基于软信息的软决策新方法研究
摘要
随着社会的进步和发展，决策方法的研究和应用已取得了很大的进展，但在
知识经济与信息社会到来的今天，人们所面临的决策问题日趋复杂，它们具有：
海量信息与小样本信息共存；确定性与不确定性共存；准确性与不准确性共存；
动态性和静态性共存；模型化与非模型化共存；单目标与多目标共存；线性与非
线性共存等特征。现有的决策方法面对上述复杂的决策问题普遍存在：复杂信息
识别困难、模型构建困难、函数与函数参数选择困难、计算复杂度高（易出现 NP
问题）等问题。比如：传统决策方法易出现建模困难（特别是在处理多因素多目
标决策问题时），现代的软计算决策方法（如：神经网络决策、遗传算法等）易出
现函数与函数参数选择困难、计算复杂度高（易出现 NP 问题）等问题，新近发展
起来的处理大样本问题的粗决策方法在属性约简、特征提取等方面也易出现 NP 问
题，1995 年产生的能处理小样本问题的支持向量机决策方法也存在核函数选择、
核函数中参数的确定、扩维方法确定等困难。因此，现有决策方法已不能较好地
解决多特征融合的复杂决策问题。从而，提供一套快捷、能综合处理具有各种特
征的决策方法已是当务之急。
本文通过深入分析现有复杂决策问题的特征，在大量检索国内外资料、跟踪
国际前沿技术基础上，应用多学科交叉技术，将软集合、支持向量机、粗糙集等
国际前沿技术的思想和方法引入到论文中，并将管理学、统计学、代数学、人工
智能、信息科学等科学知识相融合。在系统的观点指导下，针对上述特征，重点
研究了软信息识别、模型或因素筛选规则确定、决策方法制定等方面问题，提出
了一套基于软信息的软决策方法。最后经实际算例计算、模拟，对计算结果进行
了对比分析得出该套方法可行、有效、快捷、方便、计算量小，具有理论意义和
应用价值。
本文的主要创新之处：
1、将软集合理论应用于软信息的识别中，根据软信息的特征，通过构造软信
息特征向量映射，建立了基于软集合的信息表，提出了一种基于软集合理论的软
信息识别方法,为多因素软信息的识别提供了一条有效的途径。
2、将粗糙集理论应用于组合预测问题中，提出了一种基于粗糙集的组合预测
方法，为数据驱动下预测模型的筛选和组合系数的合理确定提供了一种有效方法。
3、将粗糙集理论的规则提取技术用于软信息的多因素动态预测问题中，利用
提取的因素与预测指标之间相关关系的概约化描述建立了预测模型，推导了预测
模型中参数的递推公式，减少了信息更新时模型参数的计算量，为多因素相关关
I
重庆大学博士学位论文
系的分析提供了一种有效的方法。
4、将粗糙集理论和代数理论与方法相结合，建立了基于粗代数的软决策模型，
提出了一种基于粗代数的软决策方法,为多因素（多目标）的软决策问题中的因素
约简与规则提取提供了高效的方法。
5、将粗糙集、支持向量机的原理与思想和代数结构（同构）理论与方法相融
合，建立了决策集合的一个二元同余关系，构造了因素集合到决策商集的一个同
构映射，提出了一种基于代数结构的软决策方法,为多因素小样本软决策问题提供
了一条有效的途径。
With the advancement and development of society, the research and application in
decision-making methods have greatly improved. But knowledge economy and
information society coming today, the decision problems we face are more and more
complicated. They have some characteristics such as: the coexistence of enormous
information and small sample information; the coexistence of certainty and uncertainty;
the coexistence of veracity and inveracity; the coexistence of dynamic quality and static
quality; the coexistence of using models and not using model; the coexistence of single
target and multi-targets ;the coexistence of linearity and nonlinearity etc. The existing
decision-making methods universally have many problems when confronted with the
complex decision problems mentioned above, such as: difficult to identify complicated
information; difficult to construct models; difficult to choose functions and parameters;
complicated to compute (NP problems appears easily) etc. For example, traditional
decision-making methods easily bring about the difficulty of modeling(especially in
dealing with multi-factors and multi-targets decision problems), modern soft computing
decision-making methods(such as neural net decision, genetic arithmetic etc)are prone
to induce the difficulty of choosing functions and parameters and lead to compute more
complicated (NP problems appears easily ),rough decision method growing up recently
which deals with big sample is apt to bring about NP problems in attribute reduction and
characteristic pick-up etc too, the support vector machine decision method appearing in
1995 which deals with small sample is still difficult to choose core function , to
confirm parameters in core function, and to ascertain the way of expanding dimension.
So, the existing decision methods can’t solve the complex decision problems which
combine multi- characteristics well. It’s urgent to provide a suit of decision methods
which can dispose decision problems fleetly and synthetically and have diversified
characteristics.
Based on great searching for internal and external information and following
closely international advanced technology, we deeply analyzes the characteristic of the
complex decision and introduce international advanced thoughts and methods such as
soft sets, support vector machine and rough sets into this paper; at the same time many
kinds of scientific knowledge for example management, statistics, algebra, artificial
intelligence, informatics and so on are melted well. In the systemic point of view, we
III
重庆大学博士学位论文
make emphases to research to distinguish soft information, determine the filter rule for
models or factors and select the decision methods; furthermore we put forward a set of
soft decision methods based on soft information. Finally using an example for
calculating and simulation and analyzing the results, we prove this set of method has the
theory value and practice value.
The main innovation of this paper is as follow:
1. Introduce the soft set theory to distinguish the soft information. According to the
characteristic of soft information, this paper builds the eigenvector mapping of soft
information and then put forward the method of distinguishing soft information
based on soft sets theory for the first time, which provides an effective way to
distinguish soft information.
2. Introduce the soft set theory to apply in the combination forecasting. Bring forward
the method of combination forecasting based on rough sets theory, which provides
an effective way to filter forecasting model and to make sure the combination
coefficient droved by data.
3. Introduce the technology of gaining rules in the rough set theory to apply in the
multi-factors dynamic forecasting. Making use of the reduction of factors and
indexes to build the forecasting model, this paper gets the formula of parameter in
forecasting model and reduces calculation of parameter
知识经济与信息社会到来的今天，人们所面临的决策问题日趋复杂，它们具有：
海量信息与小样本信息共存；确定性与不确定性共存；准确性与不准确性共存；
动态性和静态性共存；模型化与非模型化共存；单目标与多目标共存；线性与非
线性共存等特征。现有的决策方法面对上述复杂的决策问题普遍存在：复杂信息
识别困难、模型构建困难、函数与函数参数选择困难、计算复杂度高（易出现 NP
问题）等问题。比如：传统决策方法易出现建模困难（特别是在处理多因素多目
标决策问题时），现代的软计算决策方法（如：神经网络决策、遗传算法等）易出
现函数与函数参数选择困难、计算复杂度高（易出现 NP 问题）等问题，新近发展
起来的处理大样本问题的粗决策方法在属性约简、特征提取等方面也易出现 NP 问
题，1995 年产生的能处理小样本问题的支持向量机决策方法也存在核函数选择、
核函数中参数的确定、扩维方法确定等困难。因此，现有决策方法已不能较好地
解决多特征融合的复杂决策问题。从而，提供一套快捷、能综合处理具有各种特
征的决策方法已是当务之急。
本文通过深入分析现有复杂决策问题的特征，在大量检索国内外资料、跟踪
国际前沿技术基础上，应用多学科交叉技术，将软集合、支持向量机、粗糙集等
国际前沿技术的思想和方法引入到论文中，并将管理学、统计学、代数学、人工
智能、信息科学等科学知识相融合。在系统的观点指导下，针对上述特征，重点
研究了软信息识别、模型或因素筛选规则确定、决策方法制定等方面问题，提出
了一套基于软信息的软决策方法。最后经实际算例计算、模拟，对计算结果进行
了对比分析得出该套方法可行、有效、快捷、方便、计算量小，具有理论意义和
应用价值。
本文的主要创新之处：
1、将软集合理论应用于软信息的识别中，根据软信息的特征，通过构造软信
息特征向量映射，建立了基于软集合的信息表，提出了一种基于软集合理论的软
信息识别方法,为多因素软信息的识别提供了一条有效的途径。
2、将粗糙集理论应用于组合预测问题中，提出了一种基于粗糙集的组合预测
方法，为数据驱动下预测模型的筛选和组合系数的合理确定提供了一种有效方法。
3、将粗糙集理论的规则提取技术用于软信息的多因素动态预测问题中，利用
提取的因素与预测指标之间相关关系的概约化描述建立了预测模型，推导了预测
模型中参数的递推公式，减少了信息更新时模型参数的计算量，为多因素相关关
I
重庆大学博士学位论文
系的分析提供了一种有效的方法。
4、将粗糙集理论和代数理论与方法相结合，建立了基于粗代数的软决策模型，
提出了一种基于粗代数的软决策方法,为多因素（多目标）的软决策问题中的因素
约简与规则提取提供了高效的方法。
5、将粗糙集、支持向量机的原理与思想和代数结构（同构）理论与方法相融
合，建立了决策集合的一个二元同余关系，构造了因素集合到决策商集的一个同
构映射，提出了一种基于代数结构的软决策方法,为多因素小样本软决策问题提供
了一条有效的途径。
With the advancement and development of society, the research and application in
decision-making methods have greatly improved. But knowledge economy and
information society coming today, the decision problems we face are more and more
complicated. They have some characteristics such as: the coexistence of enormous
information and small sample information; the coexistence of certainty and uncertainty;
the coexistence of veracity and inveracity; the coexistence of dynamic quality and static
quality; the coexistence of using models and not using model; the coexistence of single
target and multi-targets ;the coexistence of linearity and nonlinearity etc. The existing
decision-making methods universally have many problems when confronted with the
complex decision problems mentioned above, such as: difficult to identify complicated
information; difficult to construct models; difficult to choose functions and parameters;
complicated to compute (NP problems appears easily) etc. For example, traditional
decision-making methods easily bring about the difficulty of modeling(especially in
dealing with multi-factors and multi-targets decision problems), modern soft computing
decision-making methods(such as neural net decision, genetic arithmetic etc)are prone
to induce the difficulty of choosing functions and parameters and lead to compute more
complicated (NP problems appears easily ),rough decision method growing up recently
which deals with big sample is apt to bring about NP problems in attribute reduction and
characteristic pick-up etc too, the support vector machine decision method appearing in
1995 which deals with small sample is still difficult to choose core function , to
confirm parameters in core function, and to ascertain the way of expanding dimension.
So, the existing decision methods can’t solve the complex decision problems which
combine multi- characteristics well. It’s urgent to provide a suit of decision methods
which can dispose decision problems fleetly and synthetically and have diversified
characteristics.
Based on great searching for internal and external information and following
closely international advanced technology, we deeply analyzes the characteristic of the
complex decision and introduce international advanced thoughts and methods such as
soft sets, support vector machine and rough sets into this paper; at the same time many
kinds of scientific knowledge for example management, statistics, algebra, artificial
intelligence, informatics and so on are melted well. In the systemic point of view, we
III
重庆大学博士学位论文
make emphases to research to distinguish soft information, determine the filter rule for
models or factors and select the decision methods; furthermore we put forward a set of
soft decision methods based on soft information. Finally using an example for
calculating and simulation and analyzing the results, we prove this set of method has the
theory value and practice value.
The main innovation of this paper is as follow:
1. Introduce the soft set theory to distinguish the soft information. According to the
characteristic of soft information, this paper builds the eigenvector mapping of soft
information and then put forward the method of distinguishing soft information
based on soft sets theory for the first time, which provides an effective way to
distinguish soft information.
2. Introduce the soft set theory to apply in the combination forecasting. Bring forward
the method of combination forecasting based on rough sets theory, which provides
an effective way to filter forecasting model and to make sure the combination
coefficient droved by data.
3. Introduce the technology of gaining rules in the rough set theory to apply in the
multi-factors dynamic forecasting. Making use of the reduction of factors and
indexes to build the forecasting model, this paper gets the formula of parameter in
forecasting model and reduces calculation of parameter
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