This paper shows that the usual multiplicative synthesis of alternative priorities for benefits, opportunities, costs and risks, obtained from separate Analytic Hierarchy or Network models, can be ambiguous. The ratio of benefit and opportunity priorities to cost and risk priorities can be misleading when assessing the profitability of a project. The same holds for their additive synthesis. Both types of synthesis have been advocated in AHP/ANP literature. A quotient of these priorities with weights as coefficients, not powers, will however produce sound results, provided that the four separate models are properly related to each other by weights that make the priorities on the four factors commensurate and are obtained from magnitude comparisons. Similarly, additive synthesis with properly weighted factor priorities based on relative magnitudes will produce sound results, although use of reciprocal values of costs and risks, as often advocated in the literature, is not recommended; negative costs and risks priorities should be used instead.
Paper REF showed that the usual multiplicative synthesis of alternative priorities for benefits, opportunities, costs and risks, obtained from separate analytic hierarchy or network models, can produce similar results which mean that the result is ambiguous.