Fuzzy preference relation with self-confidence (FPR-SC) uses semantic self-confidence to illustrate the hesitation of experts in affirming given preference values. However, extant ranking derivation methods of FPRs-SC suffer from self-confidence failure problem. Specifically, when the logical operations of self-confidence levels are replaced by algebraic operations on semantic subscripts, the derived rankings may be unstable or independent of the self-confidence. To address this issue, an optimal ranking model of FPR-SC with chance-constrained is proposed and extended to group decision-making. Based on the concept of ‘reliability level’ in parameter estimation, the evaluation information expressed by ‘preference values + self-confidence levels’ is first explained using probability distributions to achieve dimensional unity between qualitative self-confidence and quantitative preference. A multiplicative consistency-driven optimal model is then designed to assess the individuality of self-confidence. Guided by the ‘3σ’ principle, FPR-SC is further replaced by random variables following asymmetric bilateral truncated normal distributions. This transformation captures the inner cognition of individuals during subjective judgment, and ensures effective constraints on the numerical range through the asymmetric design. Finally, motivated by the minimization of information deviation, an FPR-SC optimal ranking model with chance-constrained is constructed, and its effectiveness is verified.

中文翻译：

---

自信心模糊偏好关系最优排序模型


模糊偏好关系与自信 （FPR-SC） 使用语义自信来说明专家在肯定给定偏好值时的犹豫。然而，现有的 FPRs-SC 排名推导方法存在自信心失败问题。具体来说，当自信水平的逻辑运算被语义下标的代数运算所取代时，推导的排名可能不稳定或独立于自信心。针对这一问题，该文提出一种机会约束的FPR-SC最优排序模型，并将其推广到群体决策中。基于参数估计中“可靠性水平”的概念，首先用概率分布解释“偏好值 + 自信心水平”所表达的评价信息，实现定性自信心和定量偏好之间的维度统一。然后设计一个乘法一致性驱动的最优模型来评估自信的个体性。在“3σ”原则的指导下，FPR-SC 在非对称双边截断正态分布之后进一步被随机变量取代。这种转换捕捉了个体在主观判断过程中的内在认知，并通过不对称设计保证了对数值范围的有效约束。最后，以信息偏差最小化为动机，构建了机会约束的FPR-SC最优排序模型，并验证了其有效性。