Optimal ranking model of fuzzy preference relations with self-confidence for addressing self-confidence failure

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.