We propose a simple algebraic representation for pairwise comparisons of AHP. The representation is an associative relation between the importances of elements and consists of basic arithmetic operations. First, we define a ratio, which is estimated by decision makers by comparing the importances of elements, as a partial differentiation of importances (Section 2). Then, we construct systems of differential equations. Algebraic representations of the importances are derived as formal solutions of the equations. We analyze pairwise comparisons and the construction of the importances from them with the representations (Section 3). The validity of using eigenvectors and C.I. in AHP is illustrated by deriving a particular solution of the equations.
pairwise comparison method, ternary comparison method, ternary diagram
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