Parivertailumatriisi

Parivertailumatriisi, in English known as a pairwise comparison matrix, is a square matrix used in decision analysis to capture judgments about the relative importance or preference of a set of elements by comparing them two at a time. Each entry aij expresses how much more important or preferred item i is relative to item j. The matrix is typically reciprocal, meaning aji = 1 / aij, and the diagonal elements are 1 because an item is equally important as itself.

Commonly the entries are drawn from Saaty’s 1–9 scale, where 1 denotes equal importance and higher numbers indicate stronger preferences, with intermediate values for nuanced judgments. The matrix thus reflects a structured qualitative assessment converted into quantitative ratios.

From a parivertailumatriisi, a priority vector or weights are derived to express the relative importance of the elements. This is usually done by computing the principal eigenvector corresponding to the largest eigenvalue, or by the geometric mean method. The resulting weights can be used directly in decision problems or aggregated with other criteria.

Consistency is a key consideration, since human judgments can be inconsistent. Measures such as the Consistency Index (CI) and the Consistency Ratio (CR) compare the observed matrix to random likelihoods to assess reliability. A CR value below a commonly used threshold (often 0.10) is considered acceptable, though stricter standards may apply in high-stakes contexts.

Applications and context: parivertailumatriisi is a central component of the Analytic Hierarchy Process (AHP) and other multi-criteria decision-making frameworks. It is used to derive weights for criteria or alternatives, enabling structured, transparent, and revisable decision analysis. Limitations include subjectivity in judgments and sensitivity to inconsistencies or small changes in the inputs.