非线性模糊规划中分段线性隶属函数的构造方法

首先给出了模糊规划中单、双边非线性隶属函数的构建技术。为了解决非线性模糊规划的求解困难问题,进一步提出了一种针对这两类非线性隶属函数进行分段线性化的方法,由高斯取整函数计算出非线性隶属函数的离散点,再根据决策者选择的基准点得到分段线性的隶属函数。构建了相应的模糊规划的规范求解形式,并对数值实例进行了测试,验证了其有效性。     

基于多目标的模糊神经网络及在pH控制过程中的应用

设计了一种基于多目标的动态模糊递归神经网络（FRNN）建模方法,用于pH中和过程的广义预测控制。所设计的多目标优化算法以提高拟合精度和简化网络结构为原则,同时优化模糊神经网络中的模糊规则数、隶属度函数中心点及其宽度,由此得到的FRNN模型可以高精度拟合pH中和过程。依据该动态模型,在控制过程的每一个控制周期得到其局部线性模型,将广义预测控制中复杂的非线性优化问题转化为简单的二次线性规划问题。仿真对比结果验证了所提方法的有效性。     

薄壳注塑制品多指标工艺参数优化

高压、高速和高料温的成型工艺使得薄壳注射成型过程更易形成缺陷,因此有必要对薄壁技术进行研究并控制其缺陷。本文综合运用人工智能、模糊理论等对薄壳注射成型缺陷进行研究,开发出了参数优化模糊专家系统,给出了知识推理的技术,建立了缺陷及工艺参数的隶属度函数及模糊规则表。采用隶属函数来反映对象特征的模糊性和模糊关系,实现了基于规则的模糊推理,并对缺陷优化模块进行了实例验证。     

化工企业生产计划优化中非线性单耗的建模方法

化工过程生产装置的原料单耗与生产负荷呈明显的非线性关系。为了得到更切合实际的化工企业生产计划优化结果,采用分段线性函数和多项式函数对非线性单耗问题建模并进行比较。案例结果表明,分段线性函数不需要回归参数,建模简单,精度较高,对于中等规模问题求解时间短,能够同时处理装置的多种原料非线性单耗,而不需要增加新的整数变量,多项式函数则不具有这些优点。分段线性函数建模方法已经在化工企业生产计划图形建模优化系统(GIOCIMS)中实现,并在中国石化巴陵分公司得到应用。     

模糊核聚类在优化模糊控制隶属函数中的应用

针对模糊控制器隶属函数的设计与优化缺乏自学习能力的缺点,将模糊核聚类算法与TrustRegion(信赖域)方法结合起来。首先利用模糊核聚类算法对模糊控制输入、输出样本集进行聚类,然后用Trust-Region最优化方法对聚类结果进行曲线拟合,实现了模糊控制输入、输出空间的划分、隶属函数类型的确定和参数的优化。在Matlab中的仿真结果表明:模糊控制器经过笔者提出的算法优化后控制品质有较大的改善和提高。     

利用基于模糊综合评判的数据包络分析优化分离序列

提出了一种分离序列综合的方法，该方法建立在模糊综合评判的数据包络分析模型基础上。利用相对隶属度函数建立了模糊综合评判模型，在此基础上采用DEA3数据包络分析评价了模糊综合评判模型。通过引入虚拟最优单元，DEA3模型能够对所有决策单元排序。从而，通过DEA3分析就可以得到最优方案。计算也表明，不能忽略系统输入、输出的选择和隶属度函数对DEA方法寻优能力的影响。     

挤出过程多目标模糊优化分析

采用越小越优型指标特征，建立了多目标挤出过程目标函数的最优点集的隶属函数，并应用模糊分析设计优越理论对橡胶挤出过程多目标优化问题的进行了研究。该方法也适用于一般橡塑加工过程中的多目标优化问题，且易于编程运算。     

板翅式换热器模糊优化设计

应用结构模糊优化理论对板翅式换热器进行多目标优化设计；给出了构造隶属函数及确定目标函数权重的方法，通过线性加权法将多目标化为单目标求解。应用此软件设计了一台换热器，其实际使用结果表明完全达到设计要求。     

基于模糊插值模型的短期负荷预测

针对隶属函数对模糊推理模型描述性能和精度的影响,为了进一步提高模糊插值模型的泛化能力,提出了一类参数可调隶属函数,调整其参数从而可改变函数的形状,使之能逼近常用的三角形、高斯型等隶属函数。用它作为插值函数,提出了基于参数可调隶属函数的模糊插值模型,利用粒子群优化算法（PSO）优化模型中参数,并将该模型应用于电力系统的短期负荷预测中,仿真结果证明了该模型的有效性。     

胶料配方对挤出过程影响的模糊优化设计分析

在建立多目标挤出过程目标函数的最优点集的隶属函数基础上，本文应用模糊优化设计理论对橡胶挤出过程多目标优化问题进行了研究，在实验的基础上，分析了不同的胶料性能对挤出过程的影响，给出了挤出目标函数为模糊最优时的胶料性能。     

Fuzzy modeling and hybrid genetic algorithm optimization of virus removal from water using microfiltration membrane

Membranes are finding increasing applications in disinfection processes including virus removal from water for municipal effluent reuse. The capability of virus removal from water by microfiltration membranes has previously been demonstrated. In this study, the capability of fuzzy logic for modeling and simulation of dead-end microfiltration process for removal of IBR and FMD viruses from water was elucidated. The main parameters indicating membrane performance i.e. flux and rejection were experimentally obtained under different conditions and compared with theoretically calculated flux and rejection using fuzzy inference system. The genetic algorithm which is an efficient and systematic method was employed in the design of fuzzy model for optimization of the poorly understood, irregular and complex membership function with improved performance. Hybrid genetic algorithm was used for optimizing the parameters that are located at the Gaussian membership functions in the premise and consequent of each rule.The results indicated that fuzzy inference system predicts the key parameters i.e. flux and rejection for different operating conditions with an acceptable error. In other words FIS is able to apply for modeling the microfiltration membrane which is mathematically difficult or in many cases an unpredictable process.     

直觉模糊多核聚类算法及其在乙烯原料属性聚类中的应用

随着乙烯裂解原料种类的日益增多,原料分析仪价格昂贵,因此根据乙烯裂解原料属性进行在线聚类,对实现乙烯收率建模,优化乙烯产率、节能减耗具有重要现实意义。为了提高原料在聚类的准确性,提出了一种基于直觉模糊集理论的核聚类算法。即在定义直觉模糊集隶属度时通过引入犹豫度来表征数据的不确定信息,同时利用直觉模糊熵对多核聚类算法的损失函数重新定义,使类簇中的数据点最优化;进一步地,使用随机森林对裂解原料属性进行特征选择,依据对乙烯产率的贡献度选取聚类的主要特征属性。最后根据实际工业裂解的石脑油数据验证了所述算法的有效性。     

A data set for fuzzy colour naming

In computer vision, colour naming has been posed as a fuzzy‐set problem where each colour category is modeled by a function that assigns a membership value to any given sample. However, the success in the automation of this process relies on having an appropriate psychophysical data set for this purpose. In this article we present a data set obtained from a colour‐naming experiment. In this experiment, we used a scoring method to collect a set of judgments adequate for the fuzzy modeling of the colour‐naming task. The data set is composed of 387 colour reflectances, their CIELab and Munsell values, and the corresponding judgments provided by the subjects in the experiment. These judgments are the membership values to the 11 basic colour categories proposed by Berlin and Kay (Berlin B, Kay P. Berkeley: University of California; 1969). All these data have been made available online ( http://www.cvc.uab.es/color_naming ) and, in this article we provide a wide analysis of them. To prove the suitability of the proposed scoring methodology, we have computed a set of common statistics in colour‐naming experiments, such as consensus and consistency, on our data set. The results make it possible for us to conclude the coherence of our data with previous experiments and, thus, its usefulness for the fuzzy modeling of colour naming. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 48–56, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20172     

An Approach to Formulation of FNLP with Complex Piecewise Linear Membership Functions

Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming （FNLP） problem with piecewise linear membership functions （PLMFs）. However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.     

基于FCMISVM的自适应软测量建模算法及其在PX吸附分离过程中的应用

To overcome the problem that soft sensor models cannot be updated with the process changes, a soft sensor modeling algorithm based on hybrid fuzzy c-means (FCM) algorithm and incremental support vector machines (ISVM) is proposed. This hybrid algorithm FCMISVM includes three parts: samples clustering based on FCM algorithm, learning algorithm based on ISVM, and heuristic sample displacement method. In the training process, the training samples are first clustered by the FCM algorithm, and then by training each clustering with the SVM algorithm, a sub-model is built to each clustering. In the predicting process, when an incremental sample that represents new operation information is introduced in the model, the fuzzy membership function of the sample to each clustering is first computed by the FCM algorithm. Then, a corresponding SVM sub-model of the clustering with the largest fuzzy membership function is used to predict and perform incremental learning so the model can be updated on-line. An old sample chosen by heuristic sample displacement method is then discarded from the sub-model to control the size of the working set. The proposed method is applied to predict the p-xylene (PX) purity in the adsorption separation process. Simulation results indicate that the proposed method actually increases the model’s adaptive abilities to various operation conditions and improves its generalization capability.     

FUZZY MODELING AND CONTROL OF BATCH BEER FERMENTATION+

Fuzzy reasoning based modeling of heuristic control rules are employed for control of batch beer fermentation. The effect of different types of membership functions, viz., line, triangular and phi membership functions is evaluated for the fuzzy subset. Various fuzzy model based controllers are presented using two approaches, namely simple fuzzy controller of few rules (FCFR) and rigorous fuzzy controller of many rules (FCM R), and also applied for the temperature control of fermenter. Zadeh's logic and Lukasiewicz's logic are adopted for computing the compositional rule of fuzzy logic inference. The results demonstrate that the proposed fuzzy controllers show better performance than the conventional controllers. FCFR approach provides better control performance, but needs optimum tuning or selection of gains for the fuzzy input and output variables, whereas FCMR approach is preferred due to flexibility in the operation of many control rules. Further, FCMR approach is free from optimum tuning or selection of gains for the fuzzy input and output variables.     

Fuzzy rule-based inference of reasons for high effluent quality in municipal wastewater treatment plant

A fuzzy inference system (FIS), which could classify the state of effluent quality if it was high or not and identify visually the reasons for the high effluent quality in municipal wastewater treatment plants (WWTPs), was developed in this study. The decision tree algorithm and fuzzy technique were applied in the development of this system. By applying the classification and regression tree (CART) algorithm as a decision tree algorithm, the knowledge related to effluent quality was extracted and IF-THEN rules with crisp boundary values were generated. By applying the fuzzy technique, the fuzzification of these rules was conducted, where the trapezoidal and triangular membership function was used as a membership function type. And a Mamdani model with the Max-min operation was used as an inference model and the center of area (CoA) method was used for deffuzification. The accuracy achieved by using the developed system to classify the effluent state was confirmed by comparing the result with measured data. Furthermore, the developed system was demonstrated to be a useful tool for inferring the reasons for the high effluent quality.     

Classification of colors through fuzzy statistical experiment

The membership function describing the degree of association of a color sample to a specified color name is estimated experimentally through fuzzy statistical experiment. Here, we are interested in the surface color of opaque materials including red, orange, yellow, green, blue, purple, white, gray, and black. The characteristics of the membership function for these colors are found to be affected appreciably by the light source used.