计算智能及其在气象信息分析中的应用
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摘要
人类智能的宏观分析能力主要体现在人们能从极不相同的粒度上观察和分析同一问题，人们不仅能在不同粒度的世界上进行问题求解，而且能够很快地从一个粒度世界跳到另一个粒度世界，往返自如，毫无困难。基于商空间粒度计算理论不但可以表示对象的属性，而且可以表示对象之间的结构关系，同时可描述各种不同粒度世界之间转移、变换、合成和分解等关系，这正是描述人类智能宏观分析能力的有力工具。
人类智能的微观分析能力主要体现在可以从大量事物学习中归纳出规律。这种能力可以通过建立学习模型来实现。作为构造性机器学习方法基础的覆盖算法正是满足条件的学习模型之一，通过对覆盖算法的研究可以模拟人类智能微观学习能力。
本文分别研究了商空间粒度计算理论和覆盖算法这两个模拟人类智能两大特点的模型，并将它们有机地结合在一起，以期为人类的某些智力行为建立适当的形式化模型，利用计算机再显人类智能的部分功能。本文将其应用于安徽省冬小麦产量预测中，给出了不同粒度下的预测模型，并通过实例说明该模型具有时间和空间普适性。
主要工作包括：
1．研究了商结构在商空间粒度计算理论中的突出作用。
研究了商空间粒度计算理论中求解商空间的方法，讨论了如何分别从描述问题的三个因素——论域、属性、结构出发获取商空间，并给出具体思路，为第三章所述的基于粒度计算的覆盖算法提供理论基础，第六章所述的基于粒度计算的安徽省冬小麦产量的预测模型也是以此为基础；重点研究了商结构在商空间理论中的重要作用，将其作为商空间理论与粗糙集理论的主要区别之一。
2．提出基于粒度计算的覆盖算法；将覆盖算法用于聚类研究。
简要介绍了覆盖算法的雏形——领域覆盖及其交叉覆盖算法，结合商空间理论中属性颗粒化求解商空间的思想和合成方法，提出基于粒度计算的覆盖算法；将覆盖算法引入聚类领域，指出覆盖算法不但可以用于分类，也可以适用于聚类研究。
3．提出覆盖算法的“最小覆盖原理”。
从认识论的观点出发，对覆盖算法提出“最小覆盖原理”，并从几何意义上对最小覆盖的性质、特点进行深入研究，得出最小覆盖的充分必要条件，依此给出相应的求最小覆盖的算法；讨论了最小覆盖算法的复杂性；最后利用规划方法求解最小覆盖算法。
4．给出概率模型下的覆盖算法。
将核函数思想和全局最优思想引入覆盖算法，给出概率模型下的覆盖算法。该算法将覆盖算法中的决策函数改为核函数，然后从概率论中的“最大似然原理”的角度对覆盖算法进行优化，自动求解核函数中的参数，以解决一般核函数中参数选择的难题。
5．以安徽省的部分城市建站以来的气象及其冬小麦产量信息为研究对象，建立不同粒度下的预测模型。
1)构造原空间下的问题描述，安徽省每个城市每年的信息构成论域中的一个元素——样本，该样本由两大部分构成——特征属性和决策属性。
2)分析了气象产量预测的一般方法，并说明这些方法存在的弊端，在此基础上加以改进，用以实现本文所建模型中决策属性处理模块的功能，经过产量阶段划分后，采用灰色模型求得相对气象产量，作为样本的决策属性。
3)对论域和特征属性分别采用商空间计算理论中求解商空间的方法处理，以期从不同角度获取不同粒度下的预测模型。
a)对论域颗粒化的方法：以江淮地区的城市为例，把结构上或功能上关系密切的元素划分为一类，得到[X]_(江淮)，由此构造以江淮地区为整体的预测模型；
b)对属性颗粒化的方法：对样本的特征属性即光水温进行不同时间段的划分，分别构成由[f]_旬、[f]_月、[f]_(混合)获取的商空间。
4)最后在不同的空间中采用覆盖算法对这些样本进行学习，获得学习规则后，加以后处理获得预测产量值。
5)该预测模型还将江淮地区不同城市不同时间的样本混合在一起学习测试，也可得到满意结果，说明该模型有空间时间普适性。
本文的主要创新之处：
1．从认识论的观点出发，对覆盖算法提出“最小覆盖原理”，从几何意义上对最小覆盖的性质、特点进行深入研究，得出最小覆盖的充分必要条件，依此给出相应的求最小覆盖的算法；讨论了最小覆盖算法的迭代次数估计。
2．结合了商空间理论中属性颗粒化求解商空间的思想和合成方法，提出了基于粒度计算的覆盖算法。
3．将商空间粒度计算理论和覆盖算法相结合，应用于安徽省冬小麦的产量预测，建立了安徽省冬小麦不同粒度下的产量预测模型。
The macroscopical analysis of human intelligence is mainly presented by the ability to conceptualize the world at different granules and translate from one abstraction level to the others easily. The theory of quotient space granular computing represents the attributes of an object as well as the relationship among objects, and at the same time, describes the transition, transformation, mergence and decomposition among different grain-size worlds, therefore, this theory is a powerful tool to describe the macroscopical analysis ability human intelligence.
The microscopical learning of human intelligence is mainly presented by the ability to summarize rules by learning large amounts of things, which can be realized through learning models. Covering algorithm, as the basis of constructive machine learning method, is one of the models that accord, which can simulate the microscopical learning ability of human intelligence.
This dissertation studies quotient space granular computing theory and covering algorithm, which are the two models simulating human intelligence in two different ways, aimed at establishing formalized model for certain intelligent behavior and re-displaying partial function of human intelligence. The combination of the both is applied in the yield forecast of the winter wheat in Anhui Province, which forms the forecast models at different grain-size worlds. Experiments illustrate the universality of models.
The dissertation includes:
1. The outstanding function of quotient structure in quotient space granular computing theory is analyzed.
To construct a proper abstraction level for a problem solver, how to obtain quotient space from the aspects of domain, attribute and structure are discussed to form a concrete idea, which serve as the theoretical basis for covering algorithm based on granular computing in Chapter Three, and the forecast model of winter wheat in Anhui Province based on granular computing in Chapter Six. The study is emphasis on the important function of quotient structure in quotient space theory, which is also considered as one of the major differences between quotient spacea theory and rough set theory.
2. The covering algorithm based on granular computing is put forward, and the covering algorithm is applied in clustering fields.
The rudiment of covering algorithm, including domain covering algorithm and alternative covering algorithm, is briefly introduced in this dissertation. Covering algorithm based on granular computing is put forward with relation to mergence method and attribute-granulation method in quotient space theory. Moreover, covering algorithm is introduced into clustering field, and that covering algorithm is applicable to clustering as well as classification is also indicated.
3. The principle of "minimum covering" in covering algorithm is put forward.
The principle of "minimum covering" in covering algorithm is put forward from the epistemological points of view, and the properties and characteristics of the minimum covering are further explored. The principle of"minimum covering" on covering algorithm is put forward from the perspective of geometry to form the sufficient and necessary conditions of minimum covering, and accordingly, the minimum covering algorithm. The complexity of minimum covering algorithm is also discussed. At last the minimum covering is solved with a programming way.
4. Probability Model of Covering Algorithm is given.
The kernel function and the idea of global optimization are introduced into covering algorithm to form the probability model of covering algorithm. In this algorithm, the decision function of covering algorithm has been changed into kernel function, and then the optimization is processed from the point of maximum likelihood principle of the statistical model to realize the automatic computing of the parameter of kernel function, which offers a way to solve the problem of parameter selection of kernel function.
5. Forecasting modcls in different graih-size worlds are formed, according to the information of local weather and the yield of winter wheat collected from observatories that have been established in some of the cities in Anhui Province.
1) Issue description is constructed in original space. The annual information from each city of Anhui Province forms an element in domain, namely, sample, which comprises two parts- characteristic attributes and decision attribute.
2) The general methods of weather yield forecast are analyzed in this dissertation, and the disadbantages of these methods are pointed up. The improvement, accordingly, is put forward to realize the function of the process module of decision making attribute in the model constructed in this dissertation. After the yield phases are divided, the gray model is adopted to calculate the relative weather yield, which serves as the decision attribute of the sample.
3) The methods of domain-granulation and attribute-granulation in quotient space theory are adopted to form different forecast models at different grain-size worlds.
a) The granulation of domain: Cities between Yangtze River and Huai Rivers are set as examples. The elements which are closely related in structure or function belong to the same classification called [X]_(jianghuai), which forms a forecast model, setting areas between Yangtze River and Huai Rivers as the whole.
b) The granulation of attribute: The characteristic attributes of the sample, such as sunlight, water and temperature, are granulated by time stages to construct the quotient set [f]_(ten-days), [f]_(month) and [f]_(mix), respectively.
4) At last, covering algorithm is adopted to carry out rules on these samples collected at different granules, and then forecast the real amount of yield.
5) Samples about different cities between Yangtze River and Huai River are also mixed for learning and the results are satisfactory, which demonstrate the model is universal
The innovations of this dissertation are as follows:
1. The principle of"minimum covering" of covering algorithm is put forward from the epistemological points of view, and the properties and characteristics of the minimum covering are further explored from the perspective of geometry to form the sufficient and necessary conditions of minimum covering, and accordingly, the minimum covering algorithm. The estimation of iteration times of minimum covering algorithm is also discussed.
2. Covering algorithm based on granular computing is put forward with relation to mergence method and attribute-granulation method in quotient space theory.
3. The combination of both quotient space theory and covering algorithm is applied in the yield forecast of the winter wheat in Anhui Province to form yield forecast models at different grain-size worlds.
人类智能的微观分析能力主要体现在可以从大量事物学习中归纳出规律。这种能力可以通过建立学习模型来实现。作为构造性机器学习方法基础的覆盖算法正是满足条件的学习模型之一，通过对覆盖算法的研究可以模拟人类智能微观学习能力。
本文分别研究了商空间粒度计算理论和覆盖算法这两个模拟人类智能两大特点的模型，并将它们有机地结合在一起，以期为人类的某些智力行为建立适当的形式化模型，利用计算机再显人类智能的部分功能。本文将其应用于安徽省冬小麦产量预测中，给出了不同粒度下的预测模型，并通过实例说明该模型具有时间和空间普适性。
主要工作包括：
1．研究了商结构在商空间粒度计算理论中的突出作用。
研究了商空间粒度计算理论中求解商空间的方法，讨论了如何分别从描述问题的三个因素——论域、属性、结构出发获取商空间，并给出具体思路，为第三章所述的基于粒度计算的覆盖算法提供理论基础，第六章所述的基于粒度计算的安徽省冬小麦产量的预测模型也是以此为基础；重点研究了商结构在商空间理论中的重要作用，将其作为商空间理论与粗糙集理论的主要区别之一。
2．提出基于粒度计算的覆盖算法；将覆盖算法用于聚类研究。
简要介绍了覆盖算法的雏形——领域覆盖及其交叉覆盖算法，结合商空间理论中属性颗粒化求解商空间的思想和合成方法，提出基于粒度计算的覆盖算法；将覆盖算法引入聚类领域，指出覆盖算法不但可以用于分类，也可以适用于聚类研究。
3．提出覆盖算法的“最小覆盖原理”。
从认识论的观点出发，对覆盖算法提出“最小覆盖原理”，并从几何意义上对最小覆盖的性质、特点进行深入研究，得出最小覆盖的充分必要条件，依此给出相应的求最小覆盖的算法；讨论了最小覆盖算法的复杂性；最后利用规划方法求解最小覆盖算法。
4．给出概率模型下的覆盖算法。
将核函数思想和全局最优思想引入覆盖算法，给出概率模型下的覆盖算法。该算法将覆盖算法中的决策函数改为核函数，然后从概率论中的“最大似然原理”的角度对覆盖算法进行优化，自动求解核函数中的参数，以解决一般核函数中参数选择的难题。
5．以安徽省的部分城市建站以来的气象及其冬小麦产量信息为研究对象，建立不同粒度下的预测模型。
1)构造原空间下的问题描述，安徽省每个城市每年的信息构成论域中的一个元素——样本，该样本由两大部分构成——特征属性和决策属性。
2)分析了气象产量预测的一般方法，并说明这些方法存在的弊端，在此基础上加以改进，用以实现本文所建模型中决策属性处理模块的功能，经过产量阶段划分后，采用灰色模型求得相对气象产量，作为样本的决策属性。
3)对论域和特征属性分别采用商空间计算理论中求解商空间的方法处理，以期从不同角度获取不同粒度下的预测模型。
a)对论域颗粒化的方法：以江淮地区的城市为例，把结构上或功能上关系密切的元素划分为一类，得到[X]_(江淮)，由此构造以江淮地区为整体的预测模型；
b)对属性颗粒化的方法：对样本的特征属性即光水温进行不同时间段的划分，分别构成由[f]_旬、[f]_月、[f]_(混合)获取的商空间。
4)最后在不同的空间中采用覆盖算法对这些样本进行学习，获得学习规则后，加以后处理获得预测产量值。
5)该预测模型还将江淮地区不同城市不同时间的样本混合在一起学习测试，也可得到满意结果，说明该模型有空间时间普适性。
本文的主要创新之处：
1．从认识论的观点出发，对覆盖算法提出“最小覆盖原理”，从几何意义上对最小覆盖的性质、特点进行深入研究，得出最小覆盖的充分必要条件，依此给出相应的求最小覆盖的算法；讨论了最小覆盖算法的迭代次数估计。
2．结合了商空间理论中属性颗粒化求解商空间的思想和合成方法，提出了基于粒度计算的覆盖算法。
3．将商空间粒度计算理论和覆盖算法相结合，应用于安徽省冬小麦的产量预测，建立了安徽省冬小麦不同粒度下的产量预测模型。
The macroscopical analysis of human intelligence is mainly presented by the ability to conceptualize the world at different granules and translate from one abstraction level to the others easily. The theory of quotient space granular computing represents the attributes of an object as well as the relationship among objects, and at the same time, describes the transition, transformation, mergence and decomposition among different grain-size worlds, therefore, this theory is a powerful tool to describe the macroscopical analysis ability human intelligence.
The microscopical learning of human intelligence is mainly presented by the ability to summarize rules by learning large amounts of things, which can be realized through learning models. Covering algorithm, as the basis of constructive machine learning method, is one of the models that accord, which can simulate the microscopical learning ability of human intelligence.
This dissertation studies quotient space granular computing theory and covering algorithm, which are the two models simulating human intelligence in two different ways, aimed at establishing formalized model for certain intelligent behavior and re-displaying partial function of human intelligence. The combination of the both is applied in the yield forecast of the winter wheat in Anhui Province, which forms the forecast models at different grain-size worlds. Experiments illustrate the universality of models.
The dissertation includes:
1. The outstanding function of quotient structure in quotient space granular computing theory is analyzed.
To construct a proper abstraction level for a problem solver, how to obtain quotient space from the aspects of domain, attribute and structure are discussed to form a concrete idea, which serve as the theoretical basis for covering algorithm based on granular computing in Chapter Three, and the forecast model of winter wheat in Anhui Province based on granular computing in Chapter Six. The study is emphasis on the important function of quotient structure in quotient space theory, which is also considered as one of the major differences between quotient spacea theory and rough set theory.
2. The covering algorithm based on granular computing is put forward, and the covering algorithm is applied in clustering fields.
The rudiment of covering algorithm, including domain covering algorithm and alternative covering algorithm, is briefly introduced in this dissertation. Covering algorithm based on granular computing is put forward with relation to mergence method and attribute-granulation method in quotient space theory. Moreover, covering algorithm is introduced into clustering field, and that covering algorithm is applicable to clustering as well as classification is also indicated.
3. The principle of "minimum covering" in covering algorithm is put forward.
The principle of "minimum covering" in covering algorithm is put forward from the epistemological points of view, and the properties and characteristics of the minimum covering are further explored. The principle of"minimum covering" on covering algorithm is put forward from the perspective of geometry to form the sufficient and necessary conditions of minimum covering, and accordingly, the minimum covering algorithm. The complexity of minimum covering algorithm is also discussed. At last the minimum covering is solved with a programming way.
4. Probability Model of Covering Algorithm is given.
The kernel function and the idea of global optimization are introduced into covering algorithm to form the probability model of covering algorithm. In this algorithm, the decision function of covering algorithm has been changed into kernel function, and then the optimization is processed from the point of maximum likelihood principle of the statistical model to realize the automatic computing of the parameter of kernel function, which offers a way to solve the problem of parameter selection of kernel function.
5. Forecasting modcls in different graih-size worlds are formed, according to the information of local weather and the yield of winter wheat collected from observatories that have been established in some of the cities in Anhui Province.
1) Issue description is constructed in original space. The annual information from each city of Anhui Province forms an element in domain, namely, sample, which comprises two parts- characteristic attributes and decision attribute.
2) The general methods of weather yield forecast are analyzed in this dissertation, and the disadbantages of these methods are pointed up. The improvement, accordingly, is put forward to realize the function of the process module of decision making attribute in the model constructed in this dissertation. After the yield phases are divided, the gray model is adopted to calculate the relative weather yield, which serves as the decision attribute of the sample.
3) The methods of domain-granulation and attribute-granulation in quotient space theory are adopted to form different forecast models at different grain-size worlds.
a) The granulation of domain: Cities between Yangtze River and Huai Rivers are set as examples. The elements which are closely related in structure or function belong to the same classification called [X]_(jianghuai), which forms a forecast model, setting areas between Yangtze River and Huai Rivers as the whole.
b) The granulation of attribute: The characteristic attributes of the sample, such as sunlight, water and temperature, are granulated by time stages to construct the quotient set [f]_(ten-days), [f]_(month) and [f]_(mix), respectively.
4) At last, covering algorithm is adopted to carry out rules on these samples collected at different granules, and then forecast the real amount of yield.
5) Samples about different cities between Yangtze River and Huai River are also mixed for learning and the results are satisfactory, which demonstrate the model is universal
The innovations of this dissertation are as follows:
1. The principle of"minimum covering" of covering algorithm is put forward from the epistemological points of view, and the properties and characteristics of the minimum covering are further explored from the perspective of geometry to form the sufficient and necessary conditions of minimum covering, and accordingly, the minimum covering algorithm. The estimation of iteration times of minimum covering algorithm is also discussed.
2. Covering algorithm based on granular computing is put forward with relation to mergence method and attribute-granulation method in quotient space theory.
3. The combination of both quotient space theory and covering algorithm is applied in the yield forecast of the winter wheat in Anhui Province to form yield forecast models at different grain-size worlds.
引文
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