三参数区间灰数的决策和预测方法研究

发布时间：2018-01-13 05:04

本文关键词：三参数区间灰数的决策和预测方法研究　出处：《河南农业大学》2015年硕士论文　论文类型：学位论文

【摘要】：在科学、技术、社会、经济、哲学、思维等众多领域中,人们都要对当前时事和它未来的发展趋势做出决策和预测,但是,由于客观世界的复杂性、不确定性以及人们能力的局限性,对不确定性的事物往往不能做出准确决策和预测,因此,需要借助于科学的方法来判断现在,预知未来。由于决策和预测对象的不确定性,或人们认识程度的不确定,现实中三参数区间灰数类型的决策和预测数据广泛存在。因此,在灰色系统理论和不确定性理论研究的基础上,本文根据目前灰色系统理论的研究现状,对三参数区间灰数的决策和预测方法进行了探讨:(1)论述了三参数区间灰数决策和预测的相关理论知识。介绍了三参数区间灰数的定义及运算法则,综述了目前较为常用的三参数区间灰数决策矩阵的标准化处理方法,总结了两种多属性决策方法,总结了灰色GM)1,1(预测模型。(2)探讨了三参数区间灰数的距离熵模型及决策研究。定义了三参数区间灰数的距离熵模型,证明了其定理和性质。利用三参数区间灰数距离熵的思想,首先,建立了三参数区间灰数多属性决策的赋权模型,使决策转化为权重已知情况下的三参数区间灰数多属性决策问题,并通过实例说明了模型的有效性和适用性;其次,论述了三参数区间灰数的决策指标体系约简方法,完成对冗余指标的约简工作,最后通过实例验证了该方法的可行性和适用性。(3)探讨了三参数区间灰数的灰色关联决策方法。通过对传统邓氏灰色关联度的改造,计算各决策方案对正、负理想方案的灰色关联度,得到各方案的相对关联度,从而对各决策方案进行优劣排序,并通过实例进行了对比分析,说明了决策方法的实用性和有效性。(4)针对三参数区间灰数的预测问题,探讨了三参数区间灰数的预测方法。利用集值统计的原理,通过对原始三参数区间灰数预测序列的改造,使其转化为实数序列,进而进行GM)1,1(预测,完成对三参数区间灰数的预测,并通过实例验证了方法的可行性和适用性。上述决策和预测方法简单有效,操作简便,为灰色系统理论的发展提供了有利的理论支持,拓展了灰色理论的应用范围和发展空间。
[Abstract]:In many fields, such as science, technology, society, economy, philosophy, thinking and so on, people have to make decisions and forecasts about current affairs and its future development trend, but because of the complexity of the objective world. Uncertainty and the limitation of people's ability often can't make accurate decision and forecast for uncertain things. Therefore, we need to use scientific methods to judge the present. Because of the uncertainty of decision making and prediction object, or the uncertainty of people's cognition, the decision and prediction data of three parameter interval grey number type exist widely in reality. Based on the research of grey system theory and uncertainty theory, this paper is based on the present research status of grey system theory. In this paper, the decision and prediction method of three parameter interval grey number is discussed. The related theoretical knowledge of three parameter interval grey number decision and prediction is discussed, and the definition and operation rule of three parameter interval grey number are introduced. This paper summarizes the standard processing methods of three-parameter interval grey number decision matrix, summarizes two kinds of multi-attribute decision making methods, and summarizes the grey GM)1. 1 (prediction model. 2) the distance entropy model and decision making of three parameter interval grey number are discussed, and the distance entropy model of three parameter interval grey number is defined. The theorem and properties are proved. Using the idea of three-parameter interval grey number distance entropy, the weight model of three-parameter interval grey number multi-attribute decision making is established. The decision is transformed into a three-parameter interval grey number multi-attribute decision making problem with known weights, and the validity and applicability of the model are illustrated by an example. Secondly, the reduction method of three parameter interval grey number decision index system is discussed, and the reduction of redundant index is completed. Finally, the feasibility and applicability of the method are verified by an example. (3) the grey relational decision method of three parameter interval grey number is discussed. Through the transformation of the traditional Deng's grey correlation degree, the positive results of each decision plan are calculated. The grey correlation degree of negative ideal scheme is obtained, and the relative correlation degree of each scheme is obtained, so that the advantages and disadvantages of each decision scheme are sorted, and the comparative analysis is carried out through an example. The practicability and validity of the decision method are explained. (4) aiming at the prediction problem of three parameter interval grey number, the prediction method of three parameter interval grey number is discussed, and the principle of set value statistics is used. Through the transformation of the original three-parameter interval grey number prediction sequence, it can be transformed into real number sequence, and then GM1 / 1 prediction can be carried out to complete the prediction of the three-parameter interval grey number. The feasibility and applicability of the method are verified by an example. The above decision and prediction methods are simple, effective and easy to operate, which provides a favorable theoretical support for the development of grey system theory. The application scope and development space of grey theory are expanded.
【学位授予单位】：河南农业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F224

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