The 2-tuple linguistic modeling is a popular tool for computing with words in decision making. In order to deal with the linguistic term sets that are not uniformly and symmetrically distributed, the ...numerical scale model has been developed to generalize the 2-tuple linguistic modeling. In the numerical scale model, the key task of the 2-tuple based models is the definition of a numerical scale function that establishes a one to one mapping between the linguistic information and numerical values. In this paper, we propose a consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets in the decision making problems with linguistic preference relations. This consistency-driven methodology is based on a natural premise regarding the consistency of preference relations. If linguistic preference relations provided by experts are of acceptable consistency, the corresponding transformed numerical preference relations by the established interval numerical scale are also consistent. Compared with the existing approach based on canonical characteristic values, the consistency-driven methodology provides a new way to set the interval numerical scale without the need of the semantics defined by interval type-2 fuzzy sets. Meanwhile, interval multiplicative preference relations are used in the pairwise comparisons method and the presented theory can be utilized in the pairwise comparisons method as it provides a novel approach to automatic construct interval multiplicative preference relations. Finally, we present the framework for the use of the consistency-driven automatic methodology in linguistic group decision making problems and two numerical examples are given to illustrate the feasibility and validity of this proposal.
In group decision making, it is sensible to achive minimum consensus cost (MCC) because the consensus reaching process resources are often limited. In this endeavour, though, there are still two ...issues that require paying attention to: (1) the impact of decision rules, including decision weights and aggregation functions, on MCC; and (2) the impact of non-cooperative behaviors on MCC. Hence, this paper analytically reveals the decision rules to minimize MCC or maximize MCC. Furthermore, detailed simulation experiments show the joint impact of non-cooperative behavior and decisions rules on MCC, as well as revealing the effect of the consensus within the established MCC target.
•Trust and reputation systems in social networks are analysed.•Approaches of opinion dynamics in group decision making are reviewed.•Main challenges and future research are pointed out.
On-line ...platforms foster the communication capabilities of the Internet to develop large-scale influence networks in which the quality of the interactions can be evaluated based on trust and reputation. So far, this technology is well known for building trust and harnessing cooperation in on-line marketplaces, such as Amazon (www.amazon.com) and eBay (www.ebay.es). However, these mechanisms are poised to have a broader impact on a wide range of scenarios, from large scale decision making procedures, such as the ones implied in e-democracy, to trust based recommendations on e-health context or influence and performance assessment in e-marketing and e-learning systems. This contribution surveys the progress in understanding the new possibilities and challenges that trust and reputation systems pose. To do so, it discusses trust, reputation and influence which are important measures in networked based communication mechanisms to support the worthiness of information, products, services opinions and recommendations. The existent mechanisms to estimate and propagate trust and reputation, in distributed networked scenarios, and how these measures can be integrated in decision making to reach consensus among the agents are analysed. Furthermore, it also provides an overview of the relevant work in opinion dynamics and influence assessment, as part of social networks. Finally, it identifies challenges and research opportunities on how the so called trust based network can be leveraged as an influence measure to foster decision making processes and recommendation mechanisms in complex social networks scenarios with uncertain knowledge, like the mentioned in e-health and e-marketing frameworks.
Linguistic distribution expressions provide a flexible way for decision makers to express their opinions in linguistic decision making. When working with a linguistic distribution, words mean ...different things for different people, i.e., decision makers have personalized individual semantics (PISs) regarding words. Therefore, in this paper, we propose a consistency-driven methodology to manage distribution linguistic preference relations (DLPRs) with PISs. This methodology can not only estimate the ignorance elements in incomplete DLPRs but also obtain the personalized numerical meanings of linguistic expressions to decision makers. In this way, we can combine the characteristics of the personalized representation in linguistic decision making and guarantee the optimum consistency of incomplete DLPRs with ignorance elements. Detailed numerical and comparison analyses have been proposed to justify our proposal.
In this article, a novel framework to prevent manipulation behavior in consensus reaching process under social network group decision making is proposed, which is based on a theoretically sound ...optimal feedback model. The manipulation behavior classification is twofold: first, " individual manipulation " where each expert manipulates his/her own behavior to achieve higher importance degree (weight); and second, " group manipulation " where a group of experts force inconsistent experts to adopt specific recommendation advices obtained via the use of a fixed feedback parameter. To counteract " individual manipulation ," a behavioral weights assignment method modeling sequential attitude ranging from " dictatorship " to " democracy " is developed, and then a reasonable policy for group minimum adjustment cost is established to assign appropriate weights to experts. To prevent " group manipulation ," an optimal feedback model is investigated where objective function is the individual adjustments cost and constraints related to the group threshold of consensus. This approach allows the inconsistent experts to balance group consensus and adjustment cost, which enhances their willingness to adopt the recommendation advices and consequently the group reaching consensus on the decision-making problem at hand. A numerical example is presented to illustrate and verify the proposed optimal feedback model.
•A review of the consensus processes in social network group decision making is presented.•Two approaches are identified: consensus based on trust relationships and based on opinion ...evolution.•Challenges and research future fields are presented.
In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research.
In real-world Multiple Attribute Decision Making (MADM) problem, the attribute weights information may be unknown or partially known. Several approaches have been suggested to address this kind of ...incomplete MADM problem. However, these approaches depend on the determination of attribute weights, and setting different attribute weight vectors may result in different ranking positions of alternatives. To deal with this issue, this paper develops a novel MADM approach: the ranking range based MADM approach. In the novel MADM approach, the minimum and maximum ranking positions of every alternative are generated using several optimization models, and the average ranking position of every alternative is produced applying the Monte Carlo simulation method. Then, the minimum, maximum and average ranking positions of the alternative are integrated into a new ranking position of the alternative. This novel approach is capable of dealing with venture investment evaluation problems. However, in the venture investment evaluation process, decision makers will present different risk attitudes. To deal with this issue, two ranking range based MADM approaches with risk attitudes are further designed. A case study and a simulation experiment are presented to show the validity of the proposal.
When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera ...and Martinez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale. We find that the key of computational techniques based on linguistic 2-tuples is to set suitable numerical scale with the purpose of making transformations between linguistic 2-tuples and numerical values. By defining the concept of the transitive calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.
When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous ...linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.
The consistency measure is a vital basis for consensus models of group decision making using preference relations, and includes two subproblems: individual consistency measure and consensus measure. ...In the analytic hierarchy process (AHP), the decision makers express their preferences using judgement matrices (i.e., multiplicative preference relations). Also, the geometric consistency index is suggested to measure the individual consistency of judgement matrices, when using row geometric mean prioritization method (RGMM), one of the most extended AHP prioritization procedures. This paper further defines the consensus indexes to measure consensus degree among judgement matrices (or decision makers) for the AHP group decision making using RGMM. By using Chiclana et al.'s consensus framework, and by extending Xu and Wei's individual consistency improving method, we present two AHP consensus models under RGMM. Simulation experiments show that the proposed two consensus models can improve the consensus indexes of judgement matrices to help AHP decision makers reach consensus. Moreover, our proposal has two desired features: (1) in reaching consensus, the adjusted judgement matrix has a better individual consistency index (i.e., geometric consistency index) than the corresponding original judgement matrix; (2) this proposal satisfies the Pareto principle of social choice theory.
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