Published May 10, 2017
Orrin Cooper Guoqing Liu


When designing an ANP model it is important to acknowledge and properly address whether the elements in the model are dependent on or independent of each other. The decision maker must perform criteria cluster weighting comparisons individually for the criteria clusters in each column of the Supermatrix to correctly model when the criteria and alternatives are dependent on one another to accurately capture the dependence. Failing to recognize that the criteria in a criteria cluster in one column of the Supermatrix is not necessarily equal in weight to the criteria in that same criteria cluster but in another column can lead to misrepresented rankings in the final priorities. In the extreme case, it can remove all dependence from an ANP model. Two models are used to demonstrate this unintended effect on the final priorities, and also demonstrate a crucial contribution that this effect is independent of the tangibility of the criteria considered. In the third model, the solution is discussed and implemented. A proof is provided in the appendix. This criteria cluster weighting approach further extends the applicability of the ANP to additional decisions when a decision maker wishes to represent a fully-dependent ANP decision.

How to Cite

Cooper, O., & Liu, G. (2017). ACHIEVING THE DESIRED LEVEL OF DEPENDENCY IN ANP DECISION MODELS. International Journal of the Analytic Hierarchy Process, 9(1).


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Dependence, intangible elements, criteria weights

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