Kim Min-Soeng, Kim Chang-Hyun, Lee Ju-Jang
Division of Electrical Engineering, Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, 305-701 Daejon, Korea.
IEEE Trans Syst Man Cybern B Cybern. 2006 Oct;36(5):1006-23. doi: 10.1109/tsmcb.2006.872265.
Developing Takagi-Sugeno fuzzy models by evolutionary algorithms mainly requires three factors: an encoding scheme, an evaluation method, and appropriate evolutionary operations. At the same time, these three factors should be designed so that they can consider three important aspects of fuzzy modeling: modeling accuracy, compactness, and interpretability. This paper proposes a new evolutionary algorithm that fulfills such requirements and solves fuzzy modeling problems. Two major ideas proposed in this paper lie in a new encoding scheme and a new fitness function, respectively. The proposed encoding scheme consists of three chromosomes, one of which uses unique chained possibilistic representation of rule structure. The proposed encoding scheme can achieve simultaneous optimization of parameters of antecedent membership functions and rule structures with the new fitness function developed in this paper. The proposed fitness function consists of five functions that consider three evaluation criteria in fuzzy modeling problems. The proposed fitness function guides evolutionary search direction so that the proposed algorithm can find more accurate compact fuzzy models with interpretable antecedent membership functions. Several evolutionary operators that are appropriate for the proposed encoding scheme are carefully designed. Simulation results on three modeling problems show that the proposed encoding scheme and the proposed fitness functions are effective in finding accurate, compact, and interpretable Takagi-Sugeno fuzzy models. From the simulation results, it is shown that the proposed algorithm can successfully find fuzzy models that approximate the given unknown function accurately with a compact number of fuzzy rules and membership functions. At the same time, the fuzzy models use interpretable antecedent membership functions, which are helpful in understanding the underlying behavior of the obtained fuzzy models.
利用进化算法开发高木-关野模糊模型主要需要三个因素：编码方案、评估方法和适当的进化操作。同时，这三个因素的设计应使其能够考虑模糊建模的三个重要方面：建模精度、紧凑性和可解释性。本文提出了一种满足此类要求并解决模糊建模问题的新进化算法。本文提出的两个主要思想分别在于一种新的编码方案和一种新的适应度函数。所提出的编码方案由三条染色体组成，其中一条采用规则结构的独特链式可能性表示。所提出的编码方案可通过本文开发的新适应度函数实现前件隶属函数参数和规则结构的同步优化。所提出的适应度函数由五个函数组成，这些函数考虑了模糊建模问题中的三个评估标准。所提出的适应度函数引导进化搜索方向，以便该算法能够找到具有可解释前件隶属函数的更精确紧凑的模糊模型。精心设计了几种适用于所提出编码方案的进化算子。针对三个建模问题的仿真结果表明，所提出的编码方案和适应度函数在寻找精确、紧凑且可解释的高木-关野模糊模型方面是有效的。从仿真结果可以看出，所提出的算法能够成功找到模糊模型，这些模型能用紧凑数量的模糊规则和隶属函数准确逼近给定的未知函数。同时，这些模糊模型使用可解释的前件隶属函数，这有助于理解所获得模糊模型的潜在行为。
