For incomplete preference relations that are represented by multiple priors and/or multiple—possibly multivariate—utility functions, we define a certainty equivalent as well as the utility indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduce the notion of a weak and a strong certainty equivalent. We will show that our definitions contain as special cases some definitions found in the literature so far on complete or special incomplete preferences. We prove monotonicity and convexity properties of utility buy and sell prices that hold in total analogy to the properties of the scalar indifference prices for complete preferences. We show how the (weak and strong) set-valued certainty equivalent as well as the indifference price bounds can be computed or approximated by solving convex vector optimization problems. Numerical examples and their economic interpretations are given for the univariate as well as for the multivariate case.

对于由多个先验和/或多个（可能是多元）效用函数表示的不完全偏好关系，我们将确定性等价以及效用无差别价格范围定义为索赔的设定值函数。此外，我们激励并引入了弱确定性和强确定性等价的概念。我们将证明我们的定义包含特殊情况下到目前为止在文献中发现的一些关于完全或特殊不完全偏好的定义。我们证明了效用买卖价格的单调性和凸性，它们与完全偏好的标量无差异价格的属性完全相似。我们展示了如何通过解决凸向量优化问题来计算或近似（弱和强）设定值确定性等价物以及无差异价格界限。给出了单变量和多变量情况的数值示例及其经济解释。