A social network based approach for consensus achievement in multiperson decision making

Nowadays we are living the apogee of the Internet based technologies and consequently web 2.0 communities, where a large number of users interact in real time and share opinions and knowledge, is a generalized phenomenon. This type of social networks communities constitute a challenge scenario from the point of view of Group Decision Making approaches, because it involves a large number of agents coming from different backgrounds and/or with different level of knowledge and influence. In these type of scenarios there exists two main key issues that requires attention.Firstly, the large number of agents and their diverse background may lead to uncertainty and or inconsistency and so, it makes difficult to assess the quality of the information provided as well as to merge this information. Secondly, it is desirable, or even indispensable depending on the situation, to obtain a solution accepted by the majority of the members or at least to asses the existing level of agreement. In this contribution we address these two main issues by bringing together both decision Making approaches and opinion dynamics to develop a similarity-confidence-consistency based Social network that enables the agents to provide their opinions with the possibility of allocating uncertainty by means of the Intuitionistic fuzzy preference relations and at the same time interact with like-minded agents in order to achieve an agreement.     

A consistency and consensus based decision support model for group decision making with multiplicative preference relations

In group decision making (GDM) with multiplicative preference relations (also known as pairwise comparison matrices in the Analytical Hierarchy Process), to come to a meaningful and reliable solution, it is preferable to consider individual consistency and group consensus in the decision process. This paper provides a decision support model to aid the group consensus process while keeping an acceptable individual consistency for each decision maker. The concept of an individual consistency index and a group consensus index is introduced based on the Hadamard product of two matrices. Two algorithms are presented in the designed support model. The first algorithm is utilized to convert an unacceptable preference relation to an acceptable one. The second algorithm is designed to assist the group in achieving a predefined consensus level. The main characteristics of our model are that: (1) it is independent of the prioritization method used in the consensus process; (2) it ensures that each individual multiplicative preference relation is of acceptable consistency when the predefined consensus level is achieved. Finally, some numerical examples are given to verify the effectiveness of our model.     

A consensus model for group decision making problems with linguistic interval fuzzy preference relations

Sometimes, we find decision situations in which it is difficult to express some preferences by means of concrete preference degrees. In this paper, we present a consensus model for group decision making problems in which the experts use linguistic interval fuzzy preference relations to represent their preferences. This model is based on two consensus criteria, a consensus measure and a proximity measure, and on the concept of coincidence among preferences. We compute both consensus criteria in the three representation levels of a preference relation and design an automatic feedback mechanism to guide experts in the consensus reaching process.     

Consensus building in multiperson decision making with heterogeneous preference representation structures: A perspective based on prospect theory

Multiperson decision making (MPDM) models with heterogeneous preference representation structures have initiated by Chiclana et al. In this study, we propose a novel framework for MPDM problems with heterogeneous preference representation structures. This framework takes the decision makers’ psychological behaviors into consideration and is based on the prospect theory, which is one of the most influential psychological behavior decision theories. In this framework, the heterogeneous preference representation structures are all transformed into preference orderings. The preference-approval structures are introduced to determine the reference points in prospect theory, and then the prospect value function is used to obtain individual and collective prospect values. Finally, based on the prospect values and preference-approval structures, we propose the two-step feedback adjustment rules, which will adjust both the preference evaluations and the preference-approval information, to help the decision makers reach higher consensus degree. Further, we find that there are two significant observations in this framework: (1) the uses of different reference points will yield different outputs of the selection process in MPDM; (2) compared with only adjusting the preference evaluations in the existing studies, the pace of consensus reaching will be accelerated in adjusting both the preference evaluations and the preference-approval information.     

An optimization approach to multiperson decision making based on different formats of preference information

Multiperson decision making (MPDM) problems with different formats of preference information are one of the emerging research areas in decision analysis. Existing approaches for dealing with different preference formats tend to be unwieldy. This paper proposes a new method to solve the problem, in which the preference information on alternatives provided by experts can be represented in four different formats, namely: 1) utility values; 2) preference orderings; 3) multiplicative preference relations; and 4) fuzzy preference relations. An optimization model is constructed to integrate the four formats of preference and to assess ranking values of alternatives. The model is shown to be theoretically sound and complete via a series of theorems, and then a corresponding algorithm is developed. A numerical example is given to illustrate the procedure. The proposed approach is more efficient and simpler than existing approaches because it does not need to unify different formats of preferences or to aggregate individual preferences into a collective one. Therefore, it overcomes a major shortcoming of existing approaches that lose or distort the original preference information in the process of unifying the formats.     

Two flexibility degrees-driven consensus model in group decision making with intuitionistic fuzzy preference relations

A group of experts are commonly invited to find an optimal solution to a complex decision making problem. When the bipolarity of decision information should be considered in group decision making (GDM), intuitionistic fuzzy values (IFVs) have the capability to model such opinions of decision makers (DMs). This paper develops a consensus model in GDM under intuitionistic fuzzy environments with flexibility. First, it is assumed that the initial opinions of DMs are expressed as intuitionistic fuzzy preference relations (IFPRs). A novel additive consistency index is constructed to measure the deviation degree of IFPRs from fuzzy preference relations (FPRs) with additive consistency, where the non-determinacy degree of IFPRs is incorporated. The thresholds of the proposed index corresponding to IFPRs with acceptable additive consistency are discussed and computed. Second, the consensus level of DMs is defined using the similarity degree between two IFVs. An optimization problem is established by maximizing the fitness function, which is constructed by linearly combining the proposed additive consistency index and consensus level. Two flexibility degrees are offered to each DM such that the initial opinions with the bipolarity can be adjusted correspondingly. Third, individual IFPRs in GDM are optimized using the particle swarm optimization (PSO) algorithm. Numerical examples are carried out to illustrate the proposed consensus model by comparing with the existing ones. The obtained results reveal that the proposed additive consistency index can reflect the inherent property of IFPRs. Different with the previous studies, two original flexibility degrees are proposed to characterize the multi-granularity of decision information in GDM.     

An equilibrium theory for multiperson decision making with multiple probabilistic models

This paper develops an equilibrium theory for two-person two-criteria stochastic decision problems with static information patterns, wherein the decision makers (DM's) have different probabilistic models of the underlying process, the objective functionals are quadratic, and the decision spaces are general inner-product spaces. Under two different modes of decision making (viz. symmetric and asymmetric), sufficient conditions are obtained for the existence and uniqueness of equilibrium solutions (stable in the former case), and in each case a uniformly convergent iterative scheme is developed whereby the equilibrium policies of the DM's can be obtained by evaluating a number of conditional expectations. When the probability measures are Gaussian, the equilibrium solution is linear under the symmetric mode of decision making, whereas it is generically nonlinear in the asymmetric case, with the linear structure prevailing only in some special cases which are delineated in the paper.     

Optimal consensus models for group decision making under linguistic preference relations

This paper proposes an optimal consensus model to derive weights for linguistic preference relations (LPRs). Two indexes, an individual‐to‐group consensus index (ICI) and a collective consensus index (CCI), are introduced. An iterative algorithm is presented to describe the consensus reaching process. By changing the weights and modifying a pair of individuals' comparison judgments—which have largest deviation value to the group judgments—the consensus reaching process can terminate, while both ICI and CCI are controlled with predefined thresholds. The algorithm aims to preserve the decision makers’ original information as much as possible. The model and algorithm are then extended to handle the uncertain additive LPRs. Finally, two examples are given to show the effectiveness of the proposed methods.     

An influence-driven feedback system for preference similarity network clustering based consensus group decision making model

Consensus group decision making (CGDM) allows the integration within this area of study of other advanced frameworks such as Social Network Analysis (SNA), Social Influence Network (SIN), clustering and trust-based concepts, among others. These complementary frameworks help to bridge the gap between their corresponding theories in such a way that important elements are not overlooked and are appropriately taken into consideration. In this paper, a new influence-driven feedback mechanism procedure is introduced for a preference similarity network clustering based consensus reaching process. The proposed influence-driven feedback mechanism aims at identifying the network influencer for the generation of advices. This procedure ensures that valuable recommendations are coming from the expert with most similar preferences with the other experts in the group. This is achieved by adapting, from the SIN theory into the CGDM context, an eigenvector-like measure of centrality for the purpose of: (i) measuring the influence score of experts, and (ii) determining the network influencer. Based on the initial evaluations on a set of alternatives provide by the experts in a group, the proposed influence score measure, which is named the σ-centrality, is used to define the similarity social influence network (SSIN) matrix. The σ-centrality is obtained by taking into account both the endogenous (internal network connections) and exogenous (external) factors, which means that SSIN connections as well as the opinion contribution from third parties are permitted in the nomination of the network influencer. The influence-driven feedback mechanism process is designed based on the satisfying of two important conditions to ensure that (1) the revised consensus degree is above the consensus threshold and that (2) the clustering solution is improved.     

A new consensus model for group decision making using fuzzy ontology

Involving many people in decision making does not guarantee success. In practice, there are always individuals who try to exert pressure in order to persuade others who could easily be influenced. In these situations, classical group decision making models fail. Thus, there is still the necessity of developing tools to help users reach collective decisions as if they participated in a real face to face meeting. In such a way, a proper negotiation process can lead to successful solutions. Therefore, we propose a new consensus model to deal with the psychology of negotiation by using the power of a fuzzy ontology as weapon of influence in order to improve group decision scenarios making them more precise and realistic. In addition, the use of a fuzzy ontology gives us the possibility to take into account large sets of alternatives.     

A consistency model for group decision making problems with interval multiplicative preference relations

The main aim of this paper is to present a consistency model for interval multiplicative preference relation (IMPR). To measure the consistency level for IMPR, a referenced consistent IMPR of a given IMPR is defined, which has the minimum logarithmic distance from the given IMPR. Based on the referenced consistent IMPR, the consistency level of an IMPR can be measured and an IMPR with unacceptable consistency can be adjusted by a proposed algorithm such that the revised IMPR is of acceptable consistency. A consistency model for group decision making (GDM) problems with IMPRs is proposed to obtain the collective IMPR with highest consistency level. Numerical examples are provided to illustrate the validity of the proposed approaches in decision making.     

Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations

Compatibility is a very efficient tool for measuring the consensus level in group decision making (GDM) problems. The lack of acceptable compatibility can lead to unsatisfied or even incorrect results in GDM problems. Preference relations can be given in various forms, one of which called intuitionistic multiplicative preference relation is a new developed preference structure that uses an unsymmetrical scale (Saaty's 1–9 scale) to express the decision maker's preferences instead of the symmetrical scale in an intuitionistic fuzzy preference relation. This new preference relation can reflect our intuition more objectively. In this paper, we first develop some compatibility measures for intuitionistic multiplicative values and intuitionistic multiplicative preference relations in GDM. Their desirable properties are also studied in detail. Furthermore, based on compatibility measures, we further develop two different consensus models with respect to intuitionistic multiplicative preference relations for checking, reaching and improving the group consensus level. Finally, a numerical example is given to illustrate the effectiveness of our measures and models.     

A discrete consensus support model for multiple attribute group decision making

In multiple attribute group decision making (MAGDM), it is preferable that the set of experts reach a high degree of consensus amongst their opinions before applying a selection process. In this paper, we present a discrete model to support the consensus reaching process for MAGDM problems. Firstly, a consensus scheme for a set of arguments is provided, where the basic idea is to tighten the range of opinions amongst experts. Based on the well-defined scheme, a convergent algorithm is presented to autocratically guide experts to reach a predefined consensus level. In the selection process, the maximizing deviation method is applied to determine the attribute weights. Then, the choice of the best alternative(s) from the group decision matrix is obtained by the simple additive weighting method. Finally, one example is presented to show the application and effectiveness of the proposed model.     

Adaptive consensus support model for group decision making systems

In this paper, we present an adaptive consensus support model for group decision making systems based on intervals of linguistic 2-tuples. The proposed method has the following advantages: (1) the evaluating values can either be represented by linguistic terms or intervals of linguistic terms, (2) if the required consensus degree is too high, then the proposed adaptive consensus support model can modify experts’ preferences to improve convergence toward a higher consensus degree or a sufficient agreement for group decision making and (3) the proposed method is an interactive method, where each expert can modify the adjustments made by the system during the consensus reaching process if he/she does not agree with the adjustments made by the system. The proposed adaptive consensus support model can overcome the drawback of Mata et al.’s method (2009). It provides us with a useful way for adaptive consensus support for group decision making based on intervals of linguistic 2-tuples.     

Minimum cost consensus model for CRP-driven preference optimization analysis in large-scale group decision making using Louvain algorithm

Large-scale group decision-making problems based on social network analysis and minimum cost consensus models (MCCMs) have recently attracted considerable attention. However, few studies have combined them to form a complete decision-making system. Accordingly, we define the satisfaction index to optimize the classical MCCM by considering the effect of the group on individuals. Similarly, we define the consistency index to optimize the consensus reaching process (CRP). Regarding the evolution of the consensus network, the Louvain algorithm is used to divide the entire group into several subgroups to ensure that each subgroup is independent but has strong cohesion. By constructing the MCCM based on the satisfaction index and the optimized consensus-reaching process, the group opinions in each subgroup are ranked to obtain the final ranking of alternatives. Finally, to verify the validity of CRP and the practical value of the proposed model, we conduct consensus network evolution and decision-making analysis in the case of a negotiation between the government and polluting companies to achieve uniform pollution emissions. Sensitivity analysis is performed to demonstrate the stability of the subgroup weights. Furthermore, a comparative analysis using existing models verifies the effectiveness of the proposed model.     

Ratio-based similarity analysis and consensus building for group decision making with interval reciprocal preference relations

Similarity analysis and preference information aggregation are two important issues for consensus building in group decision making with preference relations. Pairwise ratings in an interval reciprocal preference relation (IRPR) are usually regarded as interval-valued And-like representable cross ratios (i.e., interval-valued cross ratios for short) from the multiplicative perspective. In this paper, a ratio-based formula is introduced to measure similarity between a pair of interval-valued cross ratios, and its desirable properties are provided. We put forward ratio-based similarity measurements for IRPRs. An induced interval-valued cross ratio ordered weighted geometric (IIVCROWG) operator with interval additive reciprocity is developed to aggregate interval-valued cross ratio information, and some properties of the IIVCROWG operator are presented. The paper devises an importance degree induced IRPR ordered weighted geometric operator to fuse individual IRPRs into a group IRPR, and discusses the derivation of its associated weights. By employing ratio-based similarity measurements and IIVCROWG-based aggregation operators, a soft consensus model including a generation mechanism of feedback recommendation rules is further proposed to solve group decision making problems with IRPRs. Three numerical examples are examined to illustrate the applicability and effectiveness of the developed models.     

A consensus model for group decision making under trapezoidal fuzzy numbers environment

Natural linguistic terms can preferably express the opinions of decision makers in complicated decision environment. Group decision making with multiplicative trapezoidal fuzzy preference relations transforming from natural linguistic terms attracts the attention of researchers for its important research significant. The developed approach is based on consensus improving process by using a new similarity measure and a trapezoidal fuzzy power ordered weighted geometric averaging (TFPOWGA) operator. In order to introduce this approach, firstly, trapezoidal fuzzy power geometric averaging operator and TFPOWGA operator are presented to aggregate trapezoidal fuzzy numbers (TFNs). Secondly, a new similarity measure for TFNs is introduced by combining centroids and areas of TFNs. We further propose a new consensus improving algorithm that consists of consensus measure and a dynamic feedback mechanism containing a multi-objective optimization model and some indirect rules. And then a selection stage is described to rank the alternatives. At last, an example is implemented to demonstrate effectiveness of the approach.

     

The fusion process with heterogeneous preference structures in group decision making: A survey

In group decision making (GDM), decision makers who have different experiential, cultural and educational backgrounds will naturally provide their preference information by heterogeneous preference structures (e.g., utility values, preference orderings, numerical preference relations and multigranular linguistic preference relations). To date, many studies have discussed GDM problems with heterogeneous preference structures. To provide a clear perspective on the fusion process with heterogeneous preference structures in GDM, this paper presents a review of three types of fusion approaches: the indirect approach, the optimization-based approach and the direct approach. Moreover, with respect to insights gained from prior researches, several open problems are proposed for the future research.     

考虑偏好冲突的多类评价信息群体决策方法

针对偏好具有冲突性且权重信息完全未知的多类评价信息多属性群体决策问题, 提出了一种基于多目标决策的求解方法.首先, 建立以决策方案相对贴近度和决策成员偏好冲突程度为目标的多目标决策模型;然后,利用极小极大方法求解该多目标决策模型,得到各方案的属性权重和决策成员权重,根据计算各个方案的相对贴近度,进而确立方案优劣排序和最优方案; 最后, 通过数值例子的计算分析表明决策方法的有效性和合理性.     

A consensus model for group decision making under interval type-2 fuzzy environment

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.