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

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

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

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

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

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

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

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

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

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]

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]

The propagation of cyber-attacks targeting modern industrial cyber-physical systems (ICPSs) is considered a sophisticated and persistent cross-layer penetration process, posing significant cyber-to-physical (C2P) risks to critical industrial infrastructures. However, existing defensive solutions for ICPSs lack the global defensive decision-making capacity against such persistent and stealthy cross-layer threats. This paper proposes a Bayesian-Stochastic hybrid game-theoretic approach that can generate optimal defensive strategies throughout the cross-layer penetration lifecycle, even without full information about attackers. Specifically, we first present a unified quantification framework to guarantee consistent utility function configurations in a cyber-physical layer integrated system. Then, we propose a state transition-based stochastic game model to characterize the dynamic evolution process of cross-layer penetration. The attack-defense interaction in each state is modeled as an incomplete-information Bayesian game to capture the inherent uncertainties of attacker information. Furthermore, a multi-agent Bayesian Q-learning (MABQL) algorithm is developed to learn the optimal defensive strategies despite incomplete information. The proposed approach is implemented and assessed based on a real-world ICPS testbed and the numerical results validate its feasibility and effectiveness for making optimal defensive decisions. [ABSTRACT FROM AUTHOR]

• Obtain uncertainty constraints among assessments in an additively consistent IVFPR. • Acquire an analytical solution of interval fuzzy utility vectors from IVFPRs. • Propose a novel acceptability checking method for IVFPRs. • Develop MCDM with highlighting individual characteristics of alternatives. Acquiring an analytical solution of interval fuzzy utility vectors (IFUVs) from interval-valued fuzzy preference relations (IVFPRs) plays a key role in improving the efficiency and performance of decision making with IVFPRs. This study devises formulas to compute uncertainty indices of interval-valued fuzzy assessments and IVFPRs, and builds uncertainty constraints among fuzzy assessments in an additively consistent IVFPR. By dividing all IVFPRs with the same size into two categories, least square models with constraints of uncertainty indices are set up and their analytical solutions are found to respectively acquire normalized IFUVs from the two categories of IVFPRs. The analytical solutions are then integrated into unified computational formulas acquiring normalized IFUVs from IVFPRs. On the basis of analytical-solution-based IFUVs, a distance based additive consistency index is devised and a novel acceptability concept is presented by taking both additive inconsistency acceptability and uncertainty acceptability into account. Subsequently, this paper proposes a multi-criteria decision making method with highlighting individual characteristics of alternatives. An illustration with one consistent IVFPR and three inconsistent IVFPRs is offered and a comparative study is implemented to validate the models presented. An annual-performance-evaluation-based outstanding teacher recommendation problem is utilized to show the practicality of the decision method proposed. [ABSTRACT FROM AUTHOR]

In decision-making systems, conflict management is an important concept that represents the degree of dissimilarity between bodies of evidence, ultimately enhancing decision-making performance. Jousselme's distance, as the most commonly employed one so far, is used to measure the distance between basic belief assignments (BBAs) in Dempster-Shafer (D-S) evidence theory. However, the Jousselme's distance has limitations, which can also be demonstrated in other methods theoretically. To address this issue, a BBA refinement method and a novel multi-granularity distance are proposed in this paper. Moreover, the methods are verified to be effective in the problems that Jousselme's distance cannot satisfy. Additionally, a hypothetical physical model is employed to verify the practicability of the proposed methods with multiple granularity. Furthermore, based on the proposed multiple granularity distance, a novel decision-making algorithm is designed. The results validate that the proposed decision-making method is beneficially applicable to classification scenarios and different real-world data. [ABSTRACT FROM AUTHOR]

The random generation of fuzzy measures under complex linear constraints holds significance in various fields, including optimization solutions, machine learning, decision making, and property investigation. However, most existing random generation methods primarily focus on addressing the monotonicity and normalization conditions inherent in the construction of fuzzy measures, rather than the linear constraints that are crucial for representing special families of fuzzy measures and additional preference information. In this paper, we present two categories of methods to address the generation of linearly constrained fuzzy measures using linear programming models. These methods enable a comprehensive exploration and coverage of the entire feasible convex domain. The first category involves randomly selecting a subset and assigning measure values within the allowable range under given linear constraints. The second category utilizes convex combinations of constrained extreme fuzzy measures and vertex fuzzy measures. Then we employ some indices of fuzzy measures, objective functions, and distances to domain boundaries to evaluate the coverage performance of these methods across the entire feasible domain. We further provide enhancement techniques to improve the coverage ratios. Finally, we discuss and demonstrate potential applications of these generation methods in practical scenarios. [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]

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]

This paper proposes a new approach for multiattribute decision making (MADM) using the proposed q -rung orthopair fuzzy Yager prioritized weighted arithmetic (q -ROFYPWA) aggregation operator (AO) of q -rung orthopair fuzzy numbers (q -ROFNs). Firstly, we propose the q -ROFYPWA AO of q -ROFNs based on Yager's t -conorm and t -norm and the concept of prioritized average AO. The proposed q -ROFYPWA AO consider the prioritized relationship among aggregating q -ROFNs. Moreover, we present several properties of the proposed q -ROFYPWA AO. Then, we propose a new MADM approach based on the proposed q -ROFYPWA AO of q -ROFNs. The propsoed MADM approach considers the prioritization among the attributes to overcome the drawbacks of the existing MADM approaches, where they cannot distinguish the ranking orders of the alternatives in some situations. The proposed MADM approach is very useful for MADM in the environment of q -ROFNs. [ABSTRACT FROM AUTHOR]

Stochastic multiplicative comparison matrices (SMCMs) are widely accepted due to their flexibility in measuring various types of decision-makers' uncertain preferences by treating the judgment as a random variable. However, few existing consistency indices for SMCMs account for the influence of uncertainty of SMCMs on consistency. This may lead to some contradictions in consistency measurement for SMCMs. This paper proposes a probabilistic consistency index (PCI) considering the uncertainty of SMCMs from a statistical perspective. The index satisfies the property of invariance under the permutation of the labels of objects. The influence of uncertainty on the PCI is discussed in detail by numerical simulation. In addition, the perfect consistency and acceptable consistency of SMCMs based on the PCI are introduced, and a general threshold determination algorithm for acceptable consistency of SMCMs based on Monte Carlo simulation is designed considering the uncertainty, the distribution and the order of an SMCM. Subsequently, a consistency improvement method for SMCMs based on stochastic programming is proposed, which preserves the original preference of decision-makers to the greatest extent. Finally, examples are given to illustrate the significance of the consistency verification by using the PCI , and the most likely preference structure is used as the ranking for SMCMs. [ABSTRACT FROM AUTHOR]

In order to find a reasonable and effective approach to describe the information contained in a specific Z -number, we introduce information entropy into Z -number environment in this paper, and investigate its applications in multi-attribute decision-making (MADM) issues. Moreover, aiming at the problem with the weighting indicated by Z -number values, we propose two novel weighting methodologies based on conditional entropy and sigmoid function, respectively. Firstly, on the basis of the maximum entropy principle, the optimization model to calculate the underlying probability distribution of Z -number is introduced. And then, we define Z -number pseudo-information entropy, and a novel Z-VIKOR method is proposed to solve a selecting regional circular economy development plan issue from the perspective of information entropy. Furthermore, we propose Z -number pseudo-conditional entropy, and the relationship between Z -number pseudo-information entropy and Z -number pseudo-conditional entropy is investigated. Subsequently, a weighting method based on information entropy of Z -number is proposed. In addition, we also introduce the weighting approach based on the sigmoid function decision-making method. Finally, we introduce a government new energy investment problem to verify and compare the effectiveness of the new weighting approaches. The new method gives a solution to the problem related to Z -number from the perspective of information entropy. • Defined pseudo-information entropy and pseudo-conditional entropy for Z -numbers. • Given a new Z -KIVOR method. • Proposed two weighting ways for Z -number environment. [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]

Multistage decision problems have attracted interest in various fields. Starting from the pioneering work of Bellman and Zadeh, a large class of comprehensive studies for fuzzy, stochastic and other settings were proposed. The main issue missed in the existing works is partial reliability of information. Indeed, partial reliability of information about states and actions is important for multistage decisions. Particularly, information about future state of a system resulting from current strategies is partially reliable due to uncertainty. To account for partial reliability aspect, Zadeh introduced the concept of a Z-number. In this paper, we use this concept to consider multistage decision making under partially reliable information. States, strategies, and goals are described by using Z-numbers. State transition matrix that describes evolution of a system in time is formed by using Z-number-based relations. This description leads to a problem of dynamic programming in Z-environment. We use Z-numbers to account for the fact that information related to state transitions is partially reliable – we are partially sure in a result of each transition. The reason behind partial reliability is complexity and uncertainty of real-world problems. A typical example and an application study are used to illustrate the approach. [ABSTRACT FROM AUTHOR]

Due to the nature of decentralization, blockchain-based applications are gradually adopted by more and more systems in different fields to replace centralized third-party agencies. Many applications, like blockchain oracles, rely on on-chain transactions to deliver information that is used to make final decisions. There have been many methods proposed to guarantee the correctness of the final results, and most of them are in terms of the management of information providers and the application's design. However, to our notice, only a few works have discussed the security threat caused by rational mining pools that are responsible for packing transactions and information into blocks and uploading them to the blockchain. Therefore in this paper, we propose a possible delayed packing attack carried out by rational mining pools against these transaction information based applications. Game theory analysis is conducted to obtain the Nash equilibrium strategy, and the price of anarchy is calculated to depict the success probability of such an attack under different circumstances. In addition, we design a countermeasure protocol based on cryptography tools to defend against the delayed packing attack. Finally, we carry out a thorough security analysis as well as corresponding experiments to prove the security and feasibility of our countermeasure. [ABSTRACT FROM AUTHOR]