Abstract
We apply the Perron theorem in multi-attribute decision making. We create a comparison matrix for decision alternatives and prove that the matrix is almost-always primitive. We use the limiting power of the matrix multiplied by a standard vector, which leads to a positive eigenvector of the matrix, as the ranking vector for decision alternatives. The proposed method does not require domain experts to assign weights for decision criteria as usually demanded by the weighted-sum model. The new method is simple to use and generates reasonable result as illustrated by an example of ranking best hospitals over twelve criteria. We also demonstrate that the weightedsum methods may not be able to reveal all possible rankings. We give one example showing that a weighted-sum method collapsed thirteen distinct rankings into a single ranking and another example showing that the weighted-sum methods could not produce the ranking that is unrenderable by linear functions.
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Notes
For each specialty, only the top 50 hospitals were published. Thus, “\({>}\)50” is assigned to the hospitals that were not ranked in the top 50 so that they can be evaluated against the ones among top 50. However, when there are multiple “\({>}\)50” hospitals on a given specialty, any two of them are treated as incomparable.
The diagonal of the comparison matrix represents that a hospital is evaluated against itself. Thus, the diagonal retains a value of 0.5, i.e., the hospital ties with itself; performing neither better nor worse than itself.
We are grateful to the referee’s insightful suggestion.
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Huang, P.H., Moh, Tt. A non-linear non-weight method for multi-criteria decision making. Ann Oper Res 248, 239–251 (2017). https://doi.org/10.1007/s10479-016-2208-2
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DOI: https://doi.org/10.1007/s10479-016-2208-2