AI 中文总结
PEJWAK提出一种轮廓回响自锚定聚合架构，通过几何耦合内生参考实现多准则决策分析，具备可审计性、精确边界行为和对数保留律，介于直接加权与非可加交互模型之间。
AI 中文摘要
PEJWAK被引入为一种用于多准则决策分析的轮廓回响自锚定聚合架构。每个准则在最终聚合之前，与源自同一备选方案的内生参考进行几何耦合，从而在保留准则身份的同时，其表达贡献受到备选方案轮廓的制约。一个通用公式将锚定函数、锚定核、保留指数、贡献系数和外层聚合规则分离开来。典型成员使用加权算术自锚，将每个保留指数设置为相应的准则重要性值，并通过归一化平方根映射推导贡献系数。分析结果确立了连续性、单调性、对角校准、内部性、全域联合连续性、精确边界行为、不可分离性、等权重二元限制中双对称性的失效，以及精确的对数保留律。一项确定性MCDA审计提供了完整的准则级分解、精确的权重稳定性区间和秩转换、贡献规则秩相、集合依赖性诊断以及基于排列的精确秩亲和性分析。典型PEJWAK无需epsilon正则化即可处理精确零值：只要剩余活动分数维持正锚，活动零值仅移除其自身的准则贡献。因此，该架构在直接加权聚合和参数密集的非可加交互模型之间提供了一种可审计的轮廓条件化聚合机制。
英文摘要
PEJWAK is introduced as a profile-echoing self-anchored aggregation architecture for multi-criteria decision analysis. Each criterion is coupled geometrically with an endogenous reference derived from the same alternative before final aggregation, so criterion identity is preserved while its expressed contribution is conditioned by the alternative's profile. A general formulation separates the anchor function, anchoring kernel, retention exponents, contribution coefficients, and outer aggregation rule. The canonical member uses a weighted-arithmetic self-anchor, sets each retention exponent equal to the corresponding criterion-importance value, and derives contribution coefficients through a normalized square-root map. Analytical results establish continuity, monotonicity, diagonal calibration, internality, full-domain joint continuity, exact boundary behavior, nonseparability, failure of bisymmetry in the equal-weight binary restriction, and an exact logarithmic retention law. A deterministic MCDA audit provides complete criterion-level decomposition, exact weight-stability intervals and rank transitions, contribution-rule rank phases, set-dependence diagnostics, and exact permutation-based rank-affinity analysis. Canonical PEJWAK handles exact zeros without epsilon regularization: an active zero removes only its own criterion contribution whenever the remaining active scores sustain a positive anchor. The architecture therefore supplies an auditable profile-conditioned aggregation mechanism between direct weighted aggregation and parameter-intensive nonadditive interaction models.
Comments41 pages, 7 figures. Published in Journal of Decisions and Operations Research, 11(3) (2026), 267-304
Journal refJournal of Decisions and Operations Research 11(3) (2026) 267-304
DOI：10.22105/dmor.2026.581617.2112
