Analytic Hierarchy Process

Analytic Hierarchy Process (AHP) is a method for decision making which compares the relative choices that one can make, weighs them, and then uses that to make the most informed decision. I stumbled upon during my time at LANL for EVMS and became interested in how this process works used to justify decision making.

Given a number of options, AHP creates a pairwise ratios of the relative benefit of using one option over another. By quantifying preference (a human factor) into a numeric scheme, justification can be made and marginal benefit can be evaluated.

AHP creates a comparison matrix of the relative preference between two options. This has a number of consequences on the shape of comparison matrix entries, $a_{ij}$. For entries along the main diagonal $i=j$, entries $a_{ii} =1$ because the relative benefit between an option to itself will always be $1$. Another relationship is that $a_{ji} = a_{ij}^{-1}$ because the reciprocal ratio comes from the inverse pairwise comparison. So long as the benefits are positive and nonzero, then all entries of the comparison matrix are $\R^+$ and finite.

First link that I found helpful was a Stack Exchange page and this tutorial.