Generalizing the modeling of fuzzy logic controllers by parameterized aggregation operators

We describe the type of reasoning used in the typical fuzzy logic controller, the Mamdani reasoning method. We point out the basic assumptions in this model. We discuss the S-OWA operators which provide families of parameterized “andlike” and “orlike” operators. We generalize the Mamdani model by introducing these operators. We introduce a method, which we call Direct Fuzzy Reasoning (DFR), which results from one choice of the parameters. We develop some learning algorithms for the new method. We show how the Takagi-Sugeno-Kang (TSK) method of reasoning is an example of this DFR method.     

Supervised learning algorithms for multi-class classification problems with partial class memberships

In several application domains such as biology, computer vision, social network analysis and information retrieval, multi-class classification problems arise in which data instances not simply belong to one particular class, but exhibit a partial membership to several classes. Existing machine learning or fuzzy set approaches for representing this type of fuzzy information mainly focus on unsupervised methods. In contrast, we present in this article supervised learning algorithms for classification problems with partial class memberships, where class memberships instead of crisp class labels serve as input for fitting a model to the data. Using kernel logistic regression (KLR) as a baseline method, first a basic one-versus-all approach is proposed, by replacing the binary-coded label vectors with [0,1]-valued class memberships in the likelihood. Subsequently, we use this KLR extension as base classifier to construct one-versus-one decompositions, in which partial class memberships are transformed and estimated in a pairwise manner. Empirical results on synthetic data and a real-world application in bioinformatics confirm that our approach delivers promising results. The one-versus-all method yields the best computational efficiency, while the one-versus-one methods are preferred in terms of predictive performance, especially when the observed class memberships are heavily unbalanced.     

Online identification of Takagi–Sugeno fuzzy models based on self-adaptive hierarchical particle swarm optimization algorithm

This paper presents an approach for online learning of Takagi–Sugeno (T-S) fuzzy models. A novel learning algorithm based on a Hierarchical Particle Swarm Optimization (HPSO) is introduced to automatically extract all fuzzy logic system (FLS)’s parameters of a T–S fuzzy model. During online operation, both the consequent parameters of the T–S fuzzy model and the PSO inertia weight are continually updated when new data becomes available. By applying this concept to the learning algorithm, a new type T–S fuzzy modeling approach is constructed where the proposed HPSO algorithm includes an adaptive procedure and becomes a self-adaptive HPSO (S-AHPSO) algorithm usable in real-time processes. To improve the computational time of the proposed HPSO, particles positions are initialized by using an efficient unsupervised fuzzy clustering algorithm (UFCA). The UFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system, enhancing the HPSO’s tuning. The approach is applied to identify the dynamical behavior of the dissolved oxygen concentration in an activated sludge reactor within a wastewater treatment plant. The results show that the proposed approach can identify nonlinear systems satisfactorily, and reveal superior performance of the proposed methods when compared with other state of the art methods. Moreover, the methodologies proposed in this paper can be involved in wider applications in a number of fields such as model predictive control, direct controller design, unsupervised clustering, motion detection, and robotics.     

Directional fuzzy clustering and its application to fuzzy modelling

The paradigm of clustering (unsupervised learning) viewed as a fundamental tool for data analysis has been found useful in fuzzy modelling. While the objective functions guiding the clustering mechanisms are by and large direction-free (namely, they do not distinguish between independent (input) and dependent (output) variables, for most of the models this discrimination becomes of vital importance. The method of directional clustering takes the directionality requirement into account by incorporating the nature of the functional relationships into the objective function guiding the formation of the clusters. The complete clustering algorithm is presented. The role of this method in a two-phase fuzzy identification scheme is also revealed in detail.     

A quantum mechanical approach to a fuzzy theory

Recently, we proposed a general measurement theory for classical and quantum systems (i.e., “objective fuzzy measurement theory”). In this paper, we propose “subjective fuzzy measurement theory”, which is characterized as the statistical method of the objective fuzzy measurement theory. Our proposal of course has a lot of advantages. For example, we can directly see “membership functions” (= “fuzzy sets”) in this theory. Therefore, we can propose the objective and the subjective methods of membership functions. As one of the consequences, we assert the objective (i.e., individualistic) aspect of Zadeh's theory. Also, as a quantum application, we clarify Heisenberg's uncertainty relation.     

Real-time stable self-learning FNN controller using genetic algorithm

A kind of real-time stable self-learning fuzzy neural network (FNN) control system is proposed in this paper. The control system is composed of two parts: (1) A FNN controller which use genetic algorithm (GA) to search optimal fuzzy rules and membership functions for the unknown controlled plant; (2) A supervisor which can guarantee the stability of the control system during the real-time learning stage, since the GA has some random property which may cause control system unstable. The approach proposed in this paper combine a priori knowledge of designer and the learning ability of FNN to achieve optimal fuzzy control for an unknown plant in real-time. The efficiency of the approach is verified by computer simulation.     

Generalized minimal cost flow problem in fuzzy nature: An application in bus network planning problem

The aim of minimal cost flow problem (MCFP) in fuzzy nature, which is denoted with FMCFP, is to find the least cost of the shipment of a commodity through a capacitated network in order to satisfy imprecise concepts in supply or demand of network nodes and capacity or cost of network links. Fuzzy supply–demand may arise in real problems, where incomplete statistical data or simulation results are used. Also, variation in the cost or capacity of links is commonly happening. In the present paper, after defining a total order on LR type fuzzy numbers, three models are studied; MCFP with fuzzy costs, MCFP with fuzzy supply–demand and a combination of two cases. For the first model, scaling negative cycle cancelling algorithm, which is a polynomial time algorithm, is proposed. For the second model, “nominal flow” is introduced which provides an efficient scheme for finding fuzzy flow. For the third model, we present an exact and some heuristic methods. Numerical examples are illustrated to demonstrate the efficiency of the proposed schemes. Finally, an application of this viewpoint in bus network planning problem is provided.     

Reinforcement learning in neurofuzzy traffic signal control

A fuzzy traffic signal controller uses simple “if–then” rules which involve linguistic concepts such as medium or long, presented as membership functions. In neurofuzzy traffic signal control, a neural network adjusts the fuzzy controller by fine-tuning the form and location of the membership functions. The learning algorithm of the neural network is reinforcement learning, which gives credit for successful system behavior and punishes for poor behavior; those actions that led to success tend to be chosen more often in the future. The objective of the learning is to minimize the vehicular delay caused by the signal control policy. In simulation experiments, the learning algorithm is found successful at constant traffic volumes: the new membership functions produce smaller vehicular delay than the initial membership functions.     

Modified optimization layer by layer algorithm for learning multilayer perceptrons

1. IntroductionThe feedforward Multilayer Perceptron (MLP) is one of the most widely used artificial neural networks among other network models. Its field of application includes patternrecognition, identification and control of dynamic systems, system modeling and nonlinearprediction of time series, etc. [1--41 founded on its nonlinear function approximation capability. Research of this type of networks has been stimulated since the discovery andpopularization of the Backpropagation learnin…     

Design of fuzzy logic controllers based on generalized T-operators

Since Zadeh first proposed the basic principle of fuzzy logic controllers in 1968, the and operators have been popular in the design of fuzzy logic controllers. In this paper, the general concept of T-operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available. Then, by computer simulations, studies are made so as to determine the relations between the various T-operators and the performance of a fuzzy logic controller. It is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the T-operators.     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

一类MIMO非线性系统的稳定自适应模糊控制

针对一类 MIMO不确定非线性系统 ,基于一种修改的李亚普诺夫函数并利用 I型模糊系统的逼近能力 ,提出一种分散自适应模糊控制器设计的新方案。该方案不但能够避免现有的一些自适应模糊 /神经网络控制器设计中对控制增益一阶导数上界的要求 ,而且能够避免控制器的奇异问题。通过理论分析 ,证明闭环控制系统是全局稳定的 ,跟踪误差收敛到零。仿真结果表明了该方法的有效性。     

Learning Fuzzy Grey Cognitive Maps using Nonlinear Hebbian-based approach

Recently, Fuzzy Grey Cognitive Maps (FGCM) has been proposed as a FCM extension. It is based on Grey System Theory, that it has become a very effective theory for solving problems within environments with high uncertainty, under discrete small and incomplete data sets. The proposed approach of learning FGCMs applies the Nonlinear Hebbian based algorithm determine the success of radiation therapy process estimating the final dose delivered to the target volume. The scope of this research is to explore an alternative decision support method using the main aspects of fuzzy logic and grey systems to cope with the uncertainty inherent in medical domain and physicians uncertainty to describe numerically the influences among concepts in medical domain. The Supervisor-FGCM, trained by NHL algorithm adapted in FGCMs, determines the treatment variables of cancer therapy and the acceptance level of final radiation dose to the target volume. Three clinical case studies were used to test the proposed methodology with meaningful and promising results and prove the efficiency of the NHL algorithm for FGCM approach.     

自组织结构的变论域模糊控制

针对变论域模糊控制,提出一种新的自组织结构的变论域模糊控制方法。自组织结构算法可以调整变论域模糊系统结构以及动态获得模糊规则,进一步减小变论域模糊控制项的稳态逼近误差。通过进一步理论分析可知,自组织结构算法仅仅保证了系统瞬时的切换是平稳的,但不能保证系统的闭环稳定性。给出了所提出控制方法的适用条件。通过与固定模糊系统结构的变论域模糊控制比较,仿真结果表明,所提出控制方法不仅使得系统的稳态跟踪误差更平稳,而且使得输入控制信号更加平滑。     

A general fuzzy control scheme for nonlinear processes with stability analysis

In this paper we develop a general fuzzy control scheme for nonlinear processes. Assuming little knowledge about the dynamics of the controlled process, the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation. A simple local controller is then designed at each fuzzy locality. A fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm. By employing a newly developed structure-adaptive fuzzy modelling scheme, the appropriate fuzzy rule-base for the inference mechanism can be extracted stably and efficiently. The conditions for the stability of the global controller are rigourously established. Simulation results are presented to illustrate the effectiveness of the scheme.     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

Rule-based models of multivariable functions

This study is devoted to fuzzy rule based modelling of multiple-input single-output nonlinear numerical relationships. The model under investigation is viewed as a collection of conditional statements “if state Ω_i then y = g_i(x, a_i)”, i = 1, 2,…, N with Ω_i being a fuzzy relation defined in the space of the input variables. In contrast to the commonly encountered identification approach that is dwelled upon discrete experimental data, the one proposed in this study is concerned with explicitly articulated nonlinear input-output relationship. The main thrust is in the development of a fuzzy partition of the input variables completed through a sequence of fuzzy relations rather than Cartesian products of fuzzy sets. This approach allows us to maintain the number of necessary rules under control and avoid a combinatorial explosion otherwise inevitable in situations of highly multivariable functions. Introduced are criteria of separability and function variability whose objective is to guide a distribution and granularity of the linguistic labels forming the condition part of the rules.     

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.     

基于GA-BP的模糊神经网络控制器与Elman辨识器的系统设计

提出了一种基于神经网络的模糊控制系统 ,该系统由模糊神经网络控制器和模型辨识网络组成 .文中介绍了模糊神经网络控制器采用遗传算法离线优化与 BP算法在线调整 ,给出了具体控制算法 ,推导了变形 Elmam网络的系统辨识算法 .仿真结果表明了此法的可行性和有效性 .     

A quasi-linear fuzzy measure of multi-attributes

Evaluations of multi-attributes using fuzzy measures and fuzzy integrals have been recently found to be useful in the classification processes of complex systems. However, one of the existing problems in using the aggregation operation of fuzzy integral is the identification of fuzzy measures or the “fuzzy densities” in terms of the g_λ-measure. This paper presents a new methodology to assess the weights of each individual attribute and the combinatorial subsets of these attributes. The measures of multi-attributes are considered herein as the regionalized variables in space Rⁿ, whose spatial values are characterized by the membership function of a fuzzy set. The present algorithm is based on the concept of the theory of regionalized variables which provides a mathematical framework for estimating the unknown values of the variables whose magnitudes are dependent on the spatial continuity expressed by a semi-variogram, and the optimal estimation of kriging method. This is a quasi-linear approach as the estimation is based on a linear-unbiased estimator, but the combined evidences do not hold additivity due to the basic assumption and formulation.