It is known in the AHP that when dealing with intangible alternatives they are compared with respect to the criteria and the resulting priorities are multiplied by the priorities of the respective criteria and then synthesized in either the distributive or the ideal mode. When the criteria are tangible the alternatives need to be measured on ratio scales. Since ratio scales of measurement differ, they must be standardized and then weighted by the priorities of the criteria to trade off a unit of one scale against a unit of another. Of course ratio scales suffer from the defect that they use a unit of \measurement uniformly whether the measurements are large or small. But the meaning and significance of these measurements may not reflect our actual preference for them because our ability to appreciate values differs when they are very large or very small. We need to obtain these measurements in relative form through prioritization and comparisons. If we insist on using them as they are, we must convert them to relative priorities by dividing each value by the total values. But we cannot do that without noting that the weights of the criteria in this case depend on the measurements of the alternatives with respect to these criteria.
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