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- Title
A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions.
- Authors
Farquhar, Peter H.
- Abstract
This paper establishes a fundamental decomposition theorem in multiattribute utility theory. The methodology uses fractional hypercubes to generate a variety of attribute independence conditions that are necessary and sufficient for various decompositions: the additive, Keeney's quasi-additive, Fishburn's diagonal, and others. These other nonadditive utility decompositions contain some nonseparable interaction terms and are therefore applicable to decision problems not covered by earlier models. The paper defines a fractional hypercube and introduces the corresponding multiple element conditional preference order. The main theorem is produced from the solution of equations that are derived from transformations of linear functions that preserve these conditional preference orders. The computations and scaling required in implementing the main result are demonstrated by obtaining four utility decompositions on three attributes: apex, diagonal, quasi-pyramid, and semicube. We illustrate the methodology with geometric structures that correspond to the fractional hypercubes.
- Subjects
UTILITY functions; MATHEMATICAL decomposition; MULTIPLE criteria decision making; MATHEMATICAL transformations; LINEAR algebraic groups; SOLID geometry
- Publication
Operations Research, 1975, Vol 23, Issue 5, p941
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.23.5.941