【作者】 穆葆宏；

【导师】 张月琴；

【作者基本信息】 太原理工大学 ， 计算机软件与理论， 2007， 硕士

【摘要】 粒计算的目的是建立一种体现人类问题求解特征的一般模型，其基本思想是在不同的粒度层次上进行问题求解。粒是粒计算的最基本的原语，它是一簇点(对象、物体)由于难以区别，或相似、或接近、或某种功能而结合在一起所构成的。从粒计算的角度来看，问题求解的商空间理论用拓扑来描述论域的结构、用等价关系来完成粒化，借助于自然映射实现在不同粒度层次上的转换。商空间理论作为一种问题求解的方法，有着坚实的理论基础，它采用多侧面、多角度的问题求解方法，可以在解决问题时缩小求解难度，降低计算量。商空间理论把定性的思维和定量的分析有机地统一起来，合理地对复杂问题进行粒度描述，把复杂问题分解为可求解的、不同粒度的学习规则，然后再合成相关的规则，最终得到复杂问题的综合规则。传统的基于距离或相似度的聚类算法一般都基于“特征矢量”的方法，这种方法并不适宜用来处理个体数据。往往由于进行了数据矢量转化操作而造成信息丢失，最终可能会导致聚类结果的不准确。覆盖方法最优之处在于覆盖领域完全真实地反映了样本的分布情况，本文中分析了覆盖算法中需要进一步研究的三个问题：第一个是对该算法识别的正确率与泛化能力之间矛盾的解决，第二个是如何改进覆盖方法，第三是如何提高泛化能力。基于商空间理论，作者提出了对于覆盖算法的改进思想，它能在基本保持分类能力的前提下，提高分类的速度和识别的精度。从对平面双螺旋线数据的实验结果可以看出，与交叉覆盖聚类算法对比，改进的算法的正确识别率显著提高，随着训练样本数据的增加，拒识率为0，若不计训练时间，那么改进的算法是可行的。作为一种正在兴起的智能计算方法，商空间理论和覆盖算法本身还有许多地方有待发展和完善。更多还原

【Abstract】 As an emerging research sub-field of artificial intelligence, granular computing, whose philosophy is to implement the problem solving at different levels of granularity, aims to establish much more general model reflecting the process of human problem solving. Granule, a clump of points (objects) drawn together by indistinguishability, similarity, proximity or functionality, is the primitive notion of granular computing.Quotient space theory of problem solving is generalized from two directions, namely the structure of the universe of discourse and granulation criteria. In the light of granular computing quotient space theory of problem solving exploits topology to describe the structure of the universe of discourse, and utilizes equivalence relation to implement granulation, and relies on the natural mapping to realize the translations among different levels of granulariy.As a method of problem solving, quotient space theory, based on substantial theory, considering the problem from different aspects and multi-hierarchy in the process of problem solving, is a kind of powerful tool in that it can decrease the difficulty of the problem and reduce the computational cost. Unifying the quantitative analysis and the qualitative analysis by utilizing quotient space theory, complex problems are represented by different granules based quotient space. After learning rules of different granules achieved, integrate rules of the complex problem can be gained by composing relative rules.The traditional clustering algorithms based on distance or similarity are vector-based, these methods are unfit for individual behavioral data, there will be a lot of information lost and will lead to the clustering inaccurate.Directed by the theory of quotient space, a improved algorithm of covering algorithm is presented. It can keep the sorting accuracy and cut down the occupying of memory and the cost of data collecting. The simulation experiment about dual spiral data shows the feasibility of the improved alternative coving algorithm proposed above.As a means of the rising artificial intelligence, quotient space theory and covering algorithm itself need more development and consummate.更多还原