Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision-making
Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision-making
复制标题
两个宇宙概率逼近空间的模糊粗糙集及其在应急决策中的应用
DOI：
10.1111/exsy.12103
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发表时间：
2015-08-01
期刊：
影响因子：
3.3
通讯作者：
Chen, Xiangtang
中科院分区：
文献类型：
--
作者：
Sun, Bingzhen;Ma, Weimin;Chen, Xiangtang
粗糙集的概率方法仍然是粗糙集理论中的一个重要问题。虽然许多研究已经写在这个话题上，他们专注于近似一个清晰的概念在宇宙的话语，与努力近似一个模糊的概念在宇宙的话语。本文研究了模糊概念在两个论域上的概率近似空间上的粗糙近似。首先，我们提出了一个模糊集的下近似和上近似的概率近似空间在两个宇宙的定义，通过定义的条件概率的模糊事件。也就是说，我们定义了两个论域上的概率近似空间上的粗糙模糊集。然后，我们定义的模糊概率近似两个宇宙通过引入一个概率测度的近似空间在两个宇宙。然后，我们建立了两个论域上概率近似空间上的模糊粗糙集模型。同时，研究了两论域上概率近似空间上的粗糙模糊集和模糊粗糙集的一些性质。同时，我们将所提出的模型与现有的模型进行了比较，以显示本文所给出的模型的优越性。此外，本文还将基于两论域概率近似的模糊粗糙集应用于非常规突发事件应急决策中。利用两论域上概率近似的模糊粗糙集模型，建立了一种在线应急决策方法。最后，我们将我们的方法应用于一个数值例子的应急决策，以说明所提出的方法的有效性。
Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision-making in unconventional emergency management. We establish an approach to online emergency decision-making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision-making in order to illustrate the validity of the proposed method.