PEJWAK: A Profile-Echoing Self-Anchored Aggregation Architecture for Multi-Criteria Decision Analysis

Abstract

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.