Decompositions of Multiattribute Utility Functions Based on Convex Dependence
Decompositions of Multiattribute Utility Functions Based on Convex Dependence
复制标题
基于凸依赖的多属性效用函数分解
DOI：
10.1287/opre.31.3.488
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
Yutaka Nakamura
中科院分区：
文献类型：
--
作者：
H. Tamura;Yutaka Nakamura
本文描述了一种评估双属性空间上von Neumann-Morgenstern效用函数的方法及其在n属性空间上的推广。首先，我们引入了两个属性之间凸依赖的概念，其中我们考虑了条件效用函数形状的变化。然后，我们利用凸相关的概念，建立了如何分解双属性效用函数的定理。这个概念涵盖了广泛的涉及权衡的情况。凸分解作为特例包括Keeney的加性/乘法分解、Fishburn的双边分解和插值无关的Bell分解。此外，凸分解是Fishburn和Farquhar公理化的精确网格模型。最后，我们将两个属性的凸分解定理推广到任意数目的属性。
We describe a method of assessing von Neumann-Morgenstern utility functions on a two-attribute space and its extension to n-attribute spaces. First, we introduce the concept of convex dependence between two attributes, where we consider the change of shapes of conditional utility functions. Then, we establish theorems which show how to decompose a two-attribute utility function using the concept of convex dependence. This concept covers a wide range of situations involving trade-offs. The convex decomposition includes as special cases Keeney's additive/multiplicative decompositions, Fishburn's bilateral decomposition, and Bell's decomposition under the interpolation independence. Moreover, the convex decomposition is an exact grid model which was axiomatized by Fishburn and Farquhar. Finally, we extend the convex decomposition theorem from two attributes to an arbitrary number of attributes.