In the graph model for conflict resolution (GMCR), option prioritization is an important approach to obtain preferences of decision makers (DMs) over a special conflict. The preference, based on ordered preference statements, is influenced by the authenticity and the order of preference statements. Owing to ambiguous evidence and incomplete information in complex real-world conflicts, it is of great difficulty to determine crisp preference over states for DMs. Some uncertain preferences have been introduced to cope with two situations that uncertain about preference statements authenticity or prioritization. The belief structure can be used to capture vagueness or unknown in subjective judgments. In this article, we propose a belief option prioritization technique by considering two situations of preference statements to elicit preferences comprehensively and efficiently. First, a belief structure is applied to describe the uncertainty of preference statement authenticity. The belief degree represents the accuracy of each preference statement and the real preference attitude of a DM. Second, a belief distribution, associated with an ordered sequence of preference statements, is used to capture the uncertainty on the prioritization of preference statements. The belief preference over feasible states can be obtained by the scoring scheme of option prioritization based on the ordered preference statements. Last, we propose an overall belief option prioritization technique by combining two uncertain situations. The application of Gisborne Lake water export conflict is utilized to illustrate the use of belief option prioritization.

Within the context of capability-based system-of-systems (SoS), the technology selection involves multiple stakeholders interactively participating in decision-making. In this article, a novel approach based on graph model for conflict resolution (GMCR) is proposed to handle the interactive technology selection decision across capability domains. First, a GMCR methodology based decision analysis framework for technology selection is presented, which allows decision-makers (DMs) with distinct risk attitudes, preference knowledge, and degrees of foresight to independently and interactively participate in technology selection. Then, the technology selection model is established by a four-step procedure that incorporates improved fuzzy option prioritization, followed by systematical technology selection analysis to provide strategic insights for identifying potential mutually accepted technology portfolios. Finally, an illustrative example is used to demonstrate the applicability and effectiveness of the proposed approach.

Deep Neural Networks (DNNs) are susceptible to adversarial attacks, which give rise to risks in real-world applications. Understanding the mechanism of DNNs against adversarial attacks and evaluating adversarial robustness are of great interest. However, existing interpretable methods hinder the understanding of DNNs' behavior under attack by utilizing redundant information like non-robust features. Additionally, most studies use adversarial attacks to evaluate the adversarial robustness of models. The lack of interpretability of these approaches makes it difficult for evaluators to trust and track the results obtained, which hinders the improvement of model robustness. This study proposes an explainable method to evaluate adversarial robustness based on robust paths. Specifically, during the process of model feature extraction, robust features, and non-robust features are separated through the Information Bottleneck (IB) theory. The robust features enable the identification of robust neurons in DNNs, facilitating the construction of robust pathways. By analyzing these robust paths, a deeper understanding of the decision behavior of the robust model under attack can be obtained. In addition, a quantitative metirc of adversarial robustness called Robust Neuron Coverage (RNC) is proposed. Finally, the superiority of the proposed method is validated through comprehensive experiments.

The hierarchical graph model for conflict resolution (HGMCR) serves as a powerful tool for analyzing multiple interrelated conflicts, in which decision makers (DMs) at different levels are brought together and assumed to have symmetrical power. In some hierarchical conflicts, however, the DMs may vary in power and influence the ultimate conflict resolution at diverse extents. Accordingly, this paper aims to introduce the power asymmetry into basic HGMCR (B HGMCR) to resolve more complex hierarchical conflict problems. Initially, power dynamics are defined to capture the preference relations of DMs under power asymmetry. Then, matrix-based BHGMCR modeling under power asymmetry is presented, followed by the expansion of four classic stability definitions. Finally, a case study on carbon emission conflict is used to demonstrate that the proposed approach can handle the real-world hierarchical conflicts. The intervention of government power can promote carbon reform in a global perspective.

When a conflict occurs, the disputants involved and interested third parties usually expect to reach the desired equilibrium. To achieve this goal, inverse graph model for conflict resolution is an effective way to make the state of interest an equilibrium by ascertaining the required preferences. However, specifying crisp cost or effort of changing preferences over states can be challenging for decision makers (DMs) and third parties. As a result, a new inverse preference optimization model using interval optimization is introduced into the graph model by considering the uncertain cost of preference adjustment. First, the preference adjustment cost with uncertainty is formulated using interval number. Then, pessimistic preference ordering and DMs’ degrees of risk tolerance are utilized to compare cost intervals. After that, an inverse preference optimization model with uncertain adjustment cost is established. Finally, an illustrative example of the bulk water export conflict in Canada is presented to demonstrate the feasibility and effectiveness of the proposed approach.

A belief-based preference structure along with its associated elicitation approach is incorporated into the graph model for conflict resolution (GMCR) to model and analyze the multistakeholder strategic conflicts involving ambiguous evidences, incomplete information, and nonlinear causal relationships. More specifically, the relative preference is first redefined using a belief structure capable of capturing uncertainties of various types such as vagueness and/or ignorance in subjective judgments regarding the complex real-world conflicts. Next, a flexible and realistic methodology based on evidential reasoning is put forward to elicit the belief preference information over feasible states within the GMCR model. Then, 16 stability definitions (solution concepts) are extended to accommodate diverse uncertainties in preferences and facilitate the informed conflict analysis. The application and interpretation of the foregoing preference structure and associated stability definitions are demonstrated with an illustrative example.

A novel approach based on genetic algorithm (GA) is put forward to determine the possible relative preference required to reach the desired equilibria for the focal decision-makers (DMs) or the third party from the inverse perspective. More specifically, a framework of inverse graph model for conflict resolution (GMCR) modified from original GMCR incorporating GA's procedure is proposed to provide DMs with strategic insights toward inverse problems with conflict resolution. By taking full advantage of the optimization and search capability of GA, an improved preference calculation method is developed to help DMs focus limited resources on visionary strategies. Finally, an illustrative example is applied to demonstrate the applicability of the proposed approach in practice.

The combat system-of-systems (CSoSs) in high-tech information warfare, composed of different types of combat systems connected through multiple interconnections, can be abstracted as a type of complex heterogeneous network. Research on the disintegration of the operational capability of a heterogeneous combat network (HCN) is of significant military value for optimizing the planning of operation process and improving network survivability in a complex electromagnetic battlefield. Accordingly, this paper presents an integrated framework called HCN operational capability disintegration based on link prediction (OCDLP) for modeling and solving the disintegration problem regarding the operational capability of an HCN. More specifically, a heterogeneous network model of a combat network under incomplete information is first established, considering different types of functional entities and information flows. Based on this model, a link prediction model is then applied to recover the original combat network structure while taking advantage of the observed information. Next, a disintegration evaluation metric of the operational capability of an HCN is elicited to evaluate the attack efficiency after a link prediction. Last, the reliability and effectiveness of the OCDLP are illustrated through a case study. The results provide useful insight into the operation guidance and design of a more resilient CSoSs.

Recently, many efforts have been devoted to the impact of scientific papers within different citation windows. However, it is still an elusive task to predict scientific impact shortly after the publication date. In this paper, a deep learning methodology is proposed to predict long-term citation count. First, large-scale biblio-features are extracted from heterogeneous information network based on five types of links. Next, a deep learning model is designed by taking it as a regression and prediction task. Then Pearson coefficient is used to confirm the correlations between input features and future citation count. Finally, as a case study, papers of Markov Chain published in 1980 are analyzed. The result shows the proposed methodology outperforms the state-of-the-art models and gives accurate prediction of future citations.

Remaining useful life (RUL) estimation of aero-engine is a significant part of the aircraft reliability improvement and operational cost reduction. In order to solve the waste of performance data, in this study, a belief rule-based inference methodology using the evidential reasoning (RIMER) based RUL estimation process is proposed. Firstly, we take the principal component analysis (PCA) and the differential evolution (DE) algorithm to optimize the structure and parameter of the belief rule base (BRB), and then estimate the RUL of aero-engine through evidential reasoning (ER) algorithm. The practical case is investigated to validate the feasibility and efficiency of the proposed method. The experimental results show the RIMER based RUL estimation of aero-engine can support decision-making in the fields of aircraft prognostic and health management.

Search and Rescue at sea (SAR) is an important guarantee of maritime security. The similarity among search and rescue situations is the vital basis of generating instant search and rescue plan. On the basis of the process of maritime search and rescue, the influential factors of SAR situation are analyzed. Through establishing search and rescue sequence, a similarity measure model of maritime search and rescue situation is proposed based on concept lattice. Example analysis is involved.

In addition to the preferential attachment mechanism, the evolving citation history of a technical paper is also influenced by time. However, the influence pattern varies a lot in real cases, and cannot be described by a certain distribution like normal distribution. In order to find a universal model to measure the influence of time, this paper proposed a model which combines the normal distribution with Box-Cox transformation. Compared with existing models such as Logistic model, Gompertz model and Wang's model (Science, 2013), our model explain the actual scientific research rules more widely and obtain higher accuracy by conducting experiments in four cases. It can not only describe emerging research topics but also explain the "Sleeping Beauties" phenomenon.

A development planning approach combining game theory and network model is proposed to address the strategy selection and evolution for weapons system-of-systems (WSoS) characterized by an iterative and competitive development process between countries. More specifically, the development planning framework, including game player, strategy definition, and constraints (e.g., time and money), is first described, in which combat network is constructed to present the structure and evolution of WSoS. Next, the selection process of development planning strategy is studied based on damage accumulation and mitigation related to WSoS confrontation. Then, a competitive coevolution algorithm (CEA), reflecting that WSoS evolves along with the strategy selection change, is designed to find the optimal development strategy. Last, an illustrative example is used to demonstrate the feasibility and validity of the proposed approach.

Arms race is a typical conflict among rational and non-myopic decision-makers (DMs). Nevertheless, the assumption of basis graph model for conflict resolution (GMCR) is not suitable for this issue that each DM possesses identical priority disregarding the difference of their capabilities. In order to handle with this drawback, this paper proposes a novel methodology, entitled capability-based GMCR. First, performance criteria and capability parameters are investigated through feature analysis for arms race. Then, definitions and algorithms to quantify their impacts are presented for preferences elicitation. Finally, an illustrative example is utilized to demonstrate the proposed approach and analysis results are discussed to summarize related conclusions.

In order to deal with the subjectivity, epistemic uncertainty and incompleteness of input data, a novel methodology is proposed for interactive decision making between two players based on the graph model for conflict resolution (GMCR) with belief preference. First, a new GMCR model is calibrated, in which belief preferences are generated via evaluating the utilities of feasible states. Second, new definitions of unilateral improvements and four stability concepts are presented for conflict analysis. Finally, an interactive decision case on a weapon system of systems (WSoS) architecting is studied to demonstrate the feasibility of the proposed methodology.

We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.

A novel approach based on the graph model for conflict resolution (GMCR) methodology is proposed to address the problem of multistakeholder system portfolio decision analysis encountered in architecting a system of systems (SoS) with desired capabilities. More specifically, a flexible four-process framework for capability-based SoS architecting containing interactive portfolio decision analysis to promote multistakeholder design negotiations on system portfolio selections is presented. By taking full advantage of the inherent realistic and flexible design of the GMCR paradigm, an interactive portfolio decision analysis approach is designed to facilitate the systematic modeling and analysis of system portfolio decisions at the SoS level in order to achieve potential compromises among all key stakeholders having disparate preferences and interacting according to different conflict behavior patterns. This approach permits the prediction of possible mutually agreeable system portfolios for SoS architecture development. Last, the feasibility of the proposed approach is demonstrated using an illustrative example.