Minimum cost consensus models based on random opinions

In some complex group decision making cases, the opinions of decision makers (DMs) present random characteristic. However, it is difficult to determine the range of opinions by knowing only their probability distributions. In this paper, we construct cost consensus models with random opinions. The objective function is obtaining the minimum consensus budget under a certain confidence level. Nonetheless, the constraints restrict the upper limit of the consensus cost, the lower limit of DMs’ compensations, and the opinions deviation between DMs and the moderator. As such, probabilistic planning based on a genetic algorithm is designed to resolve the minimum cost consensus models based on China’s urban demolition negotiation, which can better simulate the consensus decision-making process and obtain a satisfactory solution for the random optimization consensus models. The proposed models generalize both Ben-Arieh’s minimum cost consensus model and Gong’s consensus model with uncertain opinions. Considering that the opinions of DMs and the moderator obey various distributions, the models simulate the opinion characteristics more effectively. In the case analysis, a sensitivity analysis method is adopted to obtain the minimum budget, and probabilistic planning based on genetic algorithm to obtain a satisfactory solution that is closer to reality.     

A web based consensus support system for group decision making problems and incomplete preferences

Reaching a high level of consensus among experts is critical in group decision making problems. Usually, it is the moderator task to assure that the consensus process is carried out properly and, if possible, to offer recommendations to the expert in order to change their opinions and narrow their differences.In this paper we present an implemented web based consensus support system that is able to help, or even replace, the moderator in a consensus process where experts are allowed to provide their preferences using one of many types (fuzzy, linguistic and multi-granular linguistic) of incomplete preference relations.This system is based on both consistency and consensus measures and it has been designed to provide advice to the experts to increase group consensus level while maintaining the individual consistency of each expert. The consistency measures are characterized by and computed using uninorm operators. When appropriate, the system also helps experts to reduce the incompleteness of their preference relations. The web interface allows to carry out distributed consensus processes and thus, experts do not necessarily need to physically meet together.     

The minimum cost consensus model considering the implicit trust of opinions similarities in social network group decision-making

The social network group decision-making is popular due to the advantages of social relationships in the consensus reaching process, especially the trust relationships. To explore the effects of trust on consensus, some minimum cost consensus models are proposed based on implicit trust between individuals and the moderator. The implicit trust is computed based on the similarity of opinions and it is implied into the traditional minimum cost consensus model to obtain a new quadratic programming problem and the related dual problem. The weights of individuals can be determined based on implicit trust and can be used to modify the possible deviations among individuals’ adjustment costs. A numerical example and the comparative analysis are given to analyze the effectiveness of the proposed models, which suggests that individuals are willing to give up some benefit to reach consensus due to their implicit trust to the moderator and make minor revisions to their adjustment costs due to their implicit trust to each other.     

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 consensus based group decision making methodology for strategic selection problems of supply chain coordination

In a supply chain (SC), the partners often make collective decisions to solve a number of problems which are characterized by various quantitative and qualitative criteria. This article presents a fuzzy TOPSIS and soft consensus based group decision making methodology to solve the multi-criteria decision making (MCDM) problems in supply chain coordination, i.e., selection problems. This methodology is proposed to improve the coordination in decentralized supply chains, i.e., supply chains that comprise several independent, legally separated entities with their own decision authorities. In order to address the imprecision of supply chain partners in formulating the preference value of various criteria, a fuzzy TOPSIS based methodology is proposed. Moreover, a soft consensus based group decision making approach is used for consensus forming among the supply chain partners, regarding the preference values of various criteria for different alternatives. Correlation coefficient and standard deviation (CCSD) based objective weight determination method is also used for enumeration of the weights of the criterion for fuzzy TOPSIS. To demonstrate the applicability of proposed methodology, an illustrative example has been presented.     

Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks

Two processes are necessary to solve group decision making problems: a consensus process and a selection process. The consensus process is necessary to obtain a final solution with a certain level of agreement between the experts, while the selection process is necessary to obtain such a final solution. Clearly, it is preferable that the set of experts reach a high degree of consensus before applying the selection process. In order to measure the degree of consensus, different approaches have been proposed. For example, we can use hard consensus measures, which vary between 0 (no consensus or partial consensus) and 1 (full consensus), or soft consensus measures, which assess the consensus degree in a more flexible way. The aim of this paper is to analyze the different consensus approaches in fuzzy group decision making problems and discuss their advantages and drawbacks. Additionally, we study the future trends.     

Consensus evolution networks: A consensus reaching tool for managing consensus thresholds in group decision making

The consensus reaching process (CRP) is a critical part of group decision making (GDM). In order to explore the evolution of consensus, a new CRP tool is proposed based on consensus evolution networks (CENs). The CENs are built based on the consensus degrees among decision makers (DMs) and allow us to manage the consensus thresholds and its evolution. A new consensus index is introduced based on the structured and numerical aspects of the CENs. The new consensus index can not only deeply analyze the constitution of consensus, but also determine the weights of DMs. According to the clustering coefficient, the sensitive consensus threshold is identified and the sensitive consensus evolution network (SCEN) is built. Based on the complementary SCEN, a pairwise feedback adjustment method is proposed to improve consensus. Besides, the sparsity of the CENs can act as a reference to determine the agreed consensus thresholds, which is considered an important issue in traditional models. A numerical example is used to verify the usefulness of the proposed CRP tool. The numerical results show that the evolution of consensus can be clearly found based on CENs and the pairwise method can improve consensus in only four rounds.     

Intelligent multi-stakeholder environmental management

In any group decision making, stakeholders have different powers, proficiency and also experiences. These power weights are very difficult to obtain, because group managers avoid revealing the relative powers of the stakeholders to prevent more conflict among them. Therefore, in many studies, the different powers have not been well accounted and then equal power weights have been assigned to each stakeholder. This paper will show that considering the powers is necessary and then it introduces a new intelligent approach to obtain consensus based relative power weights. This method is based on the opinions of the stakeholders on the alternatives. A case study of watershed management is used to illustrate the application of the model to a real decision making problem. A suitable aggregation operator is also used to combine the goodness measures, considering the optimism/pessimism view of the group manager. Results indicate that obtaining the stakeholders’ weights and also considering the preferences of the group manager on the risk are essential parts for soft group decision making process, especially in the environmental management problems.     

Two-stage stochastic minimum cost consensus models with asymmetric adjustment costs

When dealing with consensus cost problems with asymmetric adjustment costs, the uncertain scenarios with certain probabilities which are becoming a serious problem decision-makers have to face. However, existing optimization-based consensus models have failed to consider uncertain factors that could influence the final consensus and total consensus cost. In order to better deal with these issues, it is necessary to develop practical consensus optimal models. Thus, we establish three two-stage stochastic minimum cost consensus models with asymmetric adjustment costs that may eventually lead the way to better consensus outcomes. The impact of uncertain parameters (such as individual opinions, unit asymmetric adjustment costs, compromise limits, cost-free thresholds) are investigated by modeling three kinds of uncertain consensus models. We solve the proposed two-stage stochastic consensus problem iteratively using the L-shaped algorithm and show the convergence of the algorithm. Furthermore, a case of pollution control negotiations verifies the practicability of the proposed models. Moreover, the comparison of results with the L-shaped algorithm and CPLEX shows that the L-shaped algorithm is more effective in solving time. Some discussions and comparisons on local and global sensitivity analysis of the uncertain parameters are presented to reveal the features of the proposed models. Finally, the relationships between the minimum cost consensus model and minimum cost consensus models with asymmetric adjustment costs and the proposed models are also provided.     

A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvement of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement.     

基于深度学习特征提取与多目标优化集成修剪的选择性集成学习软测量方法

集成学习已成为一种广泛使用的软测量建模框架,但是建立高性能的集成学习软测量模型依然面临特征选择不当、基模型多样性不足、基模型估计性能不佳等诸多挑战.为此,提出一种基于堆栈自编码器多样性生成机制的选择性集成学习高斯过程回归(selective ensemble of stacked autoencoder based Gaussian process regression, SESAEGPR)软测量建模方法.该方法充分发挥深度学习在特征提取方面的优势,通过构建多样性的堆栈自编码器(stacked autoencoder, SAE)网络,建立基于隐特征的高斯过程回归(Gaussian process regression, GPR)基模型.基于模型性能提升率和进化多目标优化对SAEGPR基模型实施两次集成修剪,以降低集成模型复杂度、保持甚至进一步提升模型估计性能,最后,引入PLS Stacking集成策略实现基模型融合.所提出方法显著优于传统全局和全集成软测量建模方法,其有效性和优越性通过青霉素发酵过程和Tennessee Eastman化工过程得到验证.     

虚拟手术中软组织切割模型研究进展*

虚拟手术仿真训练系统是虚拟现实的重要应用,能够克服真实传统手术中资源少、训练不方便和可重复操作性差等问题。软组织切割是虚拟手术仿真训练系统中的重要组成部分,也是手术中最常见的操作。软组织切割模型建立的质量如何,直接决定了虚拟手术仿真的精度度和仿真度。为更好地对软组织切割模型进行深入探索,分析了虚拟手术仿真中软组织切割的研究难点。针对当前十四种有代表性的切割模型进行了研究,在此基础上对这些模型的优缺点进行了比较,并对软组织切割模型的发展趋势进行了展望。     

基于GrC的信息系统软规则及其度量关系的研究

粒计算(GranularComputing,简称GrC)是一种新的软计算方法。该文利用信息颗粒的位表示(BitRepresenta-tions)来进行信息系统软规则及其度量之间关系的研究。具体地,首先利用软规则对关联规则、决策规则、函数依赖之间的关系进行了分析,然后对关联规则度量、决策规则度量、外延的函数依赖度量的关系进行了研究,并且建立了这些度量的统一模型。     

Consensus reaching models of linguistic preference relations based on distance functions

In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable to develop a consensus process prior to the selection process. This paper proposes two consensus models with linguistic information to support the GDM consensus reaching process. Two different distance functions between linguistic preference relations are introduced to measure both individual consistency and group consensus. Based on these measures, the consensus reaching models are developed. The two models presented have the same concept that the expert whose preference is farthest from the group preference needs to update their opinion according to the group preference relation. In addition, the convergence of the models is proved. After achieving the predefined consensus level, each expert’s consistency indexes are still acceptable under the condition that the initial preference relations are of satisfactory consistency. Finally, an example is given to show the effectiveness of the models and to verify the theoretical results.     

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.     

A consensus model for multiperson decision making with different preference structures

In this paper, we present a consensus model for multiperson decision making (MPDM) problems with different preference structures based on two consensus criteria: 1) a consensus measure which indicates the agreement between experts' opinions and 2) a measure of proximity to find out how far the individual opinions are from the group opinion. These measures are calculated by comparing the positions of the alternatives between the individual solutions and collective solution. In such a way, the consensus situation is evaluated in each moment in a more realistic way. With these measures, we design a consensus support system that is able to substitute the actions of the moderator. In this system, the consensus measure is used to guide the consensus process until the final solution is achieved while the proximity measure is used to guide the discussion phases of the consensus process. The consensus support system has a feedback mechanism to guide the discussion phases based on the proximity measure. This feedback mechanism is based on simple and easy rules to help experts change their opinions in order to obtain a degree of consensus as high as possible. The main improvement of this consensus model is that it supports consensus process automatically, without moderator, and, in such a way, the possible subjectivity that the moderator can introduce in the consensus process is avoided.     

基于多样性加权相似度的集成局部加权偏最小二乘软测量建模

针对传统即时学习软测量方法仅考虑单一的相似度函数,难以有效处理复杂工业过程中的非线性特性,从而导致模型预测性能受限的问题,提出了一种基于多样性加权相似度（DWS）的集成局部加权偏最小二乘（LWPLS）软测量建模方法.首先采用随机子空间法和高斯混合聚类,构建一组多样性的训练样本子集;然后通过偏最小二乘回归分析确定输入特征权值,从而定义一组多样性加权相似度函数.在线实施阶段,对于任意的查询样本,基于多样性的相似度指标,可建立一组多样性的LWPLS软测量模型,随后引入集成学习策略实现难测变量的融合预测.在数值例子和脱丁烷塔过程中的应用结果表明了该方法的有效性.     

The relationship among soft sets,soft rough sets and topologies

Molodtsov’s soft set theory is a newly emerging tool to deal with uncertain problems. Based on the novel granulation structures called soft approximation spaces, Feng et al. initiated soft rough approximations and soft rough sets. Feng’s soft rough sets can be seen as a generalized rough set model based on soft sets, which could provide better approximations than Pawlak’s rough sets in some cases. This paper is devoted to establishing the relationship among soft sets, soft rough sets and topologies. We introduce the concept of topological soft sets by combining soft sets with topologies and give their properties. New types of soft sets such as keeping intersection soft sets and keeping union soft sets are defined and supported by some illustrative examples. We describe the relationship between rough sets and soft rough sets. We obtain the structure of soft rough sets and the topological structure of soft sets, and reveal that every topological space on the initial universe is a soft approximating space.     

常压塔柴油凝点动态软测量模型的研究

研究了某炼油厂常压塔三线柴油凝点的软测量建模问题。分析了影响柴油凝点的多种因素,并充分利用仪表分析值提供的被测变量历史信息,建立了一种神经网络和kvinson预测器相结合的动态软测量模型,该模型消除了分析值存在纯滞后的影响。针对某炼油厂常压塔三线柴油凝点的软测量,对该模型进行了验证。仿真研究表明,该模型的预报准确性要优于静态软测量模型,取得了较好的预测效果。     

Improved Decision Neural Network (IDNN) based consensus method to solve a multi-objective group decision making problem

Multi-criterion frameworks involving several subjective and quantitative factors that allow the complexity of Group Decision Making (GDM) to get worsen, especially for those problems which are having strategic dimensions. Recently, integration of multi-attribute utility theory (MAUT) and feed-forward neural network have been studied with a view to facilitate the automation of GDM. In this paper Improved Decision Neural Network (IDNN) based methodology has been developed to solve the multi-criterion decision problem in GDM. Reductions in the training data set, exploitation of indirect methods like multiplicative preference relation during the training process, and reduced number of iterations to map the MAUF are the advantages of this novel methodology. In this research, a soft consensus based group decision making methodology under linguistic assessments have been adopted for consensus forming among the groups.