Abstract: In uncertain linguistic environments, multi-attribute decision-making (MADM) problems often face challenges such as fuzzy linguistic evaluation information and dynamically changing psychological behaviors of decision-makers. Existing approaches have deficiencies in simultaneously addressing the logical consistency of linguistic evaluation information, the correlation among attributes, and the impact of risk preferences on decision outcomes. Particularly when the linguistic term set is incomplete and decision-makers exhibit behavioral characteristics such as reference dependence and loss aversion, the traditional VIKOR approach shows significant limitations in reaching group consensus and obtaining compromise solutions. To address these issues, an improved VIKOR MADM approach that integrates linguistic truth-valued lattice implication algebra and prospect theory is constructed. First, based on linguistic truth-valued lattice implication algebra, a set of operational rules for linguistic terms with logical semantics is constructed to resolve the fuzziness of linguistic evaluation information. Second, the value function of prospect theory is introduced to establish a prospect value matrix that captures the psychological behaviors of decision-makers. Then, an improved VIKOR approach is employed to compute the group compromise solution, balancing the maximization of group utility and the minimization of individual regret. Finally, a case study is conducted to verify the feasibility and effectiveness of the proposed approach, and comparative analyses with existing decision-making methods are performed to discuss its advantages. The results demonstrate that, compared with existing MADM approaches, the proposed approach can more comprehensively handle the uncertainty of linguistic information while taking into account the psychological preferences of decision-makers.

Key words: linguistic truth-valued lattice implication algebra, prospect theory, VIseKriterijumska Optimizacija I Kompromisno Resenje(VIKOR), multi-attribute decision-making

摘要： 在不确定性语言环境下,多属性决策问题常面临语言评价信息模糊, 决策者心理行为动态变化等挑战. 现有方法在兼顾语言评价信息的逻辑一致性, 属性关联性及风险偏好对决策结果的影响方面存在不足. 特别是当语言术语集不完备, 决策者表现出参考点依赖与损失规避等行为特征时, 传统VIKOR方法在群体共识达成与妥协解求解方面存在明显局限性. 针对上述问题, 可构建一种融合语言真值格蕴涵代数和前景理论的改进VIKOR多属性决策方法. 首先, 基于语言真值格蕴涵代数构建具有逻辑语义的语言术语运算规则, 以解决语言评价信息的模糊性问题. 其次, 引入前景理论的价值函数, 建立考虑决策者心理行为的前景价值矩阵. 然后, 通过改进的VIKOR方法计算群体妥协解, 平衡最大化群体效用值与最小化个体遗憾值. 最后, 通过案例分析验证所提方法的可行性与有效性, 并与现有决策方法对比分析讨论其优势. 结果表明, 相较于现有多属性决策方法, 该方法能够更全面地处理语言信息的不确定性, 同时兼顾决策者的心理偏好.

关键词: 语言真值格蕴涵代数, 前景理论, 多准则妥协解排序法, 多属性决策