模糊规则相似性计算与性能分析研究

Computing and performance analysis of similarity between fuzzy rules

针对模糊规则相似性分析和计算问题,本文对模糊规则相似性计算方法进行了研究。首先,将模糊规则相似性等价地转化为多变量模糊集相似性,并对模糊规则相似性计算方法提出3种应用性能评价指标——可区分性、维数依赖性和计算复杂性。其次,在现有两种模糊规则相似性计算方法的基础上,提出4种新的计算方法,对各种方法进行系统地性能分析和比较。最后,对模糊规则相似性计算进行仿真研究,结果表明了所提应用性能指标的有效性、计算方法的可行性及分析结果的正确性。本文研究结果为模糊规则相似性分析和计算提供了依据,尤其为基于模糊规则相似性辨识和合并的模糊系统与模糊神经网络结构简化奠定了基础,提供了一种新的设计思路。

Facing the weaknesses of the existing analysis and computing methods for the similarity between fuzzy rules （FRs）,this paper investigated the computing methods for the similarity between FRs. First, the similarity between FSs was transferred equivalently into the similarity between multivariable fuzzy sets, and then three application based performance criterions- distinguishability,dimension dependency,and computing complexity were proposed to evaluate the computing methods of the similarity between FRs. Second, four new methods were proposed based on the two existing methods for computing the similarity between FRs,and then the performance analysis and comparison between these new and existing methods were performed. Next,a simulation example for the similarity computing between FRs was provided, and the simulation shows effectiveness of the proposed performance criteria, feasibility of the computing methods, and correctness of the analysis conclusions. The results obtained in this paper provide powerful tools and guides for the similarity analysis and computing of FRs. Inparticular, they establish the methodological foundation and provide a new design approach for the merging of similar FRs in the structure simplification of fuzzy systems and fuzzy neural networks.