多规则有序决策的粗糙集模型与熵方法

发布时间：2018-05-20 15:56

本文选题：有序决策 + 粗糙集　；参考：《电子科技大学》2017年博士论文

【摘要】：随着网络信息技术的发展和普及,互联网已经发展成为当今世界上资料最多、门类最全、规模最大的异构、动态和开放的分布式资源库。有序性数据是互联网中广泛存在的一类数据,如仓储与物流、生态农业、投资风险分析等。多规则有序决策已成为Web信息知识发现中非常重要的研究方向。粗糙集理论采用粒化和近似的基本思想来刻画分类问题中的不一致性,是解决不确定分类问题的有效工具。信息熵是信息不确定性的重要度量工具。本文基于粗糙计算方法论中粒化和近似的思想,结合信息熵对不确定性的度量能力,对多规则有序列决策问题进行了深入研究,建立了多规则有序决策的粗糙集模型和信息熵方法。具体从以下几个方面进行了探索:第一,建立了多规则有序决策的多粒度偏好关系粗糙计算模型,设计了粒结构选择算法。传统的偏好(优势)关系是一种不严格的偏好表示方法,论文将传统的偏好关系拓展到严格的偏好关系,改进了偏好关系粗糙集模型,并将其扩展到了多规则有序决策领域,建立了多粒度偏好关系粗糙集模型。在现在偏好关系粗糙集中,如果一个样本要属于某偏好集的下近似,则要求所有比此样本差的样本都包含在该偏好集中,这样的下近似是没有任何意义的。改进后的偏好关系粗糙集模型克服了这一问题。如果一个样本要属于某偏好集的下近似,只要存在比该样本差的样本属于此偏好集就可以了,这更加符合实际情况。考虑到不同规则的费用和成本问题,还建立了费用敏感的多粒度偏好关系粗糙集模型。此外,还将建立的模型应用于粒结构选择,并设计了粒结构选择算法。第二,建立了多规则有序决策的多粒度模糊偏好关系粗糙计算模型,设计了偏好决策和样本压缩方法。经典的偏好关系粗糙集基于传统的偏好关系,只能表示数据之间的序关系,不能体现数据之间偏好的程度。针对现有模糊偏好关系粗糙集模型在上下近似方面与传统粗糙集思想相悖的情况,引入加性一致的模糊偏好关系,提出了改进的模糊偏好关系粗糙集模型,并将其扩展到了多规则有序决策领域,建立了多粒度模糊偏好关系粗糙集模型和费用敏感的多粒度模糊偏好关系粗糙集模型。基于提出的模型,设计了偏好决策和样本压缩算法。第三,提出了偏好不一致熵的概念,建立了多规则有序决策的信息熵模型,设计了属性约简算法和样本压缩算法。将香农信息熵扩展到有序决策领域,用偏好不一致熵来度量有序决策系统中偏好的不一致性和不确定性。偏好不一致熵是基于属性的,能够有效度量有序决策系统中由于条件属性与决策的偏好不一致导致的决策不确定性,能够很好地反应条件属性在有序决策中的重要程度,在特征选择和属性约简方面有比较好的效果。第四,定义了样本的偏好不一致熵,并扩展到加权的偏好不一致熵,提出了样本的偏好决策算法。基于属性的偏好不一致熵在样本的有序决策方面能力不足。针对偏好不一致有序系统中的样本决策问题,基于偏好信息粒子和样本的偏好不一致度,定义了样本的偏好不一致熵。样本的偏好不一致熵关注的对象是样本,能够度量特定样本引起的偏好不一致,在有序决策系统中的样本分类方面具有较好的效果。当基于全局偏好不一致熵进行分类时,能够得到与原始决策比较接近的结果。第五,提出了一种基于粗糙集的最近邻样本压缩方法(FRSC算法)。最近邻分类规则的时间复杂度和空间复杂度均与训练样本集的样本数量密切相关。随着样本数量的增加,所需要的时间和空间迅速增大。而在最近邻分类规则中,决定分类结果的往往是处于决策边界的样本。因此计算训练集的一致子集是提高最近邻分类规则效率的重要途经。粗糙集理论是通过上近似和下近似来对决策空间进行逼近,处于决策边界区域的样本往往都是下近似比较小的样本。将粗糙集方法应用于最近邻规则的训练集压缩,是一种快速计算训练集一致子集有效方法。与最近邻规则类似,在粗糙集方法中,计算上近似和下近似的时间也随训练样本数量呈指数增长。而决定上近似和下近似的同样也是决策边界的样本。因此本文提出的最近邻样本压缩方法对粗糙集的应用同样具有重要意义,可以有效提高粗糙计算效率。本文从粗糙集和信息熵两个角度对多规则有序决策问题进行了研究,建立了多规则有序决策的多粒度偏好关系粗糙计算模型和模糊偏好关系粗糙计算模型,定义了偏好不一致熵和样本的偏好不一致熵,形成了解决多规则有序决策问题的粗糙集和信息熵理论。
[Abstract]:With the development and popularization of the network information technology, the Internet has developed into a distributed resource base with the most data, the most complete categories and the largest scale in the world. The ordered data is a kind of data widely existing in the Internet, such as storage and material flow, ecological agriculture, investment risk analysis and so on. Decision making has become a very important research direction in Web information discovery. Rough set theory uses granular and approximate basic ideas to describe inconsistencies in classification problems. It is an effective tool for solving uncertain classification problems. Information entropy is an important measure tool for information uncertainty. This paper is based on the granulation of rough computing methodology. And approximate ideas, combined with the measurement of uncertainty by information entropy, the problem of multi rule and sequential decision making is studied deeply, and the rough set model and information entropy method for multi rule and orderly decision making are established. First, the multi granularity preference relation of multi rule ordered decision making is rough. The traditional preference (dominance) relationship is a non strict preference representation method. The traditional preference relation is extended to the strict preference relation, and the preference relation rough set model is improved, and it is extended to the domain of multi rule ordered decision making, and a multi granularity preference relation rough set is established. If a sample is to belong to the lower approximation of a preference set, it is required that all samples that are inferior to this sample are included in the preference set, so the lower approximation is not meaningful. The improved preference relation rough set model overcomes this problem. If a sample is to belong to a certain deviation. The lower approximation of a good set, as long as there is a sample of the difference of the sample, belongs to the preference set, which is more in line with the actual situation. Considering the cost and cost of different rules, a cost sensitive multi granularity preference relation rough set model is also established. In addition, the model is applied to the selection of grain structure and the grain structure is designed. Selection algorithm. Second, a multi granularity fuzzy preference relation rough computing model for multi rule and orderly decision making is established. The preference decision and sample compression method are designed. The classical preference relation rough set is based on the traditional preference relation, which can only express the order relation between data and the degree of preference between the data. In the case that the rough set model is inconsistent with the traditional rough set idea in the upper and lower approximation, we introduce an additive consistent fuzzy preference relationship and propose an improved fuzzy preference relation rough set model, and extend it to the multi rule ordered decision-making domain, and establish a multi granularity paste preference relational rough set model and the cost sensitive multiple. Based on the proposed model, the preference decision and sample compression algorithm are designed based on the proposed model. Third, the concept of preference inentropy is proposed, the information entropy model of the multi rule ordered decision is established, and the attribute reduction algorithm and the sample compression algorithm are designed. The Shannon information entropy is extended to the ordered decision-making field, and the bias is extended to the field of order decision. Unconformance entropy is used to measure the inconsistency and uncertainty of preference in order decision systems. Preference inentropy is based on attributes, and can effectively measure the decision uncertainty caused by the disagreement between the conditional attribute and the decision preference in an ordered decision system, and it can well counter the importance of the condition attribute in the orderly decision making. There are good results in feature selection and attribute reduction. Fourth, the preference inentropy of the sample is defined, and the weighted preference inconsistency entropy is extended. The preference decision algorithm of sample is proposed. The attribute based preference inentropy is insufficient in the order decision of the sample. This decision problem, based on the preference inconsistency of preference information particles and samples, defines the preference inconsistency of the sample. The object of the sample's preference inentropy attention is a sample, can measure the preference inconsistency caused by a specific sample, and has a better effect in the classification of samples in an ordered decision system. When the inconsistency entropy is classified, the results are close to the original decision. Fifth, a new nearest neighbor sample compression method based on rough sets (FRSC algorithm) is proposed. The time complexity and space complexity of the nearest neighbor classification rule are closely related to the number of samples in the training sample set. The time and space will increase rapidly. In the nearest neighbor classification rule, the classification result is often the sample in the decision boundary. Therefore, the calculation of the uniform subset of the training set is an important way to improve the efficiency of the nearest neighbor classification rule. The sample in the boundary area is often a small lower sample. The rough set method is applied to the training set compression of the nearest neighbor rule. It is an effective method to quickly calculate the set of the training set. Similar to the nearest neighbor rule, the approximate and near near similar time in the rough set method also increases exponentially with the number of training samples. The approximate and lower approximation are also the same as the sample of the decision boundary. Therefore, the nearest neighbor sample compression method proposed in this paper is also of great significance to the application of rough sets, which can effectively improve the efficiency of rough computing. This paper studies the multi rule ordered decision-making problem from two angles of rough set and information entropy. The rough computing model of multi granularity preference relation and the rough calculation model of fuzzy preference relation are used for regular order decision making, and the preference inentropy and the preference inentropy of preference inentropy and sample are defined, and the rough set and information entropy theory for solving the problem of multi rule and order decision are formed.
【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP18

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