A robust minimum cost consensus model based on social networks considering conflict constraints

In social network group decision-making, the conflicts among decision-makers (DMs) could lead to significant uncertainty regarding the unit adjustment costs, and excessive intra-group conflicts might impact the subsequent implementation of the decision-making solutions. To address these issues, we propose a robust minimum-cost consensus model based on social networks considering conflict constraints. Firstly, we gauge the degree of conflict based on the variance in opinions and the degree of non-symmetric trust between DMs, and construct a comprehensive weight that integrates the conflict relations and trust relations. To better restrict the conflict relationships between DMs, we introduce conflict as a constraint condition into the minimum cost consensus model and use robust optimization methods to handle the uncertainty caused by conflicts on the unit adjustment costs. Finally, the effectiveness and feasibility of the proposed model are demonstrated by taking the water pollution management problem of Poyang Lake as an example, and sensitivity analysis is conducted to uncover the characteristics of the proposed model.