期刊
FUZZY SETS AND SYSTEMS
卷 454, 期 -, 页码 56-73出版社
ELSEVIER
DOI: 10.1016/j.fss.2022.05.007
关键词
Robust optimization; Possibility theory; Imprecise probabilities; Fuzzy intervals
This paper discusses optimization problems with uncertain linear constraints. The constraint coefficients are assumed to be random vectors with partially known probability distributions. Imprecise probabilities are modeled using possibility theory. The distributionally robust approach is used to transform the imprecise constraints into deterministic counterparts, making the resulting problem computationally tractable for a wide class of optimization models, particularly for linear programming.
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is used to model imprecise probabilities. In one of interpretation, a possibility distribution (a membership function of a fuzzy set) in the set of coefficient realizations induces a necessity measure, which in turn defines a family of probability distributions in this set. The distributionally robust approach is then used to transform the imprecise constraints into deterministic counterparts. Namely, the uncertain left-hand side of each constraint is replaced with the expected value with respect to the worst probability distribution that can occur. It is shown how to represent the resulting problem by using linear or second-order cone constraints. This leads to problems which are computationally tractable for a wide class of optimization models, in particular for linear programming. (c) 2022 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据