基于改进PSO与规则约简的模糊系统优化算法

模糊系统是一种具有强可解释性和高鲁棒性的智能方法,但目前仍存在精度不高、产生的模糊规则太多等缺陷.针对目前存在的问题,论文通过改进粒子群优化算法优化模糊系统高斯型隶属度函数的参数,以及计算规则支持度约简模糊规则,提出了CPSFS和SPSFS两种模糊系统优化算法.在两个不同领域的经典数据集上的研究结果表明:1)CPSFS算法在训练集和测试集上的预测精度明显优于传统的BP神经网络、RBF神经网络、线性回归等算法;2)CPSFS算法与SPSFS算法减少了大量模糊规则,保证了模型的可解释性;3)CPSFS算法在约简模糊规则后预测精度依然表现最优,符合新时代下回归问题对于AI技术的要求.     

改进粒子群优化Takagi-Sugeno模糊径向基函数神经网络的非线性系统建模

针对复杂非线性系统建模的难点问题,提出了一种基于改进的粒子群优化算法（PSO)优化的T-S模糊径向基函数（RBF）神经网络的新型系统建模算法。该算法将T-S模糊模型良好的可解释性及RBF神经网络的自学习能力相结合,构成T-S模糊RBF神经网络用于系统建模,并采用动态调整惯性权重的改进的PSO算法结合递推最小二乘算法实现网络参数的优化调整。首先,利用所提算法进行了非线性多维函数的逼近仿真,仿真结果均方差（MSE）为0.00017,绝对值误差不大于0.04,逼近精度较高;又将该算法用于建立动态流量软测量模型,并进行了相关的实验研究,动态流量测量结果平均绝对误差小于0.15L/min,相对误差为1.97%,基本满足测量要求,并优于已有算法。上述仿真及实验研究结果表明,所提算法对于复杂非线性系统具有较高的建模精度和良好的自适应性。     

基于演进向量量化聚类的增量模糊关联分类方法

为了提高动态数据集上模糊关联分类器（FAC）的建模效率,提出了一种基于演进向量量化（eVQ）聚类的增量模糊关联分类方法。首先,采用eVQ聚类算法增量更新数量属性上的高斯隶属度函数参数;然后,扩展早剪枝更新（UWEP）算法,使之适用于增量挖掘模糊频繁项;最后,以模糊相关度（FCORR）和分类规则前件长度为度量方式裁剪并更新模糊关联分类规则库。在4个UCI标准数据集上的实验结果表明,与批量模糊关联分类建模方法相比,所提方法能够在保证分类精度和解释性的前提下,减少模糊关联分类器的训练时间;基于eVQ的高斯隶属度函数的增量更新有助于提高动态数据集上模糊关联分类器的分类精度。     

基于聚类和SVD算法的解释性模糊建模方法

提出了一种基于减法聚类算法构造解释性模糊模型的方法。首先指出模糊模型解释性的重要地位,分析影响解释性的主要因素;然后利用减法聚类算法辨识初始模糊模型,SVD算法和集合非冗余度约简初始模糊模型,从而提高其解释性;最后采用约束优化算法整体优化模型,提高其精度。PH值中和过程的模糊建模验证了该方法的有效性。     

不确定性数据中基于GSO优化MF的模糊关联规则挖掘方法

针对不确定性数据中模糊关联规则的挖掘问题,提出一种基于群搜索优化(GSO)算法优化隶属度函数(MF)的模糊关联规则挖掘方法。首先,将不确定性数据通过三元语言表示模型进行表示;然后,给定一个初始MF,并以最大化模糊项集支持度和语义可解释性作为适应度函数,通过GSO算法的优化学习获得最佳MF;最后,根据获得的最佳MF,利用改进型的FFP-growth算法来从不确定数据中挖掘模糊关联规则。实验结果表明,该方法能够根据数据集自适应优化MF,以此实现从不确定数据中有效地挖掘关联规则。     

神经模糊系统中模糊规则的优选

提出一种基于两级聚类算法的自组织神经模糊系统，该系统采用两级聚类算法（改进的最近邻域聚类算法和Gustafson-Kessel模糊聚类算法）对输入／输出数据进行模糊聚类，并由模糊聚类的划分熵确定最优划分，建立模糊模型，模型精度可由梯度下降法进一步提高。仿真结果表明，这种神经模糊系统具有结构简单、规则数少、学习速度快以及建模精度高等特点。     

基于批量模糊学习矢量量化的模糊系统辨识

提出一种基于批量模糊学习矢量量化的模糊系统辨识方法．首先通过优化方法自动调整模糊指数，使所得到的模糊规则前件隶属度函数与聚类规则得到的隶属度函数相比具有较好的可解释性；然后针对模糊系统可解释性与精度之间的困境问题，为保证参数的可理解性．利用带约束的非线性优化方法调整后件参数．并用调整参数的界评估因优化造成参数恶化的程度．仿真实验表明，利用该方法得到的模糊系统模型具有较高的透明度，满足合理的精度．     

基于混沌DNA遗传算法的模糊递归神经网络建模

本文受生物DNA分子遗传机制和混沌优化算法的启发,提出了一种混沌DNA遗传算法,用于优化T-S模糊递归神经网络（FRNN）.该方法使用碱基序列表示T-S模糊递归神经网络的前件部分参数,包括模糊规则数,隶属度函数中心点和宽度;设计更为复杂的遗传操作算子来改进遗传算法的寻优性能;利用混沌优化算法优化种群中的较差个体.同时使用递推最小二乘法（RLS）来辨识T-S模糊递归神经网络的后件部分参数.最后,采用基于混沌DNA遗传算法的T-S模糊递归神经网络对一种典型的pH中和过程进行建模。通过与其他建模方法的比较,仿真实验结果表明了所建模型的有效性.     

基于聚类和遗传算法的解释性模糊模型设计

提出了一种基于模糊聚类和遗传算法构建解释性模糊模型的设计方法。定义了模糊模型的精确性指标，给出了模糊模型解释性的必要条件。然后利用模糊聚类算法和最小二乘法辨识初始的模糊模型；采用多目标遗传算法优化模糊模型；为提高模型的解释性，在遗传算法中利用基于相似性的模糊集合和模糊规则的简化方法对模型进行约简。采用该方法对Mackey-Glass系统进行建模，仿真结果验证了该方法的有效性。     

基于多目标遗传算法的TS模糊模型设计

提出一种利用遗传算法进行TS模糊模型的优化设计方法。首先定义了TS模糊模型的精确性指标,给出模糊模型解释性的必要条件。然后利用模糊聚类算法和最小二乘法辨识初始的模糊模型;利用多目标遗传算法优化模糊模型;为提高模型的解释性,在遗传算法中利用基于相似性的模糊集合和模糊规则简化方法对模型进行约简。最后利用该方法进行一类二阶合成非线性动态系统的建模,仿真结果验证了该方法的有效性。     

Application of genetic algorithm for fuzzy rules optimization on semi expert judgment automation using Pittsburg approach

Genetic algorithm is well-known of its best heuristic search method. Fuzzy logic unveils the advantage of interpretability. Genetic fuzzy system exploits potential of optimization with ease of understanding that facilitates rules optimization. This paper presents the optimization of fourteen fuzzy rules for semi expert judgment automation of early activity based duration estimation in software project management. The goal of the optimization is to reduce linguistic terms complexity and improve estimation accuracy of the fuzzy rule set while at the same time maintaining a similar degree of interpretability. The optimized numbers of linguistic terms in fuzzy rules by 27.76% using simplistic binary encoding mechanism managed to improve accuracy by 14.29% and reduce optimization execution time by 6.95% without compromising on interpretability in addition to promote improvement of knowledge base in fuzzy rule based systems.     

Learning cooperative linguistic fuzzy rules using the best–worst ant system algorithm

Within the field of linguistic fuzzy modeling with fuzzy rule‐based systems, the automatic derivation of the linguistic fuzzy rules from numerical data is an important task. In the last few years, a large number of contributions based on techniques such as neural networks and genetic algorithms have been proposed to face this problem. In this article, we introduce a novel approach to the fuzzy rule learning problem with ant colony optimization (ACO) algorithms. To do so, this learning task is formulated as a combinatorial optimization problem. Our learning process is based on the COR methodology proposed in previous works, which provides a search space that allows us to obtain fuzzy models with a good interpretability–accuracy trade‐off. A specific ACO‐based algorithm, the Best–Worst Ant System, is used for this purpose due to the good performance shown when solving other optimization problems. We analyze the behavior of the proposed method and compare it to other learning methods and search techniques when solving two real‐world applications. The obtained results lead us to remark the good performance of our proposal in terms of interpretability, accuracy, and efficiency. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 433–452, 2005.     

A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers

The paper presents a multi-objective genetic approach to design interpretability-oriented fuzzy rule-based classifiers from data. The proposed approach allows us to obtain systems with various levels of compromise between their accuracy and interpretability. During the learning process, parameters of the membership functions, as well as the structure of the classifier's fuzzy rule base (i.e., the number of rules, the number of rule antecedents, etc.) evolve simultaneously using a Pittsburgh-type genetic approach. Since there is no particular coding of fuzzy rule structures in a chromosome (it reduces computational complexity of the algorithm), original crossover and mutation operators, as well as chromosome-repairing technique to directly transform the rules are also proposed. To evaluate both the accuracy and interpretability of the system, two measures are used. The first one – an accuracy measure – is based on the root mean square error of the system's response. The second one – an interpretability measure – is based on the arithmetic mean of three components: (a) the average length of rules (the average number of antecedents used in the rules), (b) the number of active fuzzy sets and (c) the number of active inputs of the system (an active fuzzy set or input means a set or input used by at least one fuzzy rule). Both measures are used as objectives in multi-objective (2-objective in our case) genetic optimization approaches such as well-known SPEA2 and NSGA-II algorithms. Moreover, for the purpose of comparison with several alternative approaches, the experiments are carried out both considering the so-called strong fuzzy partitions (SFPs) of attribute domains and without them. SFPs provide more semantically meaningful solutions, usually at the expense of their accuracy. The operation of the proposed technique in various classification problems is tested with the use of 20 benchmark data sets and compared to 11 alternative classification techniques. The experiments show that the proposed approach generates classifiers of significantly improved interpretability, while still characterized by competitive accuracy.     

混沌扰动模拟退火蚁群算法低碳物流路径优化

低碳物流是目前物流配送领域的热点研究课题,也是群体智能优化算法的重要应用方向。针对物流配送中碳排放的度量方法,以VRP问题为基本模型,以碳排放成本为目标函数,建立了低碳物流配送路径优化模型。为了避免基本蚁群算法出现停滞及早熟现象,提出了带混沌扰动的模拟退火蚁群算法来求解低碳物流配送路径优化模型。该算法将混沌系统及模拟退火机制引入基本蚁群算法,避免了算法陷入局部最优,增强了全局搜索能力,提高了求解效率。通过实验仿真及对比分析可知,带混沌扰动的模拟退火蚁群算法的求解结果明显优于基本蚁群算法,表明了该算法的有效性和合理性。     

Optimizing the modified fuzzy ant-miner for efficient medical diagnosis

The advantage of efficient searches belonging to ant-miner over several other approaches leads to prominent achievements on rules mining. Fuzzy ant-miner, an extension of the ant-miner provides a fuzzy mining framework for the automatic extraction of fuzzy rules from labeled numerical data. However, it is easily trapped in local optimal, especially when it applies to medical cases, where real world accuracy is elusive; and the interpretation and integration of medical knowledge is necessary. In order to relieve such a local optimal difficulty, this paper proposes OMFAM which applies simulated annealing to optimize fuzzy set parameters associated with a modified fuzzy ant-miner (MFAM). MFAM employs attributes and training case weighting. The proposed method, OMFAM was experimented with six critical medical cases for developing efficient medical diagnosis systems. The performance measurement relates to accuracy as well as interpretability of the mined rules. The performance of the OMFAM is compared with such references as MFAM, fuzzy ant-miner (FAM), and other classification methods. At last, it indicates the superiority of the OMFAM algorithm over the others.     

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

When we face a problem with a high number of variables using a standard fuzzy system, the number of rules increases exponentially and the obtained fuzzy system is scarcely interpretable. This problem can be handled by arranging the inputs in hierarchical ways. This paper presents a multi-objective genetic algorithm that learns serial hierarchical fuzzy systems with the aim of coping with the curse of dimensionality. By means of an experimental study, we have observed that our algorithm obtains good results in interpretability and accuracy with problems in which the number of variables is relatively high.     

Design of accurate classifiers with a compact fuzzy-rule base using an evolutionary scatter partition of feature space

An evolutionary approach to designing accurate classifiers with a compact fuzzy-rule base using a scatter partition of feature space is proposed, in which all the elements of the fuzzy classifier design problem have been moved in parameters of a complex optimization problem. An intelligent genetic algorithm (IGA) is used to effectively solve the design problem of fuzzy classifiers with many tuning parameters. The merits of the proposed method are threefold: 1) the proposed method has high search ability to efficiently find fuzzy rule-based systems with high fitness values, 2) obtained fuzzy rules have high interpretability, and 3) obtained compact classifiers have high classification accuracy on unseen test patterns. The sensitivity of control parameters of the proposed method is empirically analyzed to show the robustness of the IGA-based method. The performance comparison and statistical analysis of experimental results using ten-fold cross validation show that the IGA-based method without heuristics is efficient in designing accurate and compact fuzzy classifiers using 11 well-known data sets with numerical attribute values.     

求解分布式顺序统计CFAR检测器参数的新方法

复杂条件下,分布式顺序统计恒虚警率（OS-CFAR）检测系统的参数选择和检测性能分析是一个典型的非线性优化问题,通常采用数值求解和计算机搜索的方法。但在复杂条件下,特别是当传感器数量较多,或采用分布式OS-CFAR这种双门限参数检测方式时,其计算量会异常庞大。提出了一种基于模拟退火的微粒群优化算法,将模拟退火思想引入到具有杂交和高斯变异的粒子群优化算法中,并采用具有递减w算法,保证算法具有较好的全局搜索能力和较好的收敛性。使用这种方法,在进化100代后,在保证精度达到0.000 001,可使所有的系统参数同时得到优化。仿真结果表明,同遗传算法比,虽然该方法收敛速度稍慢,但是可避免遗传算法的早熟问题,同时该方法实施简单方便,便于工程应用。     

基于模糊分类关联规则的分类系统

为了构建高性能的分类系统，应用模糊集软化数量型属性的划分边界，提出了模糊分类关联规则的挖掘算法。由于模糊集能很好地贴近人类的思维方式，因此挖掘得到的模糊分类关联规则易于被人理解．接着提出了基于模糊分类关联规则的分类系统，并采用遗传优化算法训练分类系统．实例分析的结果表明，基于模糊分类关联规则的分类系统具有较好的精度和可解释性．