权重未知的多值中智数群组决策方法

Multi-Valued Neutrosophic Group Decision-Making Method with Unknown Weights

摘要: 针对现有的多值中智集群组决策存在度量选择困难的问题，本文提出了一种综合差异性度量方法。新度量不仅考虑了评判者自身提供决策信息的可靠性，还结合了多值中智数之间的差异性，从而更全面地反映决策信息的质量。在属性权重的计算中，基于综合差异性度量构建优化模型，通过最大化方案评价值与正理想方案的接近程度，同时最小化其与负理想方案的偏离程度，利用Lagrange函数获得最优属性权重。在专家权重的分配中，创新性地引入四分位法，以专家评价值与群体共识基准的差异为依据，实现权重的客观分配。最后，通过属性与专家加权集结得到综合评价值并基于得分函数对方案进行排序。实例表明，所提方法能够显著提升复杂不确定环境下决策的科学性与可靠性。

Abstract: In the field of multi-valued neutrosophic group decision-making, selecting an appropriate measure has been a significant challenge due to the inherent complexity and uncertainty. To address the challenge of selecting an appropriate measure in existing multi-valued neutrosophic group decision-making, this paper proposes a comprehensive difference measure method. The new measure not only considers the reliability of the decision information provided by the evaluators themselves but also integrates the differences between multi-valued neutrosophic numbers, thereby more comprehensively reflecting the quality of the decision information. In the calculation of attribute weights, an optimization model is constructed based on the comprehensive difference measure. By maximizing the proximity of the alternative evaluation value to the positive ideal alternative and minimizing its deviation from the negative ideal alternative, the optimal attribute weights are obtained using the Lagrange function. In the allocation of expert weights, the quartile method is innovatively introduced to achieve objective weight assignment based on the differences between expert evaluation values and the group consensus benchmark. Finally, comprehensive evaluation values are obtained through the weighted aggregation of attributes and experts, and the alternatives are ranked based on the score function. Case studies demonstrate that the proposed method can significantly enhance the scientificity and reliability of decision-making in complex and uncertain environments.