On minimum-risk problems in fuzzy random decision systems
On minimum-risk problems in fuzzy random decision systems
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模糊随机决策系统中的最小风险问题
DOI：
10.1016/s0305-0548(03)00235-1
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发表时间：
2005-02
影响因子：
4.6
通讯作者：
刘宝碇
中科院分区：
文献类型：
--
作者：
刘彦奎;刘宝碇
在决策过程中，我们可能面临一个混合环境，其中语言和频繁的不精确性并存。常见的不精确问题可以通过概率论来解决，而语言不精确问题可以通过可能性论来解决。因此，要解决这种混合决策问题，有必要将两种理论有效地结合起来。在本文中，我们将注意力集中在这种混合决策问题上，其中输入数据不精确并由模糊随机变量描述。模糊随机变量是从概率空间到模糊变量集合的映射，是优化框架中处理模糊性和随机性双重不确定性的合适工具。本文的目的是提出以模糊随机变量为特征的模糊随机事件的合理机会，使其能够通过Choquet积分与模糊随机变量的期望值算子联系起来，就像随机事件的概率与随机变量的数学期望之间的关系，以及模糊事件的可信度与模糊变量的期望值算子之间的关系一样。为此，我们以模糊测度和模糊积分理论为研究工具，通过Choquet积分提出了模糊随机事件的三种平均机会。在讨论了平均机会的对偶性之后，我们使用平均机会通过 Choquet 积分定义模糊随机变量的期望值算子。为了证明平均机会方法的合理性，我们证明了本文中定义的期望值算子与我们之前的工作中提出的一致。使用平均机会，我们提出了一类新的模糊随机最小风险问题，其中目标和约束均由平均机会定义。针对一般模糊随机最小风险优化问题，设计了一种集模糊随机模拟、遗传算法和神经网络于一体的混合智能算法，并通过算例说明了其可行性和有效性。
In a decision-making process, we may face a hybrid environment where linguistic and frequent imprecision nature coexists. The problem of frequent imprecision can be solved by probability theory, while the problem of linguistic imprecision can be tackled by possibility theory. Therefore, to solve this hybrid decision-making problem, it is necessary to combine both theories effectively. In this paper, we restrict our attention to this hybrid decision-making problem, where the input data are imprecise and described by fuzzy random variables. Fuzzy random variable is a mapping from a probability space to a collection of fuzzy variables, it is an appropriate tool to deal with twofold uncertainty with fuzziness and randomness in an optimization framework. The purpose of this paper is to present reasonable chances of a fuzzy random event characterized by fuzzy random variables so that they can connect with the expected value operators of a fuzzy random variable via Choquet integrals, just like the relation between the probability of a random event and the mathematical expectation of a random variable, and that between the credibility of a fuzzy event and the expected value operator of a fuzzy variable. Toward that end, we take fuzzy measure and fuzzy integral theory as our research tool, and present three kinds of mean chances of a fuzzy random event via Choquet integrals. After discussing the duality of the mean chances, we use the mean chances to define the expected value operators of a fuzzy random variable via Choquet integrals. To show the reasonableness of the mean chance approach, we prove the expected value operators defined in this paper coincide with those presented in our previous work. Using the mean chances, we present a new class of fuzzy random minimum-risk problems, where the objective and the constraints are all defined by the mean chances. To solve general fuzzy random minimum-risk optimization problems, a hybrid intelligent algorithm, which integrates fuzzy random simulations, genetic algorithm and neural network, is designed, and its feasibility and effectiveness are illustrated by numerical examples.
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DOI：
--
发表时间：
1995-03
期刊：
--
影响因子：
--
作者：
Young-Jou Lai;C. Hwang
通讯作者：
Young-Jou Lai;C. Hwang
影响因子：
11.9
作者：
Liu, BD
通讯作者：
Liu, BD
影响因子：
3.9
作者：
Guangyuan Wang;Qiao Zhong
通讯作者：
Guangyuan Wang;Qiao Zhong
DOI：
10.1007/978-3-7908-1781-2_24
发表时间：
1999
期刊：
--
影响因子：
--
作者：
Baoding Liu
通讯作者：
Baoding Liu
DOI：
10.1016/s0020-0255(01)00073-1
发表时间：
2001-03
期刊：
Inf. Sci.
影响因子：
--
作者：
A. Colubi;J. S. Domínguez-Menchero;Miguel Ló-Díz;D. Ralescu
通讯作者：
A. Colubi;J. S. Domínguez-Menchero;Miguel Ló-Díz;D. Ralescu