  The Ordinal Priority Approach (OPA) is a multi-attribute decision-making
(MADM) method to determine the relative importance (weights) of experts,
attributes, and alternatives. This study formally establishes the fundamental
properties of OPA, including solution efficiency, analytical solution
expression, the decomposability of optimal decision weights, and its
relationship with rank-based surrogate weights. Building on these properties,
we propose a Generalized Ordinal Priority Approach (GOPA) based on an
"estimate-then-optimize" contextual optimization framework for MADM when
preference information is incomplete. In the first stage, we derive utility
distributions for ranked alternatives in discrete and continuous prospects by
minimizing cross-entropy utility under partial preference information,
including weak order relations, absolute differences, ratio scales, and lower
bounds. Rank-based surrogate weights and risk preference utility functions
serve as the global utility structure for discrete and continuous prospects,
respectively. The elicited utility information is then introduced into the
second-stage problem to simultaneously optimize the weights of experts,
attributes, and alternatives within a normalized weight space. Metrics for
validating the group decision outcomes of GOPA, including percentage standard
deviation, correlation coefficient, and confidence level measurement, are
proposed. Theoretical analysis reveals several advantageous properties of GOPA,
including model generalizability, analytical solvability, and risk preference
independence. Furthermore, this study provides a lower bound reference for
transforming the general optimization-based weight elicitation problems into
optimization problems with stochastic dominance constraints. The applicability
of GOPA is demonstrated through an improvisational emergency supplier selection
problem.
