Three-way decision-based adaptive design scheme evaluation: A constrained circular-Fermatean fuzzy model integrating probabilistic dominance and multiple criteria preferences

Conducting optimal adaptive design scheme evaluation (ADSE) is a critical step in the rapid customization design process of mechanical products. However, existing ADSE methods have several limitations, such as the representations of evaluation information lacking flexible geometric boundedness when describing uncertainty, which fails to reflect the inherent variability in expert evaluations and may lead to evaluation bias; the weight assignment to experts and evaluation criteria mostly relies on subjective assessment, without a quantitative mechanism to measure the reliability of evaluation information; and the rankings of design schemes have the incapacity to quantify decision risks, which weaken the precision of their results. To address these challenges, this paper proposes a three-way decision-based ADSE model, which integrates constrained circular-Fermatean fuzzy (CC-FF) sets, probabilistic dominance relations, and multiple criteria preference fusion. Specifically, a geometrically constrained radius is introduced by the CC-FF sets to bound the uncertainty region, expert reliability is objectively determined from evaluation dispersion through the entropy-based weighting method, and both classification and ranking are enabled by the three-way decision framework with probabilistic dominance relations while decision risks are quantified. Finally, the effectiveness of the proposed method was validated through two practical case studies, and sensitivity analysis and comparative experiments were also conducted to illustrate its rationality and efficacy in identifying optimal schemes.