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Since in evaluating by traditional data envelopment analysis (DEA) models many decision making units (DMUs) are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed.
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As pointed out in [24], in fact, "the interpretation of the partial accessibility indicators is clear and useful for policy-makers, but it does not provide a synthetic and global measure that allows planners to compare or fully rank the level of accessibility for different regions or cities within Europe.
We could not apply non-linear models to the fully ranked data; hence, it was necessary to compare the geometric mean proportional ranks and the raw wealth data (we used the log10 scale due to highly right-skewed per capita GNI-PPP).
The calculation is described in Appendix Appendix 2: Algorithm for counting fully ranked resolutions of a fully ranked constraint tree.
We generalise this algorithm to counting resolutions of a fully ranked constraint tree.
Let T = (T, h ) be a fully ranked X‐tree with h: V→{1,…, l}.
We denote this quantity by F(n1,…, n m ), where F stands for "fully ranked".
Here we describe a more efficient algorithm for counting fully ranked trees using these recursions.
An example of a fully ranked X‐tree is given in Figure 2.
The discrete structure of the tree produced by this process is a fully ranked X‐tree.
We will calculate S r (n, r ) for the corresponding fully ranked constraint tree T.
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