An ordinal-cardinal consensus adjustment allocation mechanism for large-scale group decision making based on the consistency of distributed preference relations under fuzzy uncertainty

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Large-scale group decision making (LSGDM) problem is common in real life. With the increase in the number of alternatives and the limited rationality of human beings, consistency problem is inevitable when pairwise comparison method is used. We propose an improved consistency calculation approach to generate consistent distributed preference relations (DPRs), which adopts adjacent score intervals to calculate the score intervals of non-adjacent alternative pairs. By using optimization model, the initial DPR is preserved as much as possible on the premise of order consistency. As for the consensus analysis, the concept of relationship-possibility degree is defined to capture the ignorance and fuzzy uncertainty in assessments. An ordinal consensus measure method considering absolute position difference and relative position dissimilarity with relationship-possibility degree is proposed. Ordinal-cardinal consensus adjustment model based on DPR is then constructed to obtain the minimum consensus adjustment of decision makers or subgroups coalition which are considered as coalition payoff. In addition, to distribute the ordinal-cardinal minimum consensus adjustment reasonably, we construct a two-stage consensus adjustment allocation mechanism adopting the improved multi-weighted Shapley function in the cooperative game. Several optimization models are constructed to obtain the adjusted DPRs of decision makers or subgroups. Finally, an illustrative example is presented to demonstrate the validity of the proposed method in dealing with the decision problems of product development engineering. It is expected to make the LSGDM procedure in a more intelligent way.