基于子集融合与规则简约的磨矿过程模糊建模

针对选矿厂磨矿生产过程的模糊建模问题,本文提出一种基于模糊集融合和规则简约的模糊建模方法.该方法针对基于数据建立的磨矿过程Takagi-Sugeno模型,采用模糊C均值聚类方法对同一变量下的隶属度函数参数进行聚类,得到对不同工况具有代表性的融合后的隶属度函数,来降低过度拟合的影响.此外,本文根据规则库中的规则权值,对前件相同的冗余规则进行约简,形成最终的离线模糊规则库,有效提高了规则库的泛化能力.为验证本文方法的有效性,分别采用经典数据与实际工业数据进行了实验论证,从精度和泛化能力上体现了本文方法的优势.     

一类模糊模型的结构优化问题研究

提出了将模糊模型统计信息准则（FSIC）、基于奇异值分解（SVD）的模糊模型结构分析、模糊规则删除与合并、参数估计等方法集成的模糊模型结构迭代优化。研究表明,将SVD引入到模糊模型结构分析、结合FSIC指导模糊规则删除和合并,可从模型结构精简化、模型拟合和泛化性能等方面综合地确定最优模型结构;文中提出了实用可行的基于聚类加权组合和多重模糊聚类的规则合并算法。该迭代优化方法已成功地应用于非线性函数逼近和航空煤油干点估计器的模糊模型构造。仿真结果表明文中提出的方法简单实用,优化的模型结构比文献中给出的模型结构更加精简。     

基于聚类分析的模糊分类系统构造方法

提出一种新的利用样本数据构造模糊分类系统的方法.首先对每一类样本进行聚类分析,提出一种自适应确定各类别聚类数目的迭代算法,从而实现对特征空间的划分.然后对每个特征子空间产生一条模糊规则,将所有的规则组合在一起形成初始模糊分类系统,并对该系统进行结构简化和参数优化,在系统结构尽可能简单的前提下,进一步提高系统的分类性能.最后利用该方法对二维特征空间的两类样本和Iris数据样本进行分类.仿真结果表明,该方法能利用较少的模糊分类规则达到较高的识别率.     

Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.     

一类基于数据的解释性模糊建模方法的研究

An approach to identify interpretable fuzzy models from data is proposed. Interpretability, which is one of the most important features of fuzzy models, is analyzed first. The number of fuzzy rules is determined by fuzzy cluster validity indices. A modified fuzzy clustering algorithm,combined with the least square method, is used to identify the initial fuzzy model. An orthogonal least square algorithm and a method of merging similar fuzzy sets are then used to remove the redundancy of the fuzzy model and improve its interpretability. Next, in order to attain high accuracy, while preserving interpretability, a constrained Levenberg-Marquardt method is utilized to optimize the precision of the fuzzy model. Finally, the proposed approach is applied to a PH neutralization process, and the results show its validity.     

Fuzzy rule weight modification with particle swarm optimisation

The most challenging problem in developing fuzzy rule-based classification systems is the construction of a fuzzy rule base for the target problem. In many practical applications, fuzzy sets that are of particular linguistic meanings, are often predefined by domain experts and required to be maintained in order to ensure interpretability of any subsequent inference results. However, learning fuzzy rules using fixed fuzzy quantity space without any qualification will restrict the accuracy of the resulting rules. Fortunately, adjusting the weights of fuzzy rules can help improve classification accuracy without degrading the interpretability. There have been different proposals for fuzzy rule weight tuning through the use of various heuristics with limited success. This paper proposes an alternative approach using Particle Swarm Optimisation in the search of a set of optimal rule weights, entailing high classification accuracy. Systematic experimental studies are carried out using common benchmark data sets, in comparison to popular rule based learning classifiers. The results demonstrate that the proposed approach can boost classification performance, especially when the size of the initially built rule base is relatively small, and is competitive to popular rule-based learning classifiers.     

基于协同进化算法的TS模糊模型设计

提出一种基于协同进化算法的TS模糊模型设计方法．该方法由以下两步组成：（1）采用模糊聚类算法辨识初始的模糊模型；（2）利用协同进化算法对所获得的初始模糊模型进行结构和参数的优化．协同进化算法由两类种群组成：规则前件种群和隶属函数参数种群；其适应度函数同时考虑模型的精确性和解释性，采用两种群合作计算的策略；为提高模型的解释性，在协同进化算法中利用基于相似性的模型简化方法对模型进行约简．最后，利用该方法对Mackey-Glass系统进行辨识，仿真结果验证了方法的有效性．     

Fuzzy rule generation for adaptive scheduling in a dynamic manufacturing environment

This paper proposes a fuzzy rule-based system for an adaptive scheduling, which dynamically selects and applies the most suitable strategy according to the current state of the scheduling environment. The adaptive scheduling problem is generally considered as a classification task since the performance of the adaptive scheduling system depends on the effectiveness of the mapping knowledge between system states and the best rules for the states. A rule base for this mapping is built and evolved by the proposed fuzzy dynamic learning classifier based on the training data cumulated by a simulation method. Distributed fuzzy sets approach, which uses multiple fuzzy numbers simultaneously, is adopted to recognize the system states. The developed fuzzy rules may readily be interpreted, adopted and, when necessary, modified by human experts. An application of the proposed method to a job-dispatching problem in a hypothetical flexible manufacturing system (FMS) shows that the method can develop more effective and robust rules than the traditional job-dispatching rules and a neural network approach.     

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。     

一种基于动态聚类的模糊分类规则的生成方法

介绍了一种基于动态聚类的模糊分类规则的生成方法，这种方法能决定规则数目，隶属函数的位置及形状．首先，介绍了基于超圆雏体隶属函数的模糊分类规则的基本形式；然后，介绍动态聚类算法，该算法能将每一类训练模式动态的分为成簇，对于每簇，则建立一个模糊规则；通过调整隶属函数的斜度，来提高对训练模式分类识别率，达到对模糊分类规则进行优化调整的目的；用两个典型的数据集评测了这篇文章研究的方法，这种方法构成的分类系统在识别率与多层神经网络分类器相当，但训练时间远少于多层神经网络分类器的训练时间．     

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi–Sugeno–Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.      

GSETSK: a generic self-evolving TSK fuzzy neural network with a novel Hebbian-based rule reduction approach

Takagi–Sugeno–Kang (TSK) fuzzy systems have been widely applied for solving function approximation and regression-centric problems. Existing dynamic TSK models proposed in the literature can be broadly classified into two classes. Class I TSK models are essentially fuzzy systems that are limited to time-invariant environments. Class II TSK models are generally evolving systems that can learn in time-variant environments. This paper attempts to address the issues of achieving compact, up-to-date fuzzy rule bases and interpretable knowledge bases in TSK models. It proposes a novel rule pruning method which is simple, computationally efficient and biologically plausible. This rule pruning algorithm applies a gradual forgetting approach and adopts the Hebbian learning mechanism behind the long-term potentiation phenomenon in the brain. It also proposes a merging approach which is used to improve the interpretability of the knowledge bases. This approach can prevent derived fuzzy sets from expanding too many times to protect their semantic meanings. These two approaches are incorporated into a generic self-evolving Takagi–Sugeno–Kang fuzzy framework (GSETSK) which adopts an online data-driven incremental-learning-based approach.Extensive experiments were conducted to evaluate the performance of the proposed GSETSK against other established evolving TSK systems. GSETSK has also been tested on real world dataset using the high-way traffic flow density and Dow Jones index time series. The results are encouraging. GSETSK demonstrates its fast learning ability in time-variant environments. In addition, GSETSK derives an up-to-date and better interpretable fuzzy rule base while maintaining a high level of modeling accuracy at the same time.     

Fuzzy Reasoning as a Control Problem

Different from the dominant view of treating fuzzy reasoning as generalization of classical logical inference, in this paper fuzzy reasoning is treated as a control problem. A new fuzzy reasoning method is proposed that employs an explicit feedback mechanism to improve the robustness of fuzzy reasoning. The fuzzy rule base given a priori serves as a controlled object, and the fuzzy reasoning method serves as the corresponding controller. The fuzzy rule base and the fuzzy reasoning method constitute a control system that may be open loop or closed loop, depending on the underlying reasoning goals/constraints. The fuzzy rule base, the fuzzy reasoning method, and the corresponding reasoning goals/constraints define the three distinct ingredients of fuzzy reasoning. While various existing fuzzy reasoning methods are essentially a static mapping from the universe of single fuzzy premises to the universe of single fuzzy consequences, the new fuzzy reasoning method maps sequences of fuzzy premises to sequences of fuzzy consequences and is a function of the underlying reasoning goals/constraints. The Monte Carlo simulation shows that the new fuzzy reasoning method is much more robust than the optimal fuzzy reasoning method proposed in our previous work. The explicit feedback mechanism embedded in the fuzzy reasoning method does significantly improve the robustness of fuzzy reasoning, which is concerned with the effects of perturbations associated with given fuzzy rule bases and/or fuzzy premises on fuzzy consequences. The work presented in this paper sets a new starting point for various principles of feedback control and optimization to be applied in fuzzy reasoning or logical inference and to explore new forms of reasoning including robust reasoning and adaptive reasoning. It can be also expected that the new fuzzy reasoning method presented in this paper can be used for modeling and control of complex systems and for decision-making under complex environments.     

基于协同进化算法的高维模糊分类系统的设计

基于协同进化算法,提出一种高维模糊分类系统的设计方法．首先定义系统的精确性指标,给出解释性的必要条件,利用聚类算法辨识初始模型．相互协作的3类种群分别代表系统的特征变量、规则前件和模型隶属函数的参数,适应度函数采用3类种群合作计算的策略,在算法运行中利用基于相似性的模型简化技术约简模糊系统,最后利用该方法对Wine问题进行研究．仿真结果表明该方法能够对高维分类问题的特征变量进行选择,同时利用较少规则和模糊集合数达到较高的识别率．     

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。     

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。     

Simplification of a fuzzy mechanism with rule combination

 In this paper, a systematic approach to reduce the complexity of a fuzzy controller with the rule combination of a fuzzy rule base is presented. The complexity of a fuzzy controller is defined to be the computation load in this work. The proposed rule combination approach can be applied to the fuzzy mechanisms with product–sum and min–max inferences. With the input membership functions indexed in sequence for each input variable, the n-dimensional fuzzy rule table is represented as vectors so that the combination of the fuzzy rule base is realizable. Then the adjacent fuzzy rules with the same output consequent are combined to have smaller size of fuzzy rule base. The fuzzy mechanism with the combined rule table is shown to have the same output with the original fuzzy mechanism (without rule combination). Thus, in many applications, the rule combination approach presented in this paper can be used to reduce the complexity of the fuzzy mechanism without degrading the performances. Moreover, the Don't Care fuzzy rules are defined and it is indicated that the number of the necessary fuzzy rules might be decreased when the Don't Care fuzzy rules are taken into consideration. Further, the properties of the simplification approach for the fuzzy rule base of the fuzzy mechanism are discussed.     

基于密度峰值的加权犹豫模糊聚类算法

由于人们对事物认知的局限性和信息的不确定性,在对决策问题进行聚类分析时,传统的模糊聚类不能有效解决实际场景中的决策问题,因此有学者提出了有关犹豫模糊集的聚类算法.现有的层次犹豫模糊K均值聚类算法没有利用数据集本身的信息来确定距离函数的权值,且簇中心的计算复杂度和空间复杂度都是指数级的,不适用于大数据环境.针对上述问题,...     

Integrating fuzzy knowledge by genetic algorithms

We propose a genetic algorithm-based fuzzy knowledge integration framework that can simultaneously integrate multiple fuzzy rule sets and their membership function sets. The proposed approach consists of two phases: fuzzy knowledge encoding and fuzzy knowledge integration. In the encoding phase, each fuzzy rule set with its associated membership functions is first transformed into an intermediary representation and then further encoded as a string. The combined strings form an initial knowledge population, which is then ready for integration. In the knowledge-integration phase, a genetic algorithm is used to generate an optimal or nearly optimal set of fuzzy rules and membership functions from the initial knowledge population. Two application domains, the hepatitis diagnosis and the sugarcane breeding prediction, were used to show the performance of the proposed knowledge-integration approach. Results show that the fuzzy knowledge base derived using our approach performs better than every individual knowledge base