粒度格矩阵空间模型及其应用研究
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摘要
人们在认知和处理现实世界的问题时,常常采用从不同层次观察问题的策略,这种策略可以使用粒计算的原理更加准确、严格地来表述。因此粒计算不仅是一些理论、方法、技术或工具的总称,而且可以认为是一种看待客观世界的世界观和方法论。
粒计算可以从两大方面来进行研究:粒的构造和使用粒的计算。前者处理粒的形成、表示和解释,后者处理在问题求解中粒的运用。总的来说,粒计算是通过粒对现实问题的抽象、粒之间的关系、粒的分解和合成以及粒或者粒集之间的交互来描述和解决问题的一种方法。
本文提出并研究了一种新的粒计算模型—粒度格矩阵空间模型,该模型不仅继承了粗糙集和商空间的“等价类”和“商集”等基于划分的概念,而且吸收了模糊集处理不精确问题的方法,同样具有在模糊空间下处理问题的能力。该模型的提出架起了关系、粒、矩阵理论以及图论之间的一座桥梁,也为模糊集、粗糙集和商空间等理论的统一提供了简单可行的算法模型。主要研究工作包括:
(1)提出了粒度格矩阵空间模型,通过粒度格矩阵模拟粒以及粒层之间的关系。该模型不仅能对知识和信息进行不同层次和粗细程度的粒化,而且体现了粒化后粒层之间的关系,从而更好地挖掘内在知识。模型中的知识分层结构有利于实现不同粒和粒层之间的跳跃和往返,提供了一种知识发现和描述的新方法。
(2)提出了基于新模型的完备和不完备信息系统的知识发现算法。该算法分别以完备和不完备信息系统为研究对象,将常规的知识约简转化为矩阵的数值运算过程,提供了有别于传统方法的一种新的运算规则。通过理论分析和算例证明了该算法和现有的几种常规知识约简算法的等价性。
(3)提出了基于新模型的动态聚类算法。该算法首先利用多阶段思想,结合F统计量进行粒度层划分及确定;其次,运用基于新模型的知识发现算法,重新确定距离公式。最后,采用“动态粒度”的思想,对样本点用“粗”和“细”粒度分别处理。该算法在降低计算复杂度的情况下提高了聚类的准确性。它从应用的角度验证了该粒度模型的可行性和有效性。
(4)提出了基于新模型的图像分割算法。该算法基于图像分割问题与粒度划分的统一性,将图像转化为具有分层结构的知识体系,构造了多个单元粒度层,通过各单元粒度层分割的粒度合成取得最终的分割效果。实验证明该算法在边缘细化的处理上有明显的效果。
其中创新性工作包括:
(1)提出了粒度格矩阵空间模型,为模糊集、粗糙集和商空间等理论的统一提供了简单可行的算法模型。
(2)以完备信息系统为研究对象,通过构造粒度矩阵和粒度格矩阵,实现了基于粒度格矩阵空间模型的知识发现。
(3)以不完备信息系统为研究对象,通过构造相容粒进行知识粒化,实现了基于粒度格矩阵空间模型的知识发现。
(4)采用“动态粒度”的思想,提出了基于粒度格矩阵空间模型的动态聚类算法。该算法在降低计算复杂度的情况下提高了聚类的准确性。
(5)基于图像分割问题与粒度划分的统一性,提出了基于粒度格矩阵空间模型的图像分割算法。该算法在边缘细化的处理上较其它算法有明显的改进。
When people deal with problems in real world, they often analyze it in different levels. The strategy is described more accurately by granular computing. Therefore, granular computing is not only the sum of theory, method and tools, but also regarded as world view and methodology.
Granular computing is studied in two respects, which are construction and computation of granules. The former deals with its form, description and interpretation. The latter focus on its applications in solving problem. All in one word, granular computing describes the problem by the relationship among granules, decomposition and composition of granules.
One new granular computing model is proposed in the paper, which is granular lattice matrix space model. It not only has the merit of rough set and quotient space based on conception of division, but also solves the problem in fuzzy space, such as the way of fuzzy set. It sets up the bridge between granularity, matrix and image. Besides it, it provides a simple way to unite fuzzy set, rough set and quotient space to one model. The main researches and contributions involve four points as following.
(1)Propose the model of granular lattice matrix space. It simulates the relationship of granules and granular layers by granular matrix and granular lattice matrix. It not only granulates knowledge and information into granules, but also reflects the relation among granular layer. The knowledge hierarchy structure helps to realize transition among granules and granular layer, which provides a new method to describe knowledge.
(2)Develop knowledge discovery algorithm of incomplete and complete information system based on the model. Take incomplete and complete information system as research objects, we substitute matrix operation for general algorithms. It provides a new method different from traditional methods, and it is proved by theory analyze and examples.
(3)Propose dynamic clustering algorithm based on the model. Firstly, we takes statistic variable F to decide granular layer. Secondly, we apply knowledge discovery algorithm based on the model to define distance formula. Finally, we adopt dynamic granularity to value sample points by coarser and finer granularity. The new algorithm not only improves clustering accuracy, but also testifies the new model in application.
(4)Develop image segmentation algorithm based on the model. Based on the relation between image segmentation and granularity division, firstly we convert image into hierarchy knowledge structure, then construct unit granular layer, finally compose segmentations in each unit layer to acquire final effect. Experiments improve the algorithm has better effect in edge fining.
The innovative achievements of the paper can be concluded as following.
(1) Propose the model of granular lattice matrix space. It provides a simple way to unite fuzzy set, rough set and quotient space to one model
(2) Taking complete information system as object, we develop knowledge discovery algorithm based on the model by granular matrix and granular lattice matrix.
(3) Taking incomplete information system as object, we propose knowledge discovery algorithm based on the model by tolerance granules.
(4) Adopting dynamic granularity, we propose dynamic clustering algorithm based on the model. It improves clustering accuracy while reducing time complexity.
(5) Based on the coherence of granularity division and image, we develop image segmentation algorithm based on the model. It has better effects in edge fining than other algorithms.
粒计算可以从两大方面来进行研究:粒的构造和使用粒的计算。前者处理粒的形成、表示和解释,后者处理在问题求解中粒的运用。总的来说,粒计算是通过粒对现实问题的抽象、粒之间的关系、粒的分解和合成以及粒或者粒集之间的交互来描述和解决问题的一种方法。
本文提出并研究了一种新的粒计算模型—粒度格矩阵空间模型,该模型不仅继承了粗糙集和商空间的“等价类”和“商集”等基于划分的概念,而且吸收了模糊集处理不精确问题的方法,同样具有在模糊空间下处理问题的能力。该模型的提出架起了关系、粒、矩阵理论以及图论之间的一座桥梁,也为模糊集、粗糙集和商空间等理论的统一提供了简单可行的算法模型。主要研究工作包括:
(1)提出了粒度格矩阵空间模型,通过粒度格矩阵模拟粒以及粒层之间的关系。该模型不仅能对知识和信息进行不同层次和粗细程度的粒化,而且体现了粒化后粒层之间的关系,从而更好地挖掘内在知识。模型中的知识分层结构有利于实现不同粒和粒层之间的跳跃和往返,提供了一种知识发现和描述的新方法。
(2)提出了基于新模型的完备和不完备信息系统的知识发现算法。该算法分别以完备和不完备信息系统为研究对象,将常规的知识约简转化为矩阵的数值运算过程,提供了有别于传统方法的一种新的运算规则。通过理论分析和算例证明了该算法和现有的几种常规知识约简算法的等价性。
(3)提出了基于新模型的动态聚类算法。该算法首先利用多阶段思想,结合F统计量进行粒度层划分及确定;其次,运用基于新模型的知识发现算法,重新确定距离公式。最后,采用“动态粒度”的思想,对样本点用“粗”和“细”粒度分别处理。该算法在降低计算复杂度的情况下提高了聚类的准确性。它从应用的角度验证了该粒度模型的可行性和有效性。
(4)提出了基于新模型的图像分割算法。该算法基于图像分割问题与粒度划分的统一性,将图像转化为具有分层结构的知识体系,构造了多个单元粒度层,通过各单元粒度层分割的粒度合成取得最终的分割效果。实验证明该算法在边缘细化的处理上有明显的效果。
其中创新性工作包括:
(1)提出了粒度格矩阵空间模型,为模糊集、粗糙集和商空间等理论的统一提供了简单可行的算法模型。
(2)以完备信息系统为研究对象,通过构造粒度矩阵和粒度格矩阵,实现了基于粒度格矩阵空间模型的知识发现。
(3)以不完备信息系统为研究对象,通过构造相容粒进行知识粒化,实现了基于粒度格矩阵空间模型的知识发现。
(4)采用“动态粒度”的思想,提出了基于粒度格矩阵空间模型的动态聚类算法。该算法在降低计算复杂度的情况下提高了聚类的准确性。
(5)基于图像分割问题与粒度划分的统一性,提出了基于粒度格矩阵空间模型的图像分割算法。该算法在边缘细化的处理上较其它算法有明显的改进。
When people deal with problems in real world, they often analyze it in different levels. The strategy is described more accurately by granular computing. Therefore, granular computing is not only the sum of theory, method and tools, but also regarded as world view and methodology.
Granular computing is studied in two respects, which are construction and computation of granules. The former deals with its form, description and interpretation. The latter focus on its applications in solving problem. All in one word, granular computing describes the problem by the relationship among granules, decomposition and composition of granules.
One new granular computing model is proposed in the paper, which is granular lattice matrix space model. It not only has the merit of rough set and quotient space based on conception of division, but also solves the problem in fuzzy space, such as the way of fuzzy set. It sets up the bridge between granularity, matrix and image. Besides it, it provides a simple way to unite fuzzy set, rough set and quotient space to one model. The main researches and contributions involve four points as following.
(1)Propose the model of granular lattice matrix space. It simulates the relationship of granules and granular layers by granular matrix and granular lattice matrix. It not only granulates knowledge and information into granules, but also reflects the relation among granular layer. The knowledge hierarchy structure helps to realize transition among granules and granular layer, which provides a new method to describe knowledge.
(2)Develop knowledge discovery algorithm of incomplete and complete information system based on the model. Take incomplete and complete information system as research objects, we substitute matrix operation for general algorithms. It provides a new method different from traditional methods, and it is proved by theory analyze and examples.
(3)Propose dynamic clustering algorithm based on the model. Firstly, we takes statistic variable F to decide granular layer. Secondly, we apply knowledge discovery algorithm based on the model to define distance formula. Finally, we adopt dynamic granularity to value sample points by coarser and finer granularity. The new algorithm not only improves clustering accuracy, but also testifies the new model in application.
(4)Develop image segmentation algorithm based on the model. Based on the relation between image segmentation and granularity division, firstly we convert image into hierarchy knowledge structure, then construct unit granular layer, finally compose segmentations in each unit layer to acquire final effect. Experiments improve the algorithm has better effect in edge fining.
The innovative achievements of the paper can be concluded as following.
(1) Propose the model of granular lattice matrix space. It provides a simple way to unite fuzzy set, rough set and quotient space to one model
(2) Taking complete information system as object, we develop knowledge discovery algorithm based on the model by granular matrix and granular lattice matrix.
(3) Taking incomplete information system as object, we propose knowledge discovery algorithm based on the model by tolerance granules.
(4) Adopting dynamic granularity, we propose dynamic clustering algorithm based on the model. It improves clustering accuracy while reducing time complexity.
(5) Based on the coherence of granularity division and image, we develop image segmentation algorithm based on the model. It has better effects in edge fining than other algorithms.
引文
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