A more rigorous form of the decision matrix in which each criterion is assigned a weight reflecting its relative importance, and the final score for each option is the sum of its criterion scores multiplied by those weights. Weighted matrices are the workhorse tool for vendor selection, hiring committees, and capital-allocation decisions because they force two productive arguments to happen explicitly: which criteria matter, and how much each one matters.
The discipline of writing down the weights before scoring the options dramatically reduces the post-hoc rationalization that plagues unweighted comparisons.