Number Of Fuzzy Rules Research Articles

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

Fuzzy Modeling and H¥ Synchronization of Different Hyperchaotic Systems via T–S Models

In this paper, a unified fuzzy H¥ control approach is proposed to deal with the problem of synchronization of two different hyperchaotic systems. The T-S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. Based on the T-S fuzzy hyperchaotic models, a fuzzy H¥ synchronization controller is designed via parallel distributed compensation (PDC) techniques. The sufficient condition for the H¥ synchronization of two different hyperchaotic systems is derived by applying Lyapunov stability theory. The results are expressed in terms of LMIs, and therefore it is very convenient to check in practice. This method is a universal one for synchronization of two different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy modeling and hyperchaotic synchronization scheme.

Intelligent Control of Twin-Rotor MIMO System Using Fuzzy Inference Techniques

The flight control system of helicopter is difficult to control for their performance of high-order unstable, nonlinear, and multiple-inputs multiple-outputs (MIMO) system. The behavior of two degree-of-freedom (2-DOF) helicopter has significant cross-coupling between pitch and yaw directional motions. This study presents a control system for a 2-DOF helicopter plant which more specific presented as twin-rotor MIMO system by using fuzzy logic technique. Fuzzy logic controller (FLC) is designed by using MATLAB to improve the performance of flight control system. Thus, the designed pitch and yaw controller are tuned by adjusting the range of membership function of input variable and the number of fuzzy rules used. The designed FLC are implemented and the results of the simulation are compared with LQR controller. The proposed pitch fuzzy controller shows improvement in rise time from 0.607sec to 0.458s, settling time from 7.188s to 1.866s, and percent overshoot from 38.1% to 0% over the existing pitch LQR controller. Meanwhile, the proposed yaw fuzzy controller shows improvement in rise time from 1.361s to 0.828s, settling time from 9.120sec to 2.517 s, and percent overshoot from 23.51% to 2.86% over the existing yaw LQR controller. Hence, the simulation results show that FLC has great potential than LQR controller for the flight control system.

퍼지 클러스터링 기반 퍼지뉴럴네트워크 설계 및 적용

본 논문에서는 FCM 클러스터링 알고리즘을 기반으로 하는 퍼지뉴럴네트워크를 제안한다. 일반적으로, 퍼지규칙을 생성할 때 차원이 증가하면 퍼지 규칙의 수가 기하급수적으로 증가하는 문제를 가지고 있다. 이를 해결하기 위해, 제안된 네트워크의 퍼지 규칙은 FCM 클러스터링 알고리즘을 이용하여 입력 공간을 분산 형태로 분할함으로써 생성한다. 퍼지 규칙의 전반부 파라미터는 FCM 클러스터링 알고리즘에 의한 소속행렬로 결정된다. 퍼지 규칙의 후반부는 다항식 함수의 형태로 표현되며, 퍼지뉴럴네트워크의 학습은 뉴런의 연결을 조절함으로써 실현되고, 오류 역전파 알고리즘에 의해 행해진다. 마지막으로, 제안된 네트워크는 비선형 공정으로의 적용을 통해 성능을 평가한다. In this paper, we propose the fuzzy neural networks based on fuzzy c-means clustering algorithm. Typically, the generation of fuzzy rules have the problem that the number of fuzzy rules exponentially increases when the dimension increases. To solve this problem, the fuzzy rules of the proposed networks are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the learning of fuzzy neural networks is realized by adjusting connections of the neurons, and it follows a back-propagation algorithm. The proposed networks are evaluated through the application to nonlinear process.

AN AUTOMATED PROCEDURE FOR SELECTING PROJECT MANAGERS IN CONSTRUCTION FIRMS

Selecting a suitable project manager for construction projects is one of the most important decisions made by construction firms. In the traditional approach, interviews are conducted by senior managers of the company, who consider the project requirements and the candidates’ capabilities. However, interviewing candidates is usually time consuming and there is the risk of impaired judgment, leading to human error. Decision-making support systems are therefore very useful. In previous work, the authors proposed a fuzzy system to address the issues described above (Rashidi et al. 2011). In this paper, a simpler robust model is presented. The advantages of this new model lie in its simplicity and the fact that it is not necessary to consider many criteria in the selection procedure when using this model. This model only requires 15 fields of candidate information. In the development of this model, the first step is construction of an initial fuzzy model based on all the criteria that may be considered when selecting a project manager. The significance of the coefficients of the criteria are then determined. In the next step, the model is optimized by changing the number of fuzzy rules and reducing the number of criteria. Finally, the most appropriate model is chosen on the basis of the least number of criteria required to obtain accurate results. To show the model's capability, it is used in real interviews. The obtained results indicate the high accuracy of the model in predicting the output, that is, the best candidate in the interviews.

Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions

This paper investigates the stability of fuzzy-model-based (FMB) control system, formed by a T–S fuzzy model and a fuzzy controller connected in a close loop, based on a fuzzy-Lyapunov function. A general FMB control system that the T–S fuzzy model and fuzzy controller not sharing the same premise membership functions and/or the same number of fuzzy rules is considered. A membership-function-dependent stability analysis approach is proposed to consider the membership functions of both the T–S fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities. As the stability conditions are membership-function dependent, they are dedicated to the FMB control system with the specified membership functions under consideration. It is thus the membership-function-dependent stability conditions are more relaxed compared to the existing membership-function-independent stability conditions. A fuzzy-Lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work. In this paper, this criterion is not required and thus the stability conditions can be further relaxed. Some simulation examples are given to demonstrate the merits of the proposed approach.

TS-fuzzy modeling based on ε-insensitive smooth support vector regression

This paper establishes a connection between Takagi-Sugeno TS fuzzy systems and e-insensitive smooth support vector regression e-SSVR, a smooth strategy for solving e-SVR. In previous e-SVR-based fuzzy models, the form of membership functions is restricted by the Mercer condition. The e-SSVR formulation puts no restrictions on the kernel. Therefore, the proposed e-SSVR-based TS-fuzzy modeling method relaxes the restriction on membership functions. By applying the reduced kernel technique, the number of fuzzy rules is reduced without scarifying the generalization ability. The computational complexity is also reduced by the reduced kernel technique. The performance of our method is illustrated by extensive experiments and comparisons.

The Scrutiny of Variation in the Number of Fuzzy Rules and Membership Functions in a New Genetic-Fuzzy System in Approximation and Prediction Problems

This paper shows a new fuzzy system was improved using genetic algorithm to handle fuzzy inference system as a function approximator and time series predictor. The system was developed generality that trained with genetic algorithms (GAs) corresponding to special problem and would be evaluated with different number of rules and membership functions. Then, compare the efficacy of variation of these two parameters in behavior of the system and show the method that achieves an efficient structure in both of them. Also, the proposed GA-Fuzzy inference system successfully predicts a benchmark problem and approximates an introduced function and results have been shown.

A new fuzzy criterion-referenced assessment with a fuzzy rule selection technique and a monotonicity-preserving similarity reasoning scheme

The use of a Fuzzy Inference System FIS as a part of Criterion-referenced Assessment CRA is not new. Nevertheless, there are several limitations in combining FIS models and CRA, as follows. i It is difficult to maintain the monotonicity property of the FIS-based CRA model; ii it is difficult and impractical to form a complete fuzzy rule base when the number of required rules is large, and iii reducing fuzzy rules may cause the “tomato classification” problem. In this paper, a practical solution to overcome these limitations is provided. We adopt the sufficient conditions i.e., a mathematical foundation as a set of governing equations for designing fuzzy membership functions and fuzzy rules to preserve the monotonicity property. In this paper, our works in [21] is extended and a new procedure that comprises of the sufficient conditions, fuzzy rule reduction and a monotonicity-preserving similarity reasoning SR is proposed. The new framework reduces the number of fuzzy rules gathered from an assessor i.e., selected rules with a proposed fuzzy rule selection approach. Selected rules are identified in such that the unselected rules can be deduced via a monotonicity-preserving SR technique. We formulate the process of minimizing the number of selected rules as a constrained optimization problem and a genetic algorithm GA technique is implemented. Unselected rules are predicted with a proposed monotonicity-preserving SR scheme. The proposed approach contributes to a solution to reduce the number of fuzzy rules to be gathered from an assessor while maintaining the monotonicity property. Besides, this paper also contributes to a new application of SR in education assessment. The proposed approach is evaluated with a case study relating to a lab assessment in Universiti Malaysia Sarawak UNIMAS.

FRKAS: Knowledge Acquisition Using a Fuzzy Rule Base Approach to Insight of DNA-Binding Domains/Proteins

Numerous prediction methods of DNA-binding domains/proteins were proposed by identifying informative features and designing effective classifiers. These researches reveal that the DNA-protein binding mechanism is complicated and existing accurate predictors such as support vector machine (SVM) with position specific scoring matrices (PSSMs) are regarded as black-box methods which are not easily interpretable for biologists. In this study, we propose an ensemble fuzzy rule base classifier consisting of a set of interpretable fuzzy rule classifiers (iFRCs) using informative physicochemical properties as features. In designing iFRCs, feature selection, membership function design, and fuzzy rule base generation are all simultaneously optimized using an intelligent genetic algorithm (IGA). IGA maximizes prediction accuracy, minimizes the number of features selected, and minimizes the number of fuzzy rules to generate an accurate and concise fuzzy rule base. Benchmark datasets of DNA-binding domains are used to evaluate the proposed ensemble classifier of 30 iFRCs. Each iFRC has a mean test accuracy of 77.46%, and the ensemble classifier has a test accuracy of 83.33%, where the method of SVM with PSSMs has the accuracy of 82.81%. The physicochemical properties of the first two ranks according to their contribution are positive charge and Van Der Waals volume. Charge complementarity between protein and DNA is thought to be important in the first step of recognition between protein and DNA. The amino acid residues of binding peptides have larger Van Der Waals volumes and positive charges than those of non-binding ones. The proposed knowledge acquisition method by establishing a fuzzy rule-based classifier can also be applicable to predict and analyze other protein functions from sequences.

An Incremental Approach to TS Fuzzy Modeling

This paper proposes an incremental smooth support vector regression (ISSVR) method for TS fuzzy modeling. Under certain assumptions on membership functions, we propose an optimization problem for TS fuzzy modeling based on the structural risk minimization principle. We show that this problem is an SVR problem with non-positive definite kernels. It cannot be solved using conventional SVR. Then we establish a connection between this TS fuzzy modeling problem and smooth support vector regression (SSVR), which is a smoothing strategy for solving SVR. The problem is always solvable using SSVR because SSVR puts no restrictions on the kernel. Then we apply an incremental approach to the SSVR by selecting informative samples from the training dataset. Taking advantage of SSVR, more forms of membership functions can be used in our model compared with conventional methods. Experiments show that the proposed ISSVR-based TS fuzzy model has good generalization ability with small number of fuzzy rules.

Nonlinear Identification Using Single Input Connected Fuzzy Inference Model

The single input connected fuzzy inference model (SIC model) by Hayashi et al. can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference models. In this paper, we first show the SIC model and its learning algorithm, and clarify the applicability of the SIC model by applying it to identification of nonlinear functions.

Development of Customer Satisfaction Models for Affective Design Using Rough Set and ANFIS Approaches

Rough set (RS)- and particle swarm optimization (PSO)- based adaptive neuro-fuzzy inference system (ANFIS) approaches are proposed to generate customer satisfaction models in affective design that address fuzzy and nonlinear relationships between affective responses and design attributes. The RS theory is adopted to reduce the number of fuzzy rules generated using ANFIS and simplify the structure of ANFIS. PSO is employed to determine the parameter settings of an ANFIS from which customer satisfaction models with better modeling accuracy can be generated. A case study of mobile phone affec- tive design is used to illustrate the proposed approaches.

Backstepping Control of Electrical Load Simulator with Adaptive Tracking Performance Controller

Electrical Load simulator (ELS) is an important aerodynamics forces/torque loading device which is used for qualification of flight actuation system in ground based experiments. This paper focuses on Backstepping control design with fuzzy logic compensator for extra torque disturbance. To reduce number of fuzzy rules and processing time LuGre model based friction compensation scheme is proposed. Practically fuzzy logic compensation may induce approximation error. A novel PI type tracking performance controller is proposed to compensate tracking error due to parametric uncertainty in the ELS system and LuGre friction model. The tracking performance controller is tuned online based on saturation function based adaptive law derived from the error dynamics between state predictor and actual plant to eliminate chattering from control signal. The validity of control scheme is verified using numerical simulations for desired tracking performance.

Fuzzy-Neural Networks Based on Subtractive Clustering and its Applications in Soft Sensor

A soft sensor modeling method is presented in this paper，it selects optimal fuzzy rules by tuning the radius of a subtractive cluster center to generate a T-S fuzzy model. The radius of a cluster center is adjusted to select optimal number of fuzzy rules, to acquire a fuzzy model with perfect generalization capability. Then, the parameter is fine-tuned by means of a hybrid gradient descent (GD) and least-squares estimation (LSE) approach. Finally, the method is used to model a PDU Naphtha’s Dry Point, simulation results show that it can determine the optimal model quickly and achieve satisfactory prediction precision.

Bottleneck Prediction Method Based on Improved Adaptive Network-based Fuzzy Inference System (ANFIS) in Semiconductor Manufacturing System

Semiconductor manufacturing (SM) system is one of the most complicated hybrid processes involved continuously variable dynamical systems and discrete event dynamical systems. The optimization and scheduling of semiconductor fabrication has long been a hot research direction in automation. Bottleneck is the key factor to a SM system, which seriously influences the throughput rate, cycle time, time-delivery rate, etc. Efficient prediction for the bottleneck of a SM system provides the best support for the consequent scheduling. Because categorical data (product types, releasing strategies) and numerical data (work in process, processing time, utilization rate, buffer length, etc.) have significant effect on bottleneck, an improved adaptive network-based fuzzy inference system (ANFIS) was adopted in this study to predict bottleneck since conventional neural network-based methods accommodate only numerical inputs. In this improved ANFIS, the contribution of categorical inputs to firing strength is reflected through a transformation matrix. In order to tackle high-dimensional inputs, reduce the number of fuzzy rules and obtain high prediction accuracy, a fuzzy c-means method combining binary tree linear division method was applied to identify the initial structure of fuzzy inference system. According to the experimental results, the main-bottleneck and sub-bottleneck of SM system can be predicted accurately with the proposed method.

HCM 클러스터링 알고리즘 기반 비퍼지 추론 시스템의 비선형 특성

Abstract In fuzzy modeling for nonlinear process, the fuzzy rules are typically formed by selection of the input variables, the number of space division and membership functions. The Generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, complex nonlinear process can be modeled by generating the fuzzy rules by means of fuzzy division of input space. Therefore, in this paper, rules of non-fuzzy inference systems are generated by partitioning the input space in the scatter form using HCM clustering algorithm. The premise parameters of the rules are determined by membership matrix by means of HCM clustering algorithm. The consequence part of the rules is represented in the form of polynomial functions and the consequence parameters of each rule are identified by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process. Through this experiment, we showed that high-dimensional nonlinear systems can be modeled by a very small number of rules.

A fuzzy inference method based on association rule analysis with application to river flood forecasting

In this paper, a computationally efficient version of the widely used Takagi-Sugeno (T-S) fuzzy reasoning method is proposed, and applied to river flood forecasting. It is well known that the number of fuzzy rules of traditional fuzzy reasoning methods exponentially increases as the number of input parameters increases, often causing prohibitive computational burden. The proposed method greatly reduces the number of fuzzy rules by making use of the association rule analysis on historical data, and therefore achieves computational efficiency for the cases of a large number of input parameters. In the end, we apply this new method to a case study of river flood forecasting, which demonstrates that the proposed fuzzy reasoning engine can achieve better prediction accuracy than the widely used Muskingum-Cunge scheme.

Dynamic Hysteresis Model Based on Fuzzy Clustering Approach

Hysteretic behavior model of soft magnetic material usually used in electrical machines and electronic devices is necessary for numerical solution of Maxwell equation. In this study, a new dynamic hysteresis model is presented, based on the nonlinear dynamic system identification from measured data capabilities of fuzzy clustering algorithm. The developed model is based on a Gustafson-Kessel (GK) fuzzy approach used on a normalized gathered data from measured dynamic cycles on a C core transformer made of 0.33mm laminations of cold rolled SiFe. The number of fuzzy rules is optimized by some cluster validity measures like ‘partition coefficient’ and ’classification entropy’. The clustering results from the GK approach show that it is not only very accurate but also provides its effectiveness and potential for dynamic magnetic hysteresis modeling.

Hybrid-controlled neurofuzzy networks analysis resulting in genetic regulatory networks reconstruction.

Reverse engineering of gene regulatory networks (GRNs) is the process of estimating genetic interactions of a cellular system from gene expression data. In this paper, we propose a novel hybrid systematic algorithm based on neurofuzzy network for reconstructing GRNs from observational gene expression data when only a medium-small number of measurements are available. The approach uses fuzzy logic to transform gene expression values into qualitative descriptors that can be evaluated by using a set of defined rules. The algorithm uses neurofuzzy network to model genes effects on other genes followed by four stages of decision making to extract gene interactions. One of the main features of the proposed algorithm is that an optimal number of fuzzy rules can be easily and rapidly extracted without overparameterizing. Data analysis and simulation are conducted on microarray expression profiles of S. cerevisiae cell cycle and demonstrate that the proposed algorithm not only selects the patterns of the time series gene expression data accurately, but also provides models with better reconstruction accuracy when compared with four published algorithms: DBNs, VBEM, time delay ARACNE, and PF subjected to LASSO. The accuracy of the proposed approach is evaluated in terms of recall and F-score for the network reconstruction task.