Determination of a Representative Collective Value Function Through a Value Function-Based Consensus-Reaching Process

Consensus-reaching among decision-makers (DMs) is an important prerequisite for effective group decision-making. Determining a collective value function that is recognized by major DMs is new in consensus research. We are approaching this problem by adopting the preference disaggregation analysis (PDA) to construct a novel consensus-reaching process (CRP). More precisely, we define the value function that can restore the preference information of all DMs as the consensus value function, and determine all such value functions by the PDA method. A consensus discriminant model is constructed to determine whether DMs can reach a consensus. Considering the adjustment cost of DMs, the minimum cost consensus model, and the minimum cost inconsistency elimination model, are constructed by introducing estimation errors and 0–1 variables, respectively, thus assisting DMs to reach a consensus. Furthermore, in the process of selecting a representative collective value function from the consensus space for subsequent decision analysis, a lexicographic optimization process is applied to convert the multi-objective programming problem of DMs’ individual requirements for the collective value function into a multi-stage single-objective programming problem. This study provides a new concept of consensus and extends the classic minimum cost consensus model to the case of value functions. Finally, an illustrative example showing the proposed CRP in action is presented, while conducting sensitivity analysis to explore the impact of parameter changes on the model.