Similarity of rectangles

Krantz and Tversky found that neither (log-) height (y) and width (x), nor area (x + y) and shape (x ? y) qualify as “subjective dimensions of rectangles” because both pairs violate the decomposability condition for their dissimilarity data. However, the data suggest a nonlinear transformation of x, y into a pair of subjective dimensions u(x, y), v(x, y) for which decomposability should be approximately satisfied. An explicit statement of this mapping is given.