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

In 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]

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

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

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

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

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

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

As 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]

With the enrichment of social platforms, large-scale group decision-making (LSGDM) in social networks has gradually taken shape. In practice, experts may show limited compromise behavior during consensus reaching process (CRP), which may lead to bias or even failure in decision-making results. To tackle this issue, considering limited compromise behavior, this paper proposes a maximum satisfaction consensus (MSC) model, and focusing on LSGDM with fuzzy preference relation in social networks. Firstly, an expert weight determination algorithm integrating the interactive weights and individual weights is constructed. The interactive weights are determined by social influence strength, while the individual weights are measured by the compromise degree of limited compromise behavior and the consistency level of preferences. Subsequently, a grey clustering method is developed to classify experts into subgroups, considering both opinions similarity and limited compromise behavior similarity. In CRP, considering the limited compromise behavior, an MSC model under the limited budget determined by the minimum cost consensus (MCC) model is proposed. Based on MSC and MCC models, satisfaction-cost ratio is defined to measure the efficiency of CRP. Finally, a case study of selecting of shared bicycle operators and further discussion are conducted to verify the feasibility and superiority of the study. [ABSTRACT FROM AUTHOR]

In practical decision-making scenarios, the challenges lie in obtaining the collective opinion that the majority of decision makers are willing to accept, thereby arriving at the final decision result. Among them, both the inherent uncertainty and reliability embedded in the information may lead to a deviation from the fact in the final decision result. Moreover, individual and social behaviors have the potential to influence the acquisition of effective decision result. Based on this, this paper constructs a novel social network-based consensus model under discrete Z -number environment, taking into account the individual and social behaviors of experts. First, novel trust propagation and trust aggregation operators with discrete Z -numbers are developed, which aim to form a complete social trust network. Then, unit consensus cost function and compromise boundary function based on social trust network are given to objectively determine the unit adjustment costs and compromise boundaries of each decision maker. In addition, a minimum cost consensus model considering the coexistence and interaction between individual and social behaviors is explored. Last, the feasibility and superiority of the model are proved through a case of the agricultural supply chain. Through simulation and comparative analysis, the results show the effectiveness of novel trust propagation and aggregation operators. And the necessity of considering individual and social behaviors for consensus reaching process is presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a noval addition operation (AOP) and a novel scalar multiplication operation (SMOP) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs) based on Yager's t -conorm and t -norm. The proposed AOP and the proposed SMOP of LIVAIFNs can conquer the shortcomings of the existing AOP and the existing SMOP of LIVAIFNs. Based on the proposed AOP and the proposed SMOP of LIVAIFNs, we propose the linguistic interval-valued Atanassov intuitionistic fuzzy Yager weighted arithmetic (LIVAIYFWA) aggregation operator (AO) of LIVAIFNs. We also prove some properties of the proposed LIVAIFYWA AO of LIVAIFNs. Moreover, by using the proposed LIVAIFYWA AO of LIVAIFNs, we propose a noval group decision making (GDM) method. The proposed GDM method can conquer the drawbacks of the existing GDM methods in the context of LIVAIFNs. [ABSTRACT FROM AUTHOR]

In this paper, a novel structured collaborative sparse dictionary learning approach is proposed to improve the monitoring performance of discriminative dictionary learning for multimode processes. The mode discriminability and data reconstruction are first balanced by decomposing the dictionary coefficients into between- and within-class parts and introducing a within-class self-expression regularization term. A weight vector of between-class coefficients is subsequently exploited for accurate mode identification of data that falls into the overlapping regions between different class distributions. Moreover, in order to pinpoint the fault variables, a scalable fault isolation method is developed which imposes a constraint of statistical control limit and introduces the ℓ 1 / ℓ 2 , 0 -structured sparsity regularization terms. The mode identification capability of the proposed method is proved theoretically by Theorems 1 and 2, and a lower-bound magnitude is provided by Theorem 3 for fault isolation. Finally, extensive experiments conducted in the numerical and industrial process demonstrate that our proposed method outperforms some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

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

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

In this paper, a T-S fuzzy model is established to describe nonlinear fuzzy singular fractional order multi-agent systems (SFOMASs) exhibiting actuator saturation when the order is between 0 and 2. We focus on the case where the system state is difficult to measure or cannot be directly measured, so it needs to be estimated based on other measurable signals. To this end, a fuzzy observer is designed, which can process fuzzy or imprecise input and output signals through fuzzy processing. Then the observer-based leader-following consensus problem of fuzzy SFOMASs with actuator saturation is addressed. To address input saturation, we use some mathematical tools to represent the saturated linear feedback on the convex hull, which is then transformed into seeking the optimal solution of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is verified through the adoption of a numerical example. • A T-S fuzzy model is built to describe SFOMASs with fractional order in the interval (0 , 2). • A fuzzy observer is designed to handle fuzzy or imprecise input and output signals through fuzzification processing. • The observer-based leader-following consensus of fuzzy SFOMASs with actuator saturation is achieved. [ABSTRACT FROM AUTHOR]

In practical multi-attribute group decision-making (MAGDM) problems, it is common to utilize heterogeneous representation forms to express distinct preference information for different experts, primarily due to their diverse backgrounds. To address the problem of reducing information loss from the aggregation of experts' opinions in heterogeneous MAGDM as well as improving the interpretability of the decision-making process, this paper introduces a concept lattice-based heterogeneous MAGDM approach. The heterogeneous multi-expert formal context is first proposed to capture the heterogeneous evaluation information of alternatives provided by different experts. Then, extended multi-expert concept lattices are constructed to aggregate evaluation information of alternatives by different experts. In this case, all concepts are considered to minimize information loss during the aggregation process. Second, to obtain more reasonable decision results, the distance between the concept intents and the heterogeneous positive and negative ideal solutions is considered, and the alternatives are ranked based on this measure. In addition, the MAGDM process for each alternative is visualized using the extended multi-expert concept lattices. This representation aids in identifying key concepts, their interdependencies, and the overall impact on the decision result. Finally, numerical examples and comparative analysis validate the validity and rationality of the proposed approach in heterogeneous MAGDM. [ABSTRACT FROM AUTHOR]

• A PF-WPA-CRITIC-MARCOS framework is reported to select the preferential sustainable food supplier for resilient cities. • A hierarchical model of criteria for sustainable food supplier selection is constructed. • The deviation between input data and the interactive criteria is considered in selecting sustainable food suppliers. • A numerical case of the food supply chain is illustrated to test the proposed model. Sustainable food supplier selection (SFSS) can be handled as an uncertain decision-making issue. The Pythagorean fuzzy set (PFS), a type of non-standard fuzzy set, offers an expanded description space for articulating fuzzy and uncertain data. Accordingly, this paper proposes a Pythagorean fuzzy synthetic decision method-based selection framework for solving the SFSS problem within a subjective context. Then, the weighted distance measures for the PFS are introduced to derive the importance degrees of the experts, which can provide a more objective decision result. Then, an information fusion method with a PFS-weighted power average (WPA) operator is introduced to form a group decision matrix competent to accommodate the deviation effect. Next, an extended PF-measurement of alternatives and ranking according to compromise solution (MARCOS) method integrating PF-criteria importance through inter-criteria correlation (CRITIC) is presented to calculate the priority of each supplier, which can capture the inter-correlations between criteria. Finally, a numerical example of SFSS is implemented to show the application of the proposed synthetic decision approach. Subsequently, the sensitivity analysis of distance parameters and comparison analysis among different SFSS approaches were conducted to test the rationality and advantages of the proposed framework for resolving the SFSS problem. The results show that the reported method can provide a practical way to resolve the SFSS problems with uncertain data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new distance measure between picture fuzzy sets (PFSs) to overcome the drawbacks of the existing distance measures between PFSs. We also propose a weight-determination method to determine attributes' weights using the proposed distance measure between PFSs. We also propose a novel multi-attribute decision-making (MADM) method on the basis of the proposed distance measure between PFSs and the modified combined compromise solution (CoCoSo) method. The proposed MADM method can overcome the drawbacks of the existing MADM methods based on PFSs. It gives us a very useful way for MADM in picture fuzzy environments. [ABSTRACT FROM AUTHOR]

A variety of fuzzy sets, especially Pythagorean fuzzy sets (PFSs), are commonly utilized to describe the ambiguity of information in three-way decision (3WD) models. PFSs can handle fuzzy information well but ignore the description of stochastic information. To address this issue, in this paper, we attempt to construct a novel three-way multiattribute decision model by combining 3WD with constrained Pythagorean fuzzy sets (CPFSs) which can measure the reliability of PFSs. Firstly, we introduce the concept of constrained Pythagorean fuzzy information systems (CPFISs). Comprehensive positive and negative similarities of objects are given in a CPFIS by introducing normalization, score function, comparison rules, and positive and negative ideal solutions. Secondly, by comprehensive positive and negative similarities, novel formulas for calculating comprehensive relative utility function values are obtained and an objective method for estimating conditional probabilities is presented in the absence of decision attributes. Based on the above knowledge, we establish a similarity-based three-way multiattribute decision model in a CPFIS. Furthermore, we conduct a case analysis of appendicitis to realize the application of our proposed model and several comparative analyses to demonstrate the effectiveness and superiority of our model. Finally, the good performance of the new model is verified through experimental analyses. [ABSTRACT FROM AUTHOR]

• The two-stage robust optimization approach is introduced into the traditional minimum cost consensus model with directional constraints (MCCM-DC). • Several novel robust two-stage minimum asymmetric cost consensus models (TRMCCM-DCs) are proposed to address the uncertainty in the consensus reaching process (CRP). • The robust counterparts of TRMCCM-DCs are developed under three uncertainty circumstances. Group decision-making (GDM) problems in the real world are becoming more complex, and various uncertain factors exist. However, most scholars ignore the uncertainty in the GDM and the moderator cannot accurately predict the unit upward and downward adjustment costs of decision makers (DMs). To overcome these issues, this paper constructs the novel minimum cost consensus models with directional constraints (MCCM-DCs) based on robust optimization under uncertainty circumstances. Firstly, we construct two-stage asymmetric adjustment cost consensus models with better flexibility. The first stage focuses on establishing a consensus opinion, while the second stage entails deliberation on the adjustment deviations of the DMs. Further, considering the uncertainty of the unit adjustment cost, robust optimization is introduced to describe three different uncertainty scenarios in the second stage of the models. Then robust two-stage minimum asymmetric cost consensus models (TRMCCM-DCs) are proposed, which is closer to reality. Finally, the proposed models are applied to the case of water pollution control negotiations in the Taihu Basin in China, and further sensitivity analysis and comparison analysis are conducted to verify the validity of the models. [ABSTRACT FROM AUTHOR]

This paper aspires to explore and construct a more objective and automated large-scale group decision-making (LSGDM) model. The concept of vacillation degree based on probabilistic double hierarchy linguistic term set is proposed to describe the characteristics of decision makers (DMs). The criteria weights are obtained by entropy measure, and then a clustering method is constructed. Moreover, the autonomous learning probability is presented to characterize the extent to which DMs accept the opinions of others. The complex connections between DMs can be more clearly described by visualizing the autonomous learning. Considering the deficiencies of the existing feedback adjustment mechanism on the setting of the suggested adjustment range, the autonomous learning and opinions-updating process for internal and external subgroups are designed. Then consensus judgment method is also proposed from subgroups and group. Based on the above work, an opinions-updating model for LSGDM driven by autonomous learning is constructed. The validity of the model is verified by a case study of emergency medical service agency selection. Finally, three simulation models and comparative analysis are established to test the opinions-updating model. [ABSTRACT FROM AUTHOR]

Innovative, Resilient, and Green Supplier Selection (IRGSS) is an emerging need often viewed as a complex multi-criteria decision-making problem. However, overly stringent restrictions on the assessed values, such as q-rung ortho -pair hesitant fuzzy uncertain linguistic sets, and dependent uncertainty events affecting criterion weights threaten the decision's reliability. Thus, LPHFS-SPFUCOM-MULTIMOORA is proposed to address these challenges. First, the paper proposes novel Linguistic Polytopic Hesitant Fuzzy sets (LPHFSs), which assume the sum of the q th power of the three types of memberships is not greater than 1 and relax the constraints on the assessed values. Second, the Full Consistency Method (FUCOM) is improved to find weights by integrating the Concept of Stratification Theory (CST) and PageRank, named SPFUCOM. CST depicts the occurrence process of uncertain events and PageRank finds their occurrence probabilities considering dependency. Third, the multiplicative Multi-objective Optimization by Ratio Analysis (MULTIMOORA) is novelly applied with SPFUCOM and LPHFSs to rank suppliers. Finally, a case from an electric vehicle manufacturer is studied to illustrate the applicability of the proposed method. Through sensitivity and comparative analyses, the rationality and advantages of the proposed method are verified. This study can provide insights for managers to solve the IRGSS problem. [ABSTRACT FROM AUTHOR]

Fuel cell electric vehicles (FCEVs) are a contemporary technology that is making headway in the expanding automotive industry. To promote FCEV effectiveness, environmentally acceptable limits need to be considered during their whole life cycle. End-of-life automotive fuel cells (AFCs) are one of the major contemporary challenges facing the sustainable business of transportation companies. The paper introduces a hybrid q-rung orthopair fuzzy (q-ROF)-based methodology to handle uncertainties and vagueness. It couples and extends the criteria importance through intercriteria correlation (CRITIC) and evaluation based on distance from average solution (EDAS) methods with q-ROF sets. This research aims to provide essential methodological and practical frameworks, as well as guidelines for improving the effectiveness of engaged FCEVs in transportation companies. The q-ROF CRITIC-EDAS methodology provides a systematic method for prioritizing sustainable approaches for smart waste management of AFCs of road freight vehicles. The incorporation of the real-life case study demonstrates its practical applicability and validity. The introduced q-ROF CRITIC-EDAS model could be extensively applied to the AFC waste management in order to assist stakeholders in making decisions consistent with the sustainability objectives. • Practical and methodological frameworks for smart waste management of EOL AFCs. • The advanced hybrid q-ROF CRITIC-EDAS-based methodology is introduced. • The proposed MCGDM tool can determine the most suitable treatment of EOL AFCs. • Recommendations for solving implementation problems for end-of-life AFCs of FCEVs. • Guidelines for improving the effectiveness of FCEVs in transportation companies. [ABSTRACT FROM AUTHOR]

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance "1" can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets. [ABSTRACT FROM AUTHOR]

This paper develops several fixed-time neural networks for solving mixed variational inequalities (MVIs). The proposed networks are highly efficient and with fixed-time convergence. First, based on the conventional forward-backward-forward neural network (FNN) and sliding mode control technique, a time-invariant fixed-time FNN (FxTFNN) is designed. Next, the Euclidean norm of FNN is introduced into FxTFNN to design the modified FxTFNN (MFxTFNN). It is shown that the proposed FxTFNN and MFxTFNN have fixed-time convergence properties and their settling-time functions are independent of the initial values. The proposed FxTFNN and MFxTFNN can be used to solve the Lasso problem and apply sparse signal reconstruction and image reconstruction. In addition, by introducing time-varying coefficients based on FxTFNN and MFxTFNN, time-varying FxTFNN (TFxTFNN) and time-varying MFxTFNN (TMFxTFNN) are developed. Finally, experimental results of numerical example, signal reconstruction, and image reconstruction are used to verify the effectiveness and superiority of the proposed neural networks. [ABSTRACT FROM AUTHOR]

Most of the cancer patients cannot get the usual treatment in the advanced stage of the disease. In particular, for breast cancer, it is to use a special kind of radiation that targets the tumor while the patient holds their breath. This is called surface-guided (SG) breast radiotherapy (RT) with deep inspiration breath-hold (DIBH). This treatment is very complicated and different from the normal way of treating breast cancer. It can also have many errors and problems that are not well-studied or understood. To prevent these problems, we need to use a method called failure mode and effects analysis (FMEA). This method helps us find and rank the possible risks and how to avoid them. In keeping with this aim, this paper studies consensus-reaching process-based group decision-making (GDM) with completely unknown risk factors' weights and the gained-lost dominance score (GLDS)-based ranking process. We cannot avoid the uncertainty related to relativity information in medical science. Therefore, in this study, we offer the experts to provide their opinions using the linguistic Z number (LZN) because LZN is designed to capture such types of information in medical science. For the consensus-reaching process (CRP), the relativity among experts is considered for consensus measurement, and the minimum adjustment sum with group consensus opinion-based feedback is offered. For unknown weight of risk factors, we don't know how much each risk factor weighs. So, we use a method that combines two ways of calculating weights. One way is a subjective weight computation process, and the other way is based on the data using entropy and division. Finally, we applied our proposed CRP-based GDM approach for ranking the identified FMs related to the SG DIBH RT process. We conduct sensitive, comparative, and statistical assessments to ensure our method is reasonable and practical. • The LZN information-based FMEA for SGRT DIBH breast cancer treatment is proposed. • Relativity among experts-based three-level consensus measurement degree is proposed. • Development of minimum adjustment sum with group consensus opinion-based feedback. • The consensus-driven based acceptable FMEA expert's weights are offered. • The consensus, entropy and maximum division-based risk factors are considered. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new similarity measure (SM) between picture fuzzy sets (PFSs). The proposed SM between PFSs can overcome the drawbacks of the existing SMs between PFSs. We also propose a weight-determination approach based on the proposed SM between PFSs to determine attributes' weights in picture fuzzy environments. We also propose a new multi-attribute decision-making (MADM) approach based on the proposed SM between PFSs and the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method for MADM with picture fuzzy information. The proposed MADM approach can overcome the shortcomings of the existing MADM approaches based on PFSs. It provides us a very useful approach for MADM in picture fuzzy settings. [ABSTRACT FROM AUTHOR]

Three-way conflict analysis model, based on information systems, is about trisecting, getting coalitions and decision-making. Since the model is proposed by Yao, many models have been proposed to enrich the field of three-way conflict analysis. In this paper, we propose a new three-way conflict analysis model. Our work can be divided into four parts. First, we define new fuzzy granules and an new approximation operator to obtain better trisections. Second, we introduce dynamic information systems which are generalizations of classical information systems. The new information systems enable us to induce trisections dynamically. Third, a new Bayesian algorithm is proposed for thresholds-computing which plays an important role in inducing trisections. In the classical Bayesian approach, there are six original parameters given subjectively. And in our algorithm, the parameters are replaced by three centers and a distance measure. Finally, our new model is applied to tourism planning in two cases, one can be presented by a dynamic information system and the other one can be presented by a dispersed information system generalized from dynamic information system. [ABSTRACT FROM AUTHOR]

This paper introduces comprehensive and theoretically-driven approach to decision making under bimodal uncertainty in form of Z-numbers. The proposed decision making approach relies on synergy of consistency-driven preferences construction method, eigenvector determination method of Z-number valued matrixes proposed by author and his colleagues and modified WSM model. Consistency-driven preferences construction method is used to obtain a consistent Z-valued pair-wise comparison matrix (PCM) given inconsistent one. Indeed, initial Z-number-valued degrees of pairwise comparison of criteria importance provided by a decision maker are often inconsistent. Next, an eigenvector of the consistent Z-valued PCM is computed to derive criteria importance weights. To arrive at normalized Z-values of criteria, a normalization technique is proposed. Overall evaluations of alternatives are computed as a weighted sum of normalized criteria values. Finally, overall values are compared by using ranking of Z-numbers. The suggested decision method is rank reversal free. Correctness and feasibility of suggested method is illustrated by example. [ABSTRACT FROM AUTHOR]

In decision-making methods, it is common to assume that the experts are honest and professional. However, this is not the case when one or more experts in the pairwise-based group decision-making framework, such as the group analytic hierarchy process, try to manipulate results in their favor. This paper aims to introduce two heuristics enabling detection of manipulators and minimizing their effect on the group consensus by diminishing their weights. The first heuristic is based on the assumption that manipulators will provide judgments that can be considered outliers with respect to those of the other experts in the group. The second heuristic assumes that dishonest judgments are less consistent than the average consistency of the group. Both approaches are illustrated with numerical examples and simulations. [ABSTRACT FROM AUTHOR]

The shift to a new era of dealing with big data has driven continuous progress and development in computer science, artificial intelligence and machine learning. This change has led to the application of advanced techniques in the realm of decision science, particularly in the area of large-scale group decision-making (LSGDM). However, although these existing techniques have become the core of LSGDM methods, they are still limited in solving problems facing incomplete data. In addition, due to the rise of social media platforms such as Weibo, WeChat and Twitter, which build bridges for communication between decision makers (DMs), this brings new opportunities and challenges for consensus research. To address this set of issues, this study develops a consensus architecture that combines dynamic social network and opinion evolution in the context of an incomplete multi-attribute LSGDM. It is worth mentioning that the proposed consensus framework is a novel decision-making system that can be used to complete the estimation of the missing values and the consensus reaching process (CRP) by simulating the realistic decision-making scenarios. Firstly, considering the size of the trust value and the length of the path, a new trust propagation method is designed to achieve a more reliable estimation of the unknown trust value. Secondly, this paper establishes a missing value estimation method by virtue of the improved DeGroot model, which is able to obtain complete evaluation information by simulating the opinion formation process of DMs. Next, a hierarchical clustering algorithm with stronger robustness is constructed, which not only can adaptively complete the clustering process, but also integrally considers two attributes of trust and opinion similarity. In light of the above research, this study designs an opinion evolution and dynamic trust-driven consensus model, referred to as the DSN-DG-LSGDM model. Finally, the sensitivity analysis and experiments on a real dataset verify the significant superiority of the constructed DSN-DG-LSGDM model compared with the extant LSGDM consensus models. • A DeGroot model based on self-confidence level is designed. • An opinion evolution and dynamic trust-driven consensus framework is developed. • An adaptive clustering algorithm with dependence levels is constructed. • A more reliable trust propagation method is proposed. • A new dynamic subgroup weight calculation method is introduced. [ABSTRACT FROM AUTHOR]

When dealing with large-scale group decision-making problems, the central emphasis lies in the objective and rational acquisition of a collective opinion acceptable to the majority of decision makers. Manipulative and overconfident behaviours are two common behaviours that make the decision results deviate from the objective facts in the decision-making process. To manage manipulative and overconfident behaviours in decision-making, this paper investigated a novel consensus model based on social networks. A novel efficient clustering model is first proposed in the model, in which the subgroups' combined cohesion is considered. Furthermore, for the manipulative behaviour of decision makers, we proposed an improved method for the identification and management based on trust relationships. In the consensus reaching process, we proposed a new identification mechanism to promote consensus reaching effectively. In the feedback mechanism, the social network DeGroot model is employed to adjust the opinions of decision makers. Moreover, a management approach is proposed for the overconfident behaviour of decision makers in the social network DeGroot model. Lastly, the feasibility and applicability of the proposed model are verified by an illustrative example. Simulation experiments and comparative analysis demonstrate the effectiveness of the model in facilitating consensus reaching. [ABSTRACT FROM AUTHOR]

This paper reports a prospect theory-based consensus model in multi-attribute group decision making. First, the attribute expectations are regarded as the reference points of decision makers in prospect theory. The attribute values are transformed into the prospect values based on the value function. Then a new consensus measure is proposed to quantify the consensus level. A feedback adjustment mechanism is constructed to improve the consensus level under prospect theory. The convergence of the proposed algorithm is proved. It is found that the proposed mechanism can lessen the work burden of DMs as compared with the existing methods. Finally, the weights of attributes are computed by constructing an optimization model that maximizes the sum of prospect values. Case study and comparative analysis are offered to illustrate the novelty and advantage of the proposed model. The obtained results reveal that an increasing loss aversion enhances the difficulty of reaching consensus. [ABSTRACT FROM AUTHOR]

Four-wheeled omnidirectional mobile robots (FM-OMR) are widely used in various fields due to their excellent steering ability and adaptability. As application scenarios expand, higher requirements are placed on their trajectory tracking capabilities. FM-OMR is highly complex and difficult to model accurately, and the system contains uncertainties. Therefore, achieving accurate trajectory tracking in the presence of system uncertainty is a pressing problem. Traditional control methods struggle to accurately estimate uncertainty, and existing controllers often rely on model parameters, resulting in poor transferability. To address this issue, this paper proposes a new control method based on an online self-organizing interval type II fuzzy neural network (SOIT2FNNFSMC). This method employs an online self-organizing algorithm to dynamically compensate for uncertainty, providing greater flexibility and accuracy compared to traditional approximation networks in terms of network construction and approximation performance. A new combined reaching law is proposed based on the characteristics of traditional reaching laws, resulting in improved chattering reduction. Additionally, fractional calculus is introduced to enhance the dynamic characteristics of the controller. Simulation and experimental results demonstrate the effectiveness of this method in achieving precise trajectory tracking while handling uncertainty and not relying on model parameter features. The self-organizing algorithm proposed in this method also provides a reference for the application of SOIT2FNN in FM-OMR. [ABSTRACT FROM AUTHOR]

In this paper, a new interval-valued intuitionistic fuzzy-based algorithm is proposed to enhance low-light images. In this proposed algorithm, the low-light image is first changed to the fuzzy image by normal fuzzification. Then the above is converted to an intuitionistic fuzzy image and further to the interval-valued intuitionistic fuzzy image. After applying contrast limited adaptive histogram equalization, we derive the required image. In the experimental part, the proposed algorithm is compared with other existing algorithms including histogram equalization, contrast limited adaptive histogram equalization, histogram specification, dehazing, fractional order image enhancement, intuitionistic fuzzy, and interval-valued intuitionistic fuzzy. In terms of overall visual quality and performance metrics, the results showed that the proposed technique surpasses other current methods including entropy, absolute mean brightness error, and contrast improvement index. [ABSTRACT FROM AUTHOR]

The challenges encountered in the realm of multi-attribute group decision-making (MAGDM) involving probabilistic linguistic term sets (PLTSs) have garnered substantial attention. Within the PLTS context, this study introduces a consensus reaching process (CRP) that iteratively refines the weights assigned to decision-makers (DMs) by leveraging the principles of prospect theory (PT). The primary goal of this iterative weight adjustment process is to enhance the overall decision-making procedure when dealing with PLTSs. To circumvent any data loss during transformation and compute the prospect values of PLTSs directly, a novel transformation formula is developed. Acknowledging the distinct cognitive levels among different DMs, the integration of multiple weights into the consensus process is characterized by its dynamic and iterative nature. Concerning the measurement of consensus, this study employs a method based on the gap between prospect values, which enhances objectivity while overcoming the limitations associated with the distance formula of PLTSs. Furthermore, the feedback mechanism incorporated into the modification process incorporates dynamic adjustment parameters that are tailored to different evaluation values, thereby preventing excessive adjustments that are either too low or too high. By utilizing the newly proposed prospect value function, this research aggregates the group evaluation value and identifies the optimal alternative. In conclusion, this paper concludes with a comparative analysis involving various counterparts, shedding light on the feasibility and validity of the proposed model. • Use the cross-entropy of PLTSs to find the weights. • A prospect value function under PLTSs is designed. • Dynamic weights in the consensus process are designed. • Dynamic adjustment parameters are designed into the feedback mechanism. [ABSTRACT FROM AUTHOR]

Adaptive consensus mechanism adopts differentiating consensus improvement strategies according to different consensus levels, which is reasonable and efficient for reaching consensus in group decision making. However, previous adaptive consensus methods adopt the feedback iteration mechanism, which has drawbacks such as time-consuming, over-consensus adjustment, and failure of consensus-reaching. Therefore, this paper studies the adaptive consensus mechanism by optimization models to avoid the above issues of the feedback iteration mechanism. In our approach, corresponding optimization models are constructed to identify non-consensus judgments, non-consensus alternatives, and non-consensus decision makers, respectively. Meanwhile, the related total minimum consensus adjustments are ascertained. Since the uniqueness of the consensus adjustment scheme cannot be ensured according to the built models, we regard it as a cost allocation problem in cooperative games, and define three types of consensus adjustment cooperative games. After that, the Shapley function, a well-known single payoff index, is adopted to allocate total consensus adjustments in different cases. Additionally, we employ the optimization model to determine the modified values of non-consensus judgments by minimizing the number of adjustment judgments. Finally, numerical study and comparison are made. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) technology, which can help supply chains improve operational efficiency and reduce production costs, has gradually been adopted by many enterprises in recent years. In general, stakeholders in the supply chain have their own requirements for AI technical services. However, most traditional service supplier selection methods rarely explicitly consider the interest demands of multi-stakeholders and coordinate them, which may lead to unsatisfactory decision results. Therefore, to support the successful implementation of AI technology in supply chain management, this paper proposes a two-stage AI technical service supplier classification method that considers the requirements of multi-stakeholders. In the first stage, we identify the opinions of stakeholders via cluster analysis and determine group coordination needs while fully considering fairness concerns. Moreover, in the second stage, we evaluate and classify AI technical service suppliers based on the group opinions of stakeholders and decision makers' risk preferences. As AI technical service suppliers are mostly emerging internet enterprises, we construct a criteria system to help assess these suppliers in advance. To verify the practicability and effectiveness of our method, we conduct a case study on the automobile supply chain. Furthermore, this work can provide guidance for AI technical service suppliers to improve their enterprise construction. [ABSTRACT FROM AUTHOR]

To eliminate discrepancies among decision makers' (DMs') evaluations, consensus reaching process (CRP) is important in large scale group decision-making (GDM). In CRP, trust relationship can promote the decision group to reach consensus and limited compromise behavior can preserve the original information. However, these two key factors are constant in most of existing studies, which cannot reflect the actual situations. Therefore, this paper explores trust evolution and dynamic limited compromise behavior in CRP for probabilistic linguistic large scale GDM. Firstly, a novel clustering method is proposed to cluster DMs into several subgroups. According to trust degrees among DMs in different subgroups and that in same subgroups, trust degrees among subgroups and confidence degrees of subgroups are defined, respectively. Then, trust evolution model and dynamic limited compromise behavior model are constructed. The trust degree in the next round of adjustment is related to the current trust degree and change of similarity degree, while limited compromise behavior is related to trust degree and confidence degree. Thus, the trust evolution based minimum adjustment consensus framework with dynamic limited compromise behavior is proposed. Finally, the proposed method is applied to an actual example and comparison analyses demonstrate the practicability and superiority of this method. [ABSTRACT FROM AUTHOR]