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Topological information is provided, and research on the design of routing protocols for UAV self-assembling networks is conducted, in order to enable fleet communication transfer between UAVs and UAVs and enhance their communication transmission rate in the self-assembling network. A new routing protocol is proposed through greedy forwarding and peripheral forwarding of UAV self-assembling network communication data, UAV self-assembling network planarization processing, dynamic adjustment of routing mode based on topological information, and routing protocol decision content generation. The proposed network is described using stochastic geometry theory, with the UAV and building locations modeled as two independently distributed Poisson point processes and the building shape modeled as a rectangular body with height obeying the Rayleigh distribution. An estimated equation for typical user coverage is produced using this model. The simulation results show that the approximate expression matches with the simulation results with reduced computational complexity, which verifies the validity of the approximate analysis. By comparing it with the clustering-based routing protocol, it is concluded that the new routing protocol conditions for UAV self-assembly network can realize the communication transmission between UAVs and drones and further promote their communication transmission rate.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method.

Consensus reaching is a key issue in group decision-making, because conflicts of interest among groups are common. Democratic consensus refers to achieve a soft consensus among collective as well as ensure the effective participation and satisfaction of individuals. Multi-person multi-criteria large scale decision making (MpMcLSDM) usually involves a huge number of decision makers (DMs/participants), and different DMs usually have different interests. Thus, how to effectively manage individuals to promote democratic consensus is a current research challenge. To do that, this research develops a democratic consensus reaching process (DCRP) for MpMcLSDM problems. In the proposed approach, a clustering method that considers both the opinion similarity and individual concern similarity of DM is firstly given to decrease the complexity of MpMcLSDM issues. Subsequently, we propose to assign equal initial weight to each cluster to protect the interests of minorities. Meanwhile, a consensus contribution-based dynamic interactive weight updating method is implemented in the DCRPs to promote a high level of democratic consensus. Besides, a compromise degree-based consensus feedback strategy is developed to improve the efficiency of the DCRPs. The proposed feedback mechanism effectively considers the individual concern and adjustment willingness of DMs in the DCRPs. Finally, a case study and some comparisons are given to show the effectiveness and innovation of this research.

Hesitant fuzzy preference relations (HFPRs) are formally proposed to model the conflict situation in which each decision maker (DM) consists of multiple individuals and each individual has its own fuzzy preferences over the feasible states within the framework of the graph model for conflict resolution (GMCR). Based on HFPRs, new definitions for hesitant fuzzy Nash stability, hesitant fuzzy general metarationality, hesitant fuzzy symmetric metarationality, and hesitant fuzzy sequential stability permit stability analyses to be carried out. Moreover, a new option prioritization technique, called hesitant fuzzy option prioritization, is developed for modeling a DM’s HFPRs based on the DM’s priority sequence of preference statements, the DM’s fuzzy truth values and levels of confidence. The groundwater contamination conflict of Elmira, Ontario, Canada, is utilized as a case study to illustrate the usefulness and applicability of the hesitant fuzzy option prioritization technique and GMCR with HFPRs.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods.

Within the framework of the graph model, a matrix formulation is developed to model and analyze conflicts in which decision makers (DMs) may have reciprocal preferences. Specifically, matrix expressions are employed to represent DMs' reciprocal preference relations, unilateral movements (UMs) and fuzzy unilateral improvements (FUIs), as well as joint UMs and joint FUIs for a coalition of two or more DMs. Furthermore, a matrix methodology is provided to calculate whether a state in a conflict model, or scenario, is stable for a particular DM under various solution concepts, or stability definitions, that reflect the diversity of possible behavioral patterns for a DM in a conflict when preferences can be reciprocal. Five solution concepts associated with reciprocal preferences, Fuzzy Nash Stability, Fuzzy Symmetric Metarationality, Fuzzy General Metarationality, Fuzzy Sequential Stability, and Fuzzy Symmetric Sequential Stability, are redefined for matrix representations of both two-DM and multiple-DM conflict models. To illustrate how the matrix representation can be conveniently employed in practice, it is applied to two real-world conflicts.

Highlights • The minimum cost consensus model is proposed to coordinate the opinions of experts. • A new method of LSGDM clustering is proposed to improve CRP efficiency. • A consensus index CI reflecting the harmony degree between experts is devised. • A robust counterpart of robust optimization consensus is implemented., Recently, large-scale group decision making (LSGDM) in social network comes into being. In the practical consensus of LSGDM, the unit adjustment cost of experts is difficult to obtain and may be uncertain. Therefore, the purpose of this paper is to propose a consensus model based on robust optimization. This paper focuses on LSGDM, considering the social relationship between experts. In the presented model, an expert clustering method, combining trust degree and relationship strength, is used to classify experts with similar opinions into subgroups. A consensus index, reflecting the harmony degree between experts, is devised to measure the consensus level among experts. Then, a minimum cost model based on robust optimization is proposed to solve the robust optimization consensus problem. Subsequently, a detailed consensus feedback adjustment is presented. Finally, a case study and comparative analysis are provided to verify the validity and advantage of the proposed method.

This work was supported in part by the Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX20_0507; in part by the Fundamental Research Funds for the Central Universities under Grant B200203165 and Grant B220203013; in part by the National Natural Science Foundation of China (NSFC) under Grant 71871085; in part by the National Natural Science Foundation of Jiangsu Province under Grant BK20210634; in part by the Startup Foundation for Introducing Talent of NUIST under Grant 1521182101004; and in part by the China Scholarship Council under Grant 202106710123., Every decision may involve risks. Real-world risk issues are usually supervised by third parties. Decision-making may be affected by the absence of sufficient or reasonable trust or to the opposite, an unconditional, excessive, or blind trust, which is called trust risks. The conflict-eliminating process (CEP) aims to facilitate satisfactory consensus by decision makers (DMs) through continuous reconciliation between their opinion differences on the subject matter. This article addresses trust risks in CEP of social network group decision making (SNGDM) through third-party monitoring. A trust risk analysis-based conflict-eliminating model for SNGDM is developed. It is assumed that a third-party agency monitors the DMs’ credibility and performance, which is recorded in an objective evaluation matrix and multi-attribute trust assessment matrix (MTAM). A trust risk measurement methodology is proposed to classify the DMs’ different trust risk types and to measure the trust risk index (TRI) of a group of DMs. When TRI is unacceptable, a trust risk management mechanism that controls TRI is activated. Different management policies are applicable to DMs’ different trust risk types. There are two main methods: 1) dynamically update the MTAM based on DMs’ performance and 2) provide suggestions for modifying the DM’s information with high TRI. Besides, as part of the integrated CEP, this model includes an optimization approach to dynamically derive DMs’ reliable aggregation weights from their MTAM. Simulation experiments and an illustrative example support the feasibility and validity of the proposed model for managing trust risks in CEP of SNGDM., Postgraduate Research & Practice Innovation Program of Jiangsu Province KYCX20_0507, Fundamental Research Funds for the Central Universities B200203165 B220203013, National Natural Science Foundation of China (NSFC) 71871085, Natural Science Foundation of Jiangsu Province BK20210634, Startup Foundation for Introducing Talent of NUIST 1521182101004, China Scholarship Council 202106710123

Conflict of environmental sustainable development as a common phenomenon can be seen everywhere in life. To capture consensus problems of decision makers (DMs) in conflict, a consensus and non-consensus fuzzy preference relation (FPR) matrix is proposed to the framework of the Graph Model for Conflict Resolution (GMCR). Concentrating on the case of two DMs within GMCR paradigm, four standard fuzzy solution concepts are developed into eight fuzzy stability definitions which can fully represent DMs’ behavior characteristics of win-win and self-interested. To demonstrate how the novel GMCR methodology proposed in this paper can be conveniently utilized in practice, it is then applied to an environmental sustainable development conflict with two DMs. The results show that the general fuzzy equilibrium solutions are the intersection of consensus fuzzy equilibrium and non-consensus fuzzy equilibrium. Therefore, the GMCR technique considering DMs’ consensus can effectively predict the various possible solutions of conflict development under different DMs’ behavior preferences and provide new insights for analysts into a conflict.

With the development of intelligent decision-making, one kind of decision modes involves a large number of decision-makers (DMs), which is called large scale group decision making (LSGDM). In LSGDM, overconfidence is one of the common behaviors because of many DMs’ participation and the bounded rationality of human decision. Overconfidence usually has a negative impact on LSGDM and can even lead to failure in the final decision(s). To achieve consensus is very important for LSGDM. Different consensus models of LSGDM have been proposed, while the DMs’ overconfidence behaviors in the consensus have not been concerned. Hence, the purpose of this paper is to propose a consensus model which considers overconfidence behaviors, and the paper mainly focuses on LSGDM based on fuzzy preference relations with self-confidence (FPRs-SC). In the proposed model, a DM clustering method, which combines fuzzy preference values similarity and self-confidence similarity, is used to classify the DMs with similar opinions into a subgroup. A group consensus index which considers both the fuzzy preference values and self-confidence is presented to measure the consensus level among DMs. An overconfidence measurement is given to detect the DMs’ overconfidence behaviors in the consensus. Subsequently, the detailed overconfidence behavior analysis is presented involving two aspects: fuzzy preference values consensus and self-confidence consensus. A dynamic weight punishment mechanism is implemented for overconfident DMs to improve the consensus efficiently. The effectiveness and advantages of the presented consensus model are validated by a numerical example and comparative analysis.

Within the paradigm of the Graph Model for Conflict Resolution (GMCR), fuzzy reciprocal preference relations (FPRs) can be usually employed to handle decision makers' (DMs') certain and uncertain preferences. Due to lack of time, limited expertise, or dynamic factors, the DMs' fuzzy preferences over the alternatives or states may be incomplete. Thus, a new preference relation, the incomplete fuzzy reciprocal preference relation (IFPR), is proposed to deal with both complete and incomplete fuzzy preferences within GMCR. In this study, one key contribution is that, according to DMs' attitude to risk associated with incomplete fuzzy preferences, four extended sets of stability definitions are put forward for providing a nuanced description of human behavior for both two-DM and n-DM conflict models. Furthermore, the interrelationships of solution concepts within and across the four extensions of stability definitions are investigated. Finally, an illustrative example, the potential large-scale export of water from Lake Gisborne, Canada, is used to show the usefulness of GMCR with incomplete fuzzy reciprocal preference relations.

Due to the development of intelligent decision-making, social network group decision-making (SNGDM) has become increasingly valued. Generally, real SNGDM cases involve not only the mathematical formulation of the social network analysis but also the experts’ psychological behaviors. Self-confidence, an expert's psychological implication of self-statement, is a significant topic in SNGDM problems, while it is overlooked in most existing research. To address this issue, this study takes experts’ self-confidence into account in SNGDM. All experts use self-confident fuzzy preference relations (SC-FPRs) to express their opinions. Subsequently, we have developed a novel self-confidence-based consensus approach for SNGDM with SC-FPRs. A dynamic importance degree of experts which combines the external trust and internal self-confidence is proposed to determine their weights. A consensus index considering self-confidence is defined to assess the consensus level among experts. Meanwhile, a trust-based feedback mechanism is presented to improve the consensus efficiency. The rule of the feedback mechanism is that experts dynamically adjust their self-confidence levels while revising the preferences. Using a self-confidence score function , an alternative that has the highest self-confidence score can be selected as the best solution. An illustrative example and some comparisons are given to verify the feasibility and effectiveness of the proposed method.

In group decision making (GDM), to facilitate an acceptable consensus among the experts from different fields, time and resources are paid for persuading experts to modify their opinions. Thus, consensus costs are important for the GDM process. Notwithstanding, the unit costs in the common linear cost functions are always fixed, yet experts will generally express more resistance if they have to make more compromises. In this study, we use the quadratic cost functions, the marginal costs of which increase with the opinion changes. Aggregation operators are also considered to expand the applications of the consensus methods. Moreover, this paper further analyzes the minimum cost consensus models under the weighted average (WA) operator and the ordered weighted average (OWA) operators, respectively. Corresponding approaches are developed based on strictly convex quadratic programming and some desirable properties are also provided. Finally, some examples and comparative analyses are furnished to illustrate the validity of the proposed models.