tetrametric

Tetrametric is an adjective used in mathematics and related fields to describe a distance function or metric that is built from four constituent measurements or semi-metrics. In this sense, a tetrametric distance D on a set X is derived from four metrics d1, d2, d3, d4: X×X → [0,∞). A common formulation is D(x,y) = max{d1(x,y), d2(x,y), d3(x,y), d4(x,y)} or D(x,y) = w1 d1(x,y) + w2 d2(x,y) + w3 d3(x,y) + w4 d4(x,y) with nonnegative weights wi summing to 1. When each di is a metric, both the maximum and the weighted sum are metrics, so D satisfies non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Other monotone combinations can also yield tetrametrics under suitable conditions.

Use cases and examples: In multi-criteria similarity or clustering, four feature spaces may be fused into a single distance. In multimedia or imaging, distances may be defined over four channels (for example RGBA) or four sensor modalities. The term emphasizes the four-component structure rather than introducing a new abstract axiom set.

Etymology and usage: The term tetrametric derives from tetra- meaning four and metric meaning distance measure. It is not a widely standardized term and appears mainly in specialized or informal writings describing composite or product metrics.