Maximum Fuzzy Consensus Feedback Mechanism With Minimum Cost and Private Interest in Group Decision-Making

In group decision-making, the consensus reaching process (CRP) is usually designed as an interactive discussion and negotiation process to guide decision-makers in modifying their opinions. In CRP, consensus measure may mean agreement among most but not all the decision-makers, and the actual or virtual moderator may provide modification suggestions with his/her own interests besides the consensus-oriented suggestions. With consideration of fuzzy consensus and private interest of the moderator, this article presents two optimal feedback mechanisms with private interest (PIFM), which aim to minimize the consensus cost with an established consensus threshold and maximize the fuzzy consensus measure with a given cost budget. First, the fuzzy consensus measure is defined by means of specificity and coverage of information granule. Then, two PIFMs based on the minimum consensus cost and maximum fuzzy consensus are proposed to obtain the optimal modified individual opinions, and these two PIFMs are equivalently transformed into the mixed 0-1 programming models. In what follows, we develop an interactive CRP based on the proposed PIFMs, where the optimal modified individual opinions are considered as the modification references in the feedback mechanism. Finally, detailed experiment studies are conducted to demonstrate the effectiveness and validity of the proposed methods.