Minimum Cost Consensus Model Research Articles

Distributionally Robust Chance Constrained Optimization Model for the Minimum Cost Consensus

As a solution method that not only considers the probability distribution information of data, but also ensures that the results are not too conservative, more and more researches have been made on the distributionally robust optimization method. Based on the minimum cost consensus model, this paper proposes a new minimum cost consensus model with distributionally robust chance constraints (DRO-MCC). Firstly, Conditional Value-at-Risk (CVaR) is used to approximate the chance constraints in the cost model. Secondly, when the information of the first and second moments of random variables affecting the unit adjustment cost are known, the min-max problem is obtained based on the moment method and dual theory, and a tractable semidefinite programming problem can be easily processed through further transformation. Finally, in order to evaluate the robustness of the proposed model, the results of different parameters are compared, and the DRO-MCC is compared with the robust optimization model (RO-MCC) and the minimum cost consensus model (MCC). The example proves that MCC is too optimistic and RO-MCC is too conservative. In contrast, DRO-MCC overcomes the conservatism of robust optimization and considers the probability information of data, so the result is more ideal.

Dual Models and Return Allocations for Consensus Building Under Weighted Average Operators

Recent studies have examined minimum cost consensus models from the moderator’s perspective. However, current dual models aimed at deriving a maximum return have been limited to special cases. A further problem has been the return allocation to the individuals. With this in mind, this article presents two general dual consensus models, the first of which is a minimum cost consensus model, and the second of which allows the different individuals to have different tolerance levels. In both models the individual opinions and the group opinion are connected using a weighted average operator. To understand the economic significance of these models, some properties, such as the weak duality property, the optimality property, and the strong duality property are given. The relationships between the individual opinions, the unit costs, and the unit returns are also proven, and the core return allocation problem is addressed. It was found that in both cases, the costs the moderator needed to pay to a given individual were precisely equal to the returns the individual deserved. Numerical case studies were used to illustrate the proposed models, with the simulation results providing insights into the practical use of these optimization consensus models.

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

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

A Cost Consensus Metric for Consensus Reaching Processes based on a comprehensive minimum cost model

Consensus Reaching Processes (CRPs) have recently acquired much more importance within Group Decision Making real-world problems because of the demand of either agreed or consensual solutions in such decision problems. Hence, many CRP models have been proposed in the specialized literature, but so far there is not any clear objective to evaluate their performance in order to choose the best CRP model. Therefore, this research aims at developing an objective metric based on the cost of modifying experts’ opinions to evaluate CRPs in GDM problems. First, a new and comprehensive minimum cost consensus model that considers distance to global opinion and consensus degree is presented. This model obtains an optimal agreed solution with minimum cost but this solution is not dependent on experts’ opinion evolution. Therefore, this optimal solution will be used to evaluate CRPs in which experts’ opinion evolution is considered to achieve an agreed solution for the GDM. Eventually, a comparative performance analysis of different CRPs on a GDM problem will be provided to show the utility and validity of this cost metric.

Soft consensus cost models for group decision making and economic interpretations

In a group decision-making (GDM) process, experts reach a consensus after discussion and persuasion, which requires a moderator to spend time and resource to persuade experts to change their original opinions. Since a unanimous agreement is hard to achieve and costly, a consensus degree or soft consensus was used and various approaches have been proposed to measure the level of consensus in GDM. Though cost is an important factor in GDM, few works have calculated consensus cost occurred during the process. Moreover, the degree of consensus was not considered in the minimum cost consensus study. The objective of this paper is to propose consensus models under a certain degree of consensus, which considers both consensus degree and cost in GDM. To do this, we develop a generalized soft cost consensus model under a certain degree of consensus, which is built by defining a consensus level function and a generalized aggregation operator. A soft minimum cost consensus model is constructed based on arithmetic weighted average operator (AWAO), and the maximum return model is constructed through its dual model. The cost (compensation) is studied from both the perspectives of a moderator and individual experts. The relationships between the two soft consensus cost models are analyzed, and the economic significance of the models are also discussed. Numerical examples are used to explain the proposed models. In addition, to show the usability of the proposed models in real-world context, we apply the proposed models to a loan consensus scenario using data from an online peer-to-peer lending platform.

The optimization-based aggregation and consensus with minimum-cost in group decision making under incomplete linguistic distribution context

In real decision making, due to the limitation of knowledge, problem complexity and time pressure, it is natural that decision makers express their opinions with incomplete linguistic information. This paper developed a novel consensus model for group decision making (GDM) with incomplete linguistic distribution assessments (ILDAs). Firstly, we defined the concept of ILDAs and the consensus measure for GDM with ILDAs. Then, we presented a consensus-oriented aggregation model, which can obtain a collective opinion with maximum consensus, and further developed a minimum-cost consensus model with variable unit consensus cost. Following this, based on the proposed aggregation and consensus models, we proposed a novel consensus reaching process for GDM with ILDAs. Finally, a numerical example is conducted to demonstrate the validity of the proposed consensus reaching process.

Modeling the minimum cost consensus problem in an asymmetric costs context

The unit costs of up- and down-adjustments are not equal in some real-life minimum cost consensus (MCC) problems, such as when each individual has two different cost coefficients that depend on the adjustment direction of his/her opinion. To solve these problems, the MCC model with directional constraints (MCCM-DC) is constructed on the basis of goal programming theory and the rectilinear distance function. To analyse the impact of individuals’ limited compromises and tolerance behaviors on the consensus modeling, we further develop the ε-MCCM-DC and the threshold-based (TB)-MCCM-DC. Then, the relationships and transformation conditions of these models are investigated. Furthermore, the validity of the proposed models is demonstrated by the case of trans-boundary pollution control negotiations in China’s Taihu Lake Basin. The analysis results show the following: First, the consensus opinion obtained from MCCM-DC is more inclined to the lower cost direction, and its total consensus costs will no longer ascend after reaching a critical point with the increase of unit adjustment costs. Second, the optimal solution of MCCM-DC is the lower bound of ε-MCCM-DC and the upper bound of TB-MCCM-DC. Compared with consensus models without directional constraints, the proposed models can obtain a better consensus opinion at lower costs due to the flexibility in adjusting individual opinions and can also characterize the MCC problems in a more realistic way.

A Modified Consensus-Building Methodology for Reaching a Group Decision Using Minimum Costs

This paper presents a methodology for building a consensus among the stakeholders based on the level of importance of each evaluation criterion to choose the best final design, approach, or solution for a project. The proposed methodology adopts an improved vague set minimum-cost consensus model (MCCM) and a modified Delphi method. This paper discusses several shortcomings of the traditional MCCM and the Delphi method. It argues that humans’ resistance to change based on a numerical rating scale follows a natural logarithm pattern instead of a linear or quadratic pattern as claimed in other studies. Hence, the traditional MCCM needs to be revised accordingly. In addition, an experiment was concluded to compare the proposed consensus-building methodology with the traditional Delphi method. The experiment showed that the proposed methodology is better than the traditional Delphi method regarding using fewer rounds to reach a consensus. At last, this paper applies the proposed methodology to the field of road junction design selection.

Minimum cost consensus models based on random opinions

Abstract 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.

Modified Delphi-AHP Method Based on Minimum-Cost Consensus Model and Vague Set Theory for Road Junction Control Method Evaluation Criteria Selection

Group decision making is an important symbol of a democratic society. It helps to explore problems from wider angles and the results generated will usually be widely accepted by the public. Yet, there are drawbacks of group decision making. It usually takes more time and resources than individual decision making and also sometimes the one with a louder voice will dominate the discussion. In this paper, a group decision making framework derived that are based on the modified Delphi-AHP method based on minimum-cost consensus model (MCCM) and vague set theory is proposed to gather different experts' opinions on the evaluation criteria and their relative importance for choosing a suitable road junction control method in a multi- objectives environment. It is believed that the proposed framework can help to strengthen the advantages and to solve the above drawbacks of group decision making. A numerical case study is proposed to demonstrate the use of this framework. 

Maximum expert consensus models with linear cost function and aggregation operators

In group decision making problems, consensus is a very important issue for the aggregation of individual opinions. Based on the concept of maximum expert consensus model (MECM), this paper incorporates aggregation operators into the MECM, and proposes a novel framework of MECM. When the aggregation operator is set to be the weighted averaging operator or the ordered weighed averaging (OWA) operator, this paper equivalently transforms the MECM into mixed 0–1 linear programming problems. Additionally, this paper also shows that the minimum cost consensus model under the OWA operator with any weights can be similarly transformed into a mixed 0–1 linear programming problem. Numerical examples and a comparison analysis are used to demonstrate the validity of the proposed model.

Minimum-Cost Consensus Models Under Aggregation Operators

In group decision making, consensus models are decision aid tools and help experts modify their individual opinions to reach a closer agreement. Based on the concept of minimum-cost consensus, this paper proposes a novel framework to achieve minimum-cost consensus under aggregation operators. Analytical results indicate that the proposed framework reduces to the consensus model of Ben-Arieh <etal xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> when the selected aggregation operator is the ordered weighted averaging (OWA) operator with weight vector <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(1/2, \ldots, 0, \ldots, 1/2)^{T}$</tex> </formula> . Furthermore, this paper closely examines the minimum-cost consensus models with a linear cost function under the common aggregation operators (e.g., the weighted averaging operator and the OWA operator). Linear-programming-based approaches are also developed to solve these models. The results of this paper significantly contribute to efforts to develop the consensus model of Ben-Arieh <etal xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/>