When solving the problem of the minimum cost consensus with asymmetric adjustment costs, decision makers need to face various uncertain situations (such as individual opinions and unit adjustment costs for opinion modifications in the up and down directions). However, in the existing methods for dealing with this problem, robust optimization will lead to overly conservative results, and stochastic programming needs to know the exact probability distribution. In order to overcome these shortcomings, it is essential to develop a novelty consensus model. Thus, we propose three new minimum-cost consensus models with a distributionally robust method. Uncertain parameters (individual opinions, unit adjustment costs for opinion modifications in the up and down directions, the degree of tolerance, and the range of thresholds) were investigated by modeling the three new models, respectively. In the distributionally robust method, the construction of an ambiguous set is very important. Based on the historical data information, we chose the Wasserstein ambiguous set with the Wasserstein distance in this study. Then, three new models were transformed into a second-order cone programming problem to simplify the calculations. Further, a case from the EU Trade and Animal Welfare (TAW) program policy consultation was used to verify the practicability of the proposed models. Through comparison and sensitivity analysis, the numerical results showed that the three new models fit the complex decision environment better.

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Distributionally Robust Optimization Model for a Minimum Cost Consensus with Asymmetric Adjustment Costs Based on the Wasserstein Metric

The sudden COVID-19 epidemic has caused consumers to gradually switch to online shopping, the increasing number of online consumer reviews (OCR) on Web 2.0 sites has made it difficult for consumers and merchants to make decisions by analyzing OCR. Much of the current literature on ranking products based on OCR ignores neutral reviews in OCR, evaluates mostly given criteria and ignores consumers’ own purchasing preferences, or ranks based on star ratings alone. This study aims to propose a new decision support framework for the evaluation and selection of alternative products based on OCR. The decision support framework mainly includes three parts: 1) Data preprocessing: using Python to capture online consumer comments for data cleaning and preprocessing, and extracting key features as evaluation criteria; 2) Sentiment analysis: using Naive Bayes to analyze the sentiment of OCR, and using intuitionistic fuzzy sets to describe the emotion score; 3) Benchmark analysis: a new IFMBWM-DEA model considering the preference of decision makers is proposed to calculate the efficiency score of alternative schemes and rank them according to the efficiency score. Then, the OCR of 15 laptops crawled from JD.com platform is used to prove the usefulness and applicability of the proposed decision support framework in two aspects: on the one hand, the comparison of whether the preference of decision makers is considered, and on the other hand, the comparison with the existing ranking methods. The comparison also proves that the proposed method is more realistic, the recommendations are more scientific and the complexity of the decision is reduced.

Data-driven product ranking: A hybrid ranking approach

Individual opinion is one of the vital factors influencing the consensus in group decision-making, and is often uncertain. The previous studies mostly used probability distribution, interval distribution or uncertainty distribution function to describe the uncertainty of individual opinions. However, this requires an accurate understanding of the individual opinions distribution, which is often difficult to satisfy in real life. In order to overcome this shortcoming, this paper uses a robust optimization method to construct three uncertain sets to better characterize the uncertainty of individual initial opinions. In addition, we used three different aggregation operators to obtain collective opinions instead of using fixed values. Furthermore, we applied the numerical simulations on flood disaster assessment in south China so as to evaluate the robustness of the solutions obtained by the robust consensus models that we proposed. The results showed that the proposed models are more robust than the previous models. Finally, the sensitivity analysis of uncertain parameters was discussed and compared, and the characteristics of the proposed models were revealed.

Xiaohui Zhao

Papers

Robust minimum cost consensus models with aggregation operators under individual opinion uncertainty