Pyramid and Semicube Decompositions of Multiattribute Utility Functions

We apply the fractional hypercube decomposition theorem for multiattribute utility functions to the quasi-pyramid, the pyramid, and the semicube fractions. The resulting nonadditive utility models illustrate the broad range of decompositions that can be obtained with this fractional hypercube methodology. The pyramid decompositions have nonseparable interaction terms for each pair of attributes, whereas the semicube decomposition has nonseparable interaction terms for each proper subset of attributes. The computations and scaling illustrated here can be performed with other fractional hypercubes to produce various results between these two extremes.