parameters are then determined to introduce an equivalent definition of additively consistent TFARPRs. Pivotal properties of additively consistent TFARPRs are put forward and a computational formula is designed to obtain additive consistency indices of TFARPRs. A novel method is proposed to generate additively consistent TFARPRs from [0, 1]-valued triangular fuzzy utility vectors. By examining the equivalency of [0, 1]-valued triangular fuzzy utility vectors, a framework is presented to normalize triangular fuzzy utility vectors. A goal programming model is subsequently built to derive normalized triangular fuzzy utility vectors from TFARPRs. This optimization model is transformed into a linear program and its analytical solution is achieved for additively consistent TFARPRs. The performance and validity of the proposed models are demonstrated by three illustrations with comparative analysis. [ABSTRACT FROM AUTHOR]

• A type-2 Takagi-Sugeno fuzzy method is applied to approximate the suspension dynamics; • A fuzzy dynamic output feedback is constructed to avoid full state information; • An interval time-varying delay is considered via the Lyapunov-Krasovskii theory; • An actuator saturation control scheme is proposed for better performance. This paper proposes a fuzzy dynamic output feedback (DOF) controller for uncertain nonlinear active suspension systems (ASSs) with actuator saturation and time-varying delay. Firstly, given the time-delay and nonlinear characteristics of the suspension systems, an interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy model is introduced to characterize the uncertain nonlinear ASSs with actuator saturation. Secondly, with the Lyapunov-Krasovskii function and the reciprocally convex technique, a series of sufficient delay-dependent conditions are derived to make sure that the control system with optimized H ∞ performance and mechanical constraints is asymptotically stable. Thirdly, a DOF controller is designed to estimate the unmeasurable parameters of the system. Finally, the performance evaluation of the proposed controller is conducted through numerical and experimental tests. [ABSTRACT FROM AUTHOR]

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

Distance education quality evaluation is extremely important in improving the quality of education under COVID-19. As traditional teaching-quality evaluation methods are no longer applicable, it is crucial to construct effective evaluation methods. In the evaluation of distance education quality, decision-makers have different linguistic expression preferences, and the evaluation information may be biased due to an improper grasp of the problem. In addition, the correlation between the criteria of distance education quality evaluation is common, and the results of existing evaluation methods are quite different. In this paper, to compensate for these deficiencies, we utilize the multi-granularity probabilistic linguistic term set (MGPLTS), which can reflect the linguistic expression preference of decision-makers and the importance of linguistic terms, and propose a multi-criteria group decision-making (MCGDM) method. First, the dispersion and concentration degrees are proposed as the theoretical basis for judging the hesitancy of decision-makers' evaluation information, and the decision-maker weight adjustment model is constructed. To reflect the importance and correlation of criteria, the SWARA method and the CRITIC method are constructed as criteria weight methods. To obtain reliable decision results, decision-makers' psychological expectations are taken into account, the MULTIMOORA method is improved upon, and a new integration theory is proposed to improve its robustness. Finally, through an example case of distance education quality evaluation and comparison with other methods, the effectiveness, practicability and superiority of this method are verified. [ABSTRACT FROM AUTHOR]

The good development of health care is conducive to improve the value and prospects of society. However, health sectors of Ghana are facing a challenge in providing medical services with expected quality for an ever-increasing number of patients in response to competitive pressures. In such circumstances, the proper evaluation of hospital health-care delivery quality becomes critical. Thus, to achieve this goal, this paper proposes an integrated medical triangular fuzzy MULTIMOORA approach (IMTFMA). We firstly construct the appropriate evaluation criteria system based on the analysis of Ghana's medical services. Then, to properly evaluate the weight of the criteria in a comprehensive manner, we determine the weight of criteria from subjective and objective perspectives. Meantime, we handle the fuzzy evaluation of experts for the criterion importance with the enhanced alpha-level sets method. According to the triangular fuzzy rating for hospitals provided by respondents, we further develop a novel evaluation method based on MULTIMOORA with the axiomatic design for accurately evaluating health-care delivery quality. The research is conducted on 8 selected hospitals, including 4 public and 4 private hospitals in the Greater Accra Region of Ghana, with 24 criteria. 15 experts with rich experience in related fields and 480 respondents assessed the above 8 selected hospitals by questionnaires. According to the outcome of the empirical analysis, even though public hospitals benefit subsidy from the government, they perform abysmally low, whereas private hospitals which are self-sponsored rather perform extremely better than expectation. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) aims to rank alternatives based on their attributes and evaluation information, which provides decision support for decision-makers. Most existing MADM methods can only obtain ranking results, decision-makers usually need to subjectively choose priority alternatives to make a decision based on the preset evaluation level and ranking results, which does not meet the requirements of complex decision situations and uncertain information processing. A method is urgently needed, which can objectively produce classification results and automatically provide priority objects for decisions. Three-way decisions (3WDs) offer an effective research technique to solve decision-making problems under uncertainty and risk by objectively dividing a universal set into three pairwise disjoint parts: acceptance, non-commitment and rejection, and implementing the corresponding strategy for each part. Considering that it is difficult to accurately determine the exact value of attributes in some cases, interval numbers can be a useful concept to flexibly describe uncertain information and satisfy the decision-maker's cognition. Therefore, under an interval-valued MADM environment, this paper proposes an evaluation-based interval-valued multi-attribute three-way decision (IVMA3WD) model from an optimization viewpoint. The model achieves an effective fusion of 3WDs and MADM problems, and further expands evaluation-based 3WD models on the totally ordered set. Specifically speaking, in order to depict uncertain information in decision-making, interval numbers are used to describe the evaluation information included in the multi-attribute evaluation matrix. Then, considering a general case that there are no decision attributes in the multi-attribute evaluation matrix, we determine the evaluation function by use of the idea of the interval-valued TOPSIS method. In addition, unlike the fixed-valued loss functions in the majority of 3WD models, the relative loss function in this article is not provided straightly but computed by attribute evaluation values expressed by interval numbers. Furthermore, based on an optimization viewpoint, we construct two optimization models and attempt to find the optimal solution to obtain the threshold pair. A housing market investment decision problem is utilized as an illustrative example to find out the applicability of our built IVMA3WD model. In the end, we adopt a sensitivity analysis and a comparative analysis to demonstrate our proposed model's characteristics and advantages. [ABSTRACT FROM AUTHOR]

Recognizing the subjectivity in human judgment and the limits to human cognition, fuzzy linguistic variables and uncertain linguistic variables are widely used to express the preference information of the decision experts in Multi-Attribute Group Decision Making (MAGDM). This paper develops an MAGDM method to solve a decision problem in which the attribute values are fuzzy numbers characterized by uncertain linguistic variables, that is, dual uncertain Z -numbers. The notion of the dual uncertain Z -number is first proposed based on the classical Z -number. Next, the cloud model is introduced, together with a new notion of the dual comprehensive cloud. A method of transforming the dual uncertain Z -numbers into dual comprehensive clouds is proposed. Third, a new dual comprehensive cloud-weighted averaging operator (DCC-WA) is presented to aggregate the multiple dual comprehensive clouds. Fourth, a new dual comprehensive cloud-grey relational degree (DCC-GRD) is supplied, and a novel MAGDM method based on the DCC-GRD is proposed. Finally, a group decision making case of sustainable supplier selection is provided to validate the proposed method. A sensitivity analysis and comparison with several congeneric methods are conducted. [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]

• Complete consistent matrix corresponding to an IFPR is constructed. • Necessary and sufficient conditions for IFPRs to be multiplicatively consistent are proposed. • Ratio-based deviation matrix that takes an accurate measurement of deviation of every element in an IFPR is constructed. • Every indeterminacy degree of an IFPR is never changed in the revising process. In this paper, we propose a method for improving the multiplicative inconsistency of an intuitionistic fuzzy preference relation (IFPR) without computing any model to derive an underlying priority weight's vector with respect to alternatives. For this, a necessary and sufficient condition for the IFPR to be multiplicative consistent is proposed and proved. Based on it, a ratio-based deviation identifying matrix that takes an accurate measurement of deviation of every element in the IFPR is constructed. We prove that the greater the value of the deviation matrix is, the more inconsistent is its corresponding element in the IFPR and based on it, a convergent iterative algorithm of improving the multiplicative consistency is presented. The algorithm uses the fact that all the indeterminacy degrees of the IFPR are never changed in the revising process of multiplicative inconsistency and as a result, the most inconsistent elements are uniquely determined by suitable elements in the IFPR, respectively. The proposed method makes a great difference from the previous methods that derived the underlying priority weight's vector with respect to alternatives based on the given IFPR for improving consistency. A numerical example is provided to show the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

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

In this paper, we propose the advanced intuitionistic fuzzy Heronian mean (AIFHM) aggregation operator (AO) and the advanced intuitionistic fuzzy weighted Heronian mean (AIFWHM) AO of intuitonistic fuzzy values (IFVs). The proposed AIFHM AO and the proposed AIFWHM AO of IFVs have the advantage of condidering interrelationships among aggregating inputs. We also explore some properties of the proposed AIFHM AO and the proposed AIFWHM AO of IFVs. Furthermore, based on the proposed AIFWHM AO of IFVs, we propose a new group decision making (GDM) method. We also provide some examples to illustrate that the proposed GDM method can overcome the drawbacks of the existing GDM methods. The proposed GDM method offers us a very useful approach to deal with GDM problems in intuitionistic fuzzy environments. [ABSTRACT FROM AUTHOR]

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

We develop an agent-based artificial general intelligent system that can be implemented in compact and power-efficient electronic hardware. The hardware under development is called the Street Engine, which is a hardware-based cognitive architecture for implementing agent-based artificial intelligence. In this paper, we introduce an agent-based system to replicate simple cognitive behaviours. In the processes of this system, numerical data are converted into fuzzy symbolic representations of the surrounding environment, and reasoning rules are included in a modified Fuzzy Inference System to support the cognitive decision-making. We use a case study example, the homing behaviour of the honey bee, to demonstrate constructing production rules and implementing the cognitive and reasoning capabilities of agents. The low level cognitive behaviour is converted into a rule-based fuzzy system, and hardware-based experiments have been conducted to verify the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on heterogeneous group decision making (GDM) in the setting of incomplete preference relations, including incomplete fuzzy preference relations, incomplete multiplicative preference relations, incomplete additive linguistic preference relations, and incomplete multiplicative linguistic preference relations. Following the consistency-consensus optimization analysis, a new GDM method is proposed which can address inconsistent and incomplete preference relations. Firstly, we consider how to determine unknown information and how to obtain consistent preference relations. In contrast to the existing methods which rank the alternatives from fuzzy preference relations using the additive or multiplicative consistency analysis, this paper follows the consistency level to decide to use the additive or multiplicative consistency. Following the consensus analysis for each type of consistent preference relations, we calculate their comprehensively consistent preference relations and the priority vectors. After that, we build a consistency-based model for calculating the comprehensive priority vector. Furthermore, we offer an ordered position consensus-based method using the built optimization models. The proposed heterogeneous GDM method with incomplete preference relations provides us with a very useful way for dealing with GDM problems in heterogeneous environments. [ABSTRACT FROM AUTHOR]

In social networks, decision makers of group decision-making (GDM) can have interactive behaviors with different individual relationships. With large-scale group participation, competitive behaviors resulted from competition relationship of the decision makers represent one of the important influences. In this case, the effects of competitive behaviors also have an impact on consensus reaching process (CRP) of GDM. Thus, considering the individual competition behaviors in large-scale group social networks, this paper deeply investigates large-scale group consensus decision with increased complexity of GDM in the framework of three-way decision (TWD). More specifically, we firstly improve the K-L algorithm by considering the frequent connections between leaders and followers as well as few connection in own sub-networks under the condition of large-scale group social networks and partition networks for classifying the social roles of leaders and followers. Then, we design the identification rules of competition relationship with consideration of social roles and interest conflict. With respect to the competition relationship, referring to the decision styles of the dependent, biased and rational decision makers, this paper further explores the corresponding competitive behaviors in information interaction of social networks. According to the competitive behaviors, we construct a new optimization consensus model in CRP for the evaluation adjustment of large-scale group TWD and obtain the decision result with Bayesian decision procedure. Finally, we apply our proposed model to analyze an example of product promotion and verify its effectiveness. [ABSTRACT FROM AUTHOR]

At present, some researchers have studied the decision-making methods in a fuzzy β -covering approximation space, which not only can play the advantages of rough set theory in dealing with inaccurate data, but also inherit the ranking function of traditional decision-making methods. However, these methods merely consider the ranking problem in a single decision-maker environment and most of the decision-making problems in reality are group decision-making problems that need to consider multiple opinions. In light of this, in this paper, we propose the concept of fuzzy β -covering group approximation spaces and establish a three-way multi-criteria group decision-making method, which can solve some ranking and classification problems of objects under a group decision-making environment. Based on a fuzzy β -covering group approximation space, we firstly propose two fuzzy β -fitting neighborhoods with pessimistic and optimistic attitudes to construct a fuzzy binary relation between any two objects. Secondly, we introduce an overall loss function to estimate the risk loss of all objects when they choose different behaviors in different states under a group decision-making environment. Subsequently, based on the conditional probability estimation formula and the overall loss function, we propose a three-way group decision-making idea in a fuzzy β -covering group approximation space, which contains eight different decision-making attitudes to meet the preferences of decision-makers. Furthermore, for the ranking and classification performance of our method, we use numerical analysis, comparative analysis and Spearman analysis to illustrate the feasibility and superiority of the method, and take experimental analysis to test the stability of our method. [ABSTRACT FROM AUTHOR]

In this paper, we propose the q -rung orthopair fuzzy weighted averaging (q -ROFWA) aggregation operator (AO) of q -rung orthopair fuzzy numbers (q -ROFNs). The proposed q -ROFWA AO of q -ROFNs can overcome the drawbacks of the q -rung orthopair fuzzy interaction weighted Hamy mean (q -ROFIWHM) AO and the q -rung orthopair fuzzy power weighted Maclaurian symmetric mean (q -ROFPWMSM) AO of q -ROFNs. Moreover, we propose a new group decision making (GDM) method based on the proposed q -ROFWA AO of q -ROFNs. The proposed GDM method can overcome the drawbacks of the existing GDM methods. It provides us a very useful approach to deal with GDM problems in q -rung orthopair fuzzy environments. [ABSTRACT FROM AUTHOR]