Uncertain cost consensus modeling regarding individual behavior constraints and its application

Abstract

Group decision-making (GDM) mainly solves unstructured decision problems, involving subjective participation of various experts. In general, when solving GDM problems, decision-makers (DMs) eventually form a clear support or objection (i.e., consensus) via multiple rounds of negotiations with consensus cost. However, factors a ecting the consensus reaching process (CRP) normally include the DMs' preference structures, decision environment, the in uence of particular decision roles and etc., making the GDM full of uncertainty and unable to accurately predict the outcome in advance. Thus, a moderator on behalf of the collective interest is often introduced to increase the speed and e ciency of the GDM. Inspired by the minimum cost consensus (MCC) in the literature, this thesis aims to construct a series of new consensus optimization models to address real-life GDM problems from two perspectives of either minimizing the moderator's total cost or maximizing the individual DM's total revenue. In building these new models, we also incorporate diverse behavioral constraints, such as non-cooperation, trade-o of interest and equity or unbalanced adjustment willing. Speci cally, we conduct threefold discussions as follows: (1) Introduce uncertainty theory into the optimal consensus modeling to address unreliable results yielded when the reliability of decisions is determined only by experts due to the absence of su cient historical data. To do that, we use uncertainty distribution and belief degree as a whole to t individual preferences, and further discuss ve scenarios of uncertain chance-constrained MCC models (MCCMs) from the angles of the moderator, individual DMs and non-cooperators. Besides, we provide consensus reaching conditions and the analytic formulae of the minimum total cost through deductions. Finally, the new models are veri ed as an extension of the traditional crisp number or interval preference-based MCCMs with the application of carbon quota negotiation. (2) Extend uncertain MCCMs into the CRP framework by incorporating DM's unbalanced willing of modifying preference and designing a feedback mechanism on both preferences and weights due to democratic consensus. To do that, we build two new consensus optimization models based on the uncertain distance measure: one is to obtain a MCC on account of asymmetric costs, aggregation function and consensus measure; while the other provides a more exible way to solve GDM problems without presetting a consensus level threshold. Moreover, binary variables are used to reduce the calculation complexity resulted from piecewise functions in the new multi-coe cient goal programming models and the feasibility of the new proposal is veri ed by illustrative examples. (3) Inspired by the maximum compensation consensus models transformed from the MCCMs, we build several new consensus optimization models to obtain exible (e.g., optimal or fair) carbon quota allocation schemes within a closed-loop trading system. To solve these new models, a relaxation method based on the PSO algorithm is proposed. Moreover, since the inability to perform real-life GDM usually stems from con icts of interest based on the DMs' mutual competition, we further suggest two strategies to address the unfairness. Numerical results show that su cient interactions among the DMs are of great signi cance in achieving fairness within a trading system.