Fuzzy IF-THEN Research Articles

A neuro-fuzzy system modeling with self-constructing rule generation and hybrid SVD-based learning

We propose an approach for neuro-fuzzy system modeling. A neuro-fuzzy system for a given set of input-output data is obtained in two steps. First, the data set is partitioned automatically into a set of clusters based on input-similarity and output-similarity tests. Membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster. Then, a fuzzy IF-THEN rule is extracted from each cluster to form a fuzzy rule-base. Second, a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule-base. To decrease the size of the search space and to speed up the convergence, we develop a hybrid learning algorithm which combines a recursive singular value decomposition-based least squares estimator and the gradient descent method. The proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points. Besides, it learns faster, consumes less memory, and produces lower approximation errors than other methods.

A New Fuzzy Gain Scheduling Scheme for the PID Controllers

Abstract In this paper, a new fuzzy gain scheduling scheme for the PID controller have been proposed. Fuzzy IF-THEN rules aze used on-line to adjust the parameters of the PID controller based on the system error and its derivative. In terms of settling time, one percent peak overshoot and the integral of the time multiplied by the absolute error, the simulation results clearly indicate that the performance of the proposed scheme is better than the Ziegler-Nichols PID controller [1] and the fuzzy gain scheduling scheme of PID controller [2]. For illustration and compazison, numerical examples, using third and fourth order plants, are presented.

A Code-reduction Technique for SOM-based Image Enlargement Employing Fuzzy Inference

We propose a new image enlargement method employing a codebook-based fuzzy interpolation technique in order to realize simultaneous smoothing and sharpening in image enlargement. In the proposed method, codebooks are generated by using self-organizing maps (SOM). The codes of the generated codebooks are used to determine parameters of Gaussian membership functions in the fuzzy IF-THEN rules. Then, enlargement is achieved by a fuzzy inference. Experimental results of the proposed method show superior performances than other typical image enlargement methods. Calculation time is reduced drastically in comparison with the previous codebook-based method which has been proposed by the authors.

Fuzzy reasoning based on generalized fuzzy If-Then rules

This paper focuses on a fuzzy reasoning method based on a generalized If-Then rule. Firstly, the antecedent and the consequent of an If-Then rule are considered and expressed as a component of a kind of binary L-type fuzzy relation on the product of the universes of discourse and the range of definition for a certain fuzzy attribute. Then a generalized extension principle based on this L-type fuzzy relation (FR-GEP) is constructed. Moreover, the paper gives a detailed description of this generalized If-Then rule using 20 well-known common implication operators in the framework of the composition of L-type fuzzy relations. Consequently, an L-type binary fuzzy reasoning method based on this generalized If-Then rule is established according to FR-GEP. © 2002 Wiley Periodicals, Inc.

An intelligent sales forecasting system through integration of artificial neural networks and fuzzy neural networks with fuzzy weight elimination

Sales forecasting plays a very prominent role in business strategy. Numerous investigations addressing this problem have generally employed statistical methods, such as regression or autoregressive and moving average (ARMA). However, sales forecasting is very complicated owing to influence by internal and external environments. Recently, artificial neural networks (ANNs) have also been applied in sales forecasting since their promising performances in the areas of control and pattern recognition. However, further improvement is still necessary since unique circumstances, e.g. promotion, cause a sudden change in the sales pattern. Thus, this study utilizes a proposed fuzzy neural network (FNN), which is able to eliminate the unimportant weights, for the sake of learning fuzzy IF–THEN rules obtained from the marketing experts with respect to promotion. The result from FNN is further integrated with the time series data through an ANN. Both the simulated and real-world problem results show that FNN with weight elimination can have lower training error compared with the regular FNN. Besides, real-world problem results also indicate that the proposed estimation system outperforms the conventional statistical method and single ANN in accuracy.

Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors

This paper describes the design of the robust adaptive fuzzy controller for uncertain single-input single-output nonlinear dynamical systems with unknown nonlinearities. These unknown nonlinearities are approximated by the fuzzy system with~a set of fuzzy IF–THEN rules whose parameters are adjusted on-line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track~a given trajectory. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control algorithm based on the adaptive fuzzy model. The key assumption is that the reconstruction errors satisfy certain bounding conditions. The control law consists of two terms. One is the certainty equivalent control and the other is the bounding control. A bounding parameter adaptive law is used to obtain this bounding control. The overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded. It is also shown that, in the special case, the tracking error exponentially converges to zero even though the approximation errors exist.

Possibilistic Linear Programming with Fuzzy If-Then Rule Coefficients

In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzzy numbers. Scenario decomposed fuzzy numbers (SDFNs) reflect a fact that we may have different estimations of possible ranges of uncertain variables depending on scenarios, which are expressed by fuzzy if-then rules. The properties of SDFNs are investigated. Possibilistic linear programming problems with SDFNs are formulated by two different approaches, fractile and modality optimization approaches. It is shown that the problems are reduced to linear programming problems in fractile optimization models with the necessity measures and that the problems can be solved by a linear programming technique and a bisection method in modality optimization models with necessity measures. A simple numerical example is given.

Short-term load forecasting by a neuro-fuzzy based approach

An approach based on an artificial neural network (ANN) combined with a fuzzy system is proposed for short-term load forecasting. This approach was developed in order to reach the desired short-term load forecasting in an efficient manner. Over the past few years, ANNs have attained the ability to manage a great deal of system complexity and are now being proposed as powerful computational tools. In order to select the appropriate load as the input for the desired forecasting, the Pearson analysis method is first applied to choose two historical record load patterns that are similar to the forecasted load pattern. These two load patterns and the required weather parameters are then fuzzified and input into a neural network for training or testing the network. The back-propagation (BP) neural network is applied to determine the preliminary forecasted load. In addition, the rule base for the fuzzy inference machine contains important linguistic membership function terms with knowledge in the form of fuzzy IF–THEN rules. This produces the load correction inference from the historical information and past forecasted load errors to obtain an inferred load error. Adding the inferred load error to the preliminary forecasted load, we can obtain the finial forecasted load. The effectiveness of the proposed approach to the short-term load-forecasting problem is demonstrated using practical data from the Taiwan Power Company (TPC).

Neuro fuzzy model for adaptive filtering of oscillatory signals

In this paper we have developed a neuro fuzzy model for adaptive filtering of oscillatory signals embedded with white noise. Such type of fuzzy adaptive filters are constructed from a set of fuzzy IF-THEN rules, which change adaptively to minimise the cost function until a desired information is available. Here we have used a generalised cost function for better convergence of the error. This algorithm is simulated on a digital signal processor in order to track the signal and to filter out the disturbances present in the signal at a particular instant of time. The system presented here, can measure both types of information like numerical as well as linguistic.

A fuzzy-logic-based approach to qualitative safety modelling for marine systems

Abstract Safety assessment based on conventional tools (e.g. probability risk assessment (PRA)) may not be well suited for dealing with systems having a high level of uncertainty, particularly in the feasibility and concept design stages of a maritime or offshore system. By contrast, a safety model using fuzzy logic approach employing fuzzy IF–THEN rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analyses. A fuzzy-logic-based approach may be more appropriately used to carry out risk analysis in the initial design stages. This provides a tool for working directly with the linguistic terms commonly used in carrying out safety assessment. This research focuses on the development and representation of linguistic variables to model risk levels subjectively. These variables are then quantified using fuzzy sets. In this paper, the development of a safety model using fuzzy logic approach for modelling various design variables for maritime and offshore safety based decision making in the concept design stage is presented. An example is used to illustrate the proposed approach.

A Fuzzy-Logic-Based Approach to Subjective Safety Modelling for Maritime Products

ABSTRACTSafety assessment based on conventional tools (e.g., probability risk assessment (PRA)) may not be well suited for dealing with systems having a high level of uncertainty, particularly in the feasibility and concept design stages of a maritime or offshore system. By contrast, a safety model using fuzzy logic approach employing fuzzy IF-THEN rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analyses. A fuzzy-logic-based approach may be more appropriately used to carry out risk analysis in the initial design stages. This provides a tool for working directly with the linguistic terms commonly used in carrying out safety assessment. This paper focuses on the development and representation of linguistic variables to model risk levels subjectively. These variables are then quantified using fuzzy sets. In this paper, the development of a safety model using fuzzy logic approach for modelling various design variables for maritime and offshore safety based Decision making in the concept design stage is presented. An example is used to illustrate the proposed approach.

A sales forecasting system based on fuzzy neural network with initial weights generated by genetic algorithm

Sales forecasting is highly complex due to the influence of internal and external environments. However, reliable prediction of sales can improve the quality of business strategy. Recently, artificial neural networks (ANNs) have been applied for sales forecasting due to their promising performance in the areas of control and pattern recognition. However, further improvement is still necessary since unique circumstances such as promotion can cause sudden changes in sales patterns. Thus, the present study utilizes the proposed fuzzy neural network with initial weights generated by genetic algorithm (GFNN) for the sake of learning fuzzy IF–THEN rules for promotion obtained from marketing experts. The result from GFNN is further integrated with an ANN forecast using the time series data and the promotion length from another ANN. Model evaluation results for a convenience store (CVS) company indicate that the proposed system can perform more accurately than the conventional statistical method and a single ANN.

Effect of rule weights in fuzzy rule-based classification systems

This paper examines the effect of rule weights in fuzzy rule-based classification systems. Each fuzzy IF-THEN rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification phase. The winner rule for a new pattern is the fuzzy IF-THEN rule that has the maximum compatibility grade with the new pattern. When we use fuzzy IF-THEN rules with certainty grades, the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade. In this paper, the effect of rule weights is illustrated by drawing classification boundaries using fuzzy IF-THEN rules with/without certainty grades. It is also shown that certainty grades play an important role when a fuzzy rule-based classification system is a mixture of general rules and specific rules. Through computer simulations, we show that comprehensible fuzzy rule-based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy IF-THEN rules with certainty grades.

Self-adaptive neuro-fuzzy systems for autonomous underwater vehicle control

This paper presents a systematic approach for developing a concise self-adaptive neurofuzzy inference system (SANFIS) with a fast hybrid parameter learning algorithm for on-line learning of the control knowledge for autonomous underwater vehicle (AUV) control. The multi-layered network structure of SANFIS incorporates fuzzy basis functions for better function approximations. We investigate three SANFIS structures with three different types of fuzzy IF-THEN rule-based models and cast the rule formation problem as a clustering problem. A recursive least-squares algorithm and a modified Levenberg-Marquardt algorithm with limited memory are exploited to accelerate the parameter learning process. This hybrid parameter learning algorithm together with an on-line clustering technique and rule examination provide SANFIS with the capability of selforganizing and self-adapting its internal structure (i.e. the fuzzy rules and term sets) for learning the required control knowledge for an AUV to follow desired trajectories. Computer simulations for modeling a control system for an AUV have been conducted to validate the effectiveness of the proposed SANFIS.

MULTITUNING FUZZY CONTROL SYSTEMS DESIGN

A multituning fuzzy control system structure that involves two simple, but effective tuning mechanisms, is proposed: one is called fuzzy control rule tuning mechanism (FCRTM); the other is called dynamic scalar tuning mechanism (DSTM). In FCRTM, it is used to generate the necessary control rules with a center extension method. In DSTM, it contains three fuzzy IF-THEN rules for determining the appropriate scaling factors for the fuzzy control system. In this paper, a method based on the genetic algorithm (GA) is proposed to simultaneously choose the appropriate parameters in FCRTM and DSTM. That is, the proposed GA-based method can automatically generate the required rule base of fuzzy controller and efficiently determine the appropriate map for building the dynamic scalars of fuzzy controller. A multiobjective fitness function is proposed to determine an appropriate parameter set such that not only the selected fuzzy control structure has fewer fuzzy rules, but also the controlled system has a good control performance. Finally, an inverted pendulum control problem is given to illustrate the effectiveness of the proposed control scheme.

Fuzzy neural networks for learning fuzzy if-then rules

This study is dedicated to developing a fuzzy neural network with linguistic teaching signals. The proposed network, which can be applied either as a fuzzy expert system or a fuzzy controller, is able to process and learn the numerical information as well as the linguistic information. The network consists of two parts: (1) initial weights generation and (2) error back-propagation (EBP)-type learning algorithm. In the first part, a genetic algorithm (GA) generates the initial weights for a fuzzy neural network in order to prevent the network getting stuck to the local minimum. The second part employs the EBP-type learning algorithm for fine-tuning. In addition, the unimportant weights are eliminated during the training process. The simulated results do not only indicate that the proposed network can accurately learn the relations of fuzzy inputs and fuzzy outputs, but also show that the initial weights from the GA can coverage better and weight elimination really can reduce the training error. Moreover, real-world problem results show that the proposed network is able to learn the fuzzy IF-THEN rules captured from the retailing experts regarding the promotion effect on the sales.

A novel fuzzy logic system based on N-version programming

For the consideration of different application systems, modeling the fuzzy logic rule, and deciding the shape of membership functions are very critical issues due to they play key roles in the design of fuzzy logic control system. This paper proposes a novel design methodology of fuzzy logic control system using the neural network and fault-tolerant approaches. The connectionist architecture with the learning capability of neural network and N-version programming development of a fault-tolerant technique are implemented in the proposed fuzzy logic control system. In other words, this research involves the modeling of parameterized membership functions and the partition of fuzzy linguistic variables using neural networks trained by the unsupervised learning algorithms. Based on the self-organizing algorithm, the membership function and partition of fuzzy class are not only derived automatically, but also the preconditions of fuzzy IF-THEN rules are organized. We also provide two examples, pattern recognition and tendency prediction, to demonstrate that the proposed system has a higher computational performance and its parallel architecture supports noise-tolerant capability. This generalized scheme is very satisfactory for pattern recognition and tendency prediction problems.

特殊化の度合の異なるファジィルールにおける暗黙の階層構造を用いた多入力システムの言語的モデリング

特殊化の度合の異なるファジィルールにおける暗黙の階層構造を用いた多入力システムの言語的モデリング

Fuzzy perceptron neural networks for classifiers with numerical data and linguistic rules as inputs

This paper presents a novel learning algorithm of fuzzy perceptron neural networks (FPNNs) for classifiers that utilize expert knowledge represented by fuzzy IF-THEN rules as well as numerical data as inputs. The conventional linear perceptron network is extended to a second-order one, which is much more flexible for defining a discriminant function. In order to handle fuzzy numbers in neural networks, level sets of fuzzy input vectors are incorporated into perceptron neural learning. At different levels of the input fuzzy numbers, updating the weight vector depends on the minimum of the output of the fuzzy perceptron neural network and the corresponding nonfuzzy target output that indicates the correct class of the fuzzy input vector. This minimum is computed efficiently by employing the modified vertex method. Moreover, the fuzzy pocket algorithm is introduced into our fuzzy perceptron learning scheme to solve the nonseparable problems. Simulation results demonstrate the effectiveness of the proposed FPNN model.

Intelligent system to support judgmental business forecasting: the case of estimating hotel room demand

Forecasting is an instrumental tool for strategic decision-making in any business activity. Good forecasts can reduce the uncertainty about the future and, hence, help managers make better decisions. Virtually all statistical forecasting techniques depend on the continuity of historical data and time series and may not predict a discontinuous change in the business environment. Often times, this discontinuity is known to managers who then must rely on their judgment to make forecast adjustments. We discuss the role of judgmental forecasting and take the problem of estimating future hotel room demand as a practical business application. Next, we propose IS-JFK: an intelligent system to support judgmental forecasting and knowledge of managers. To account for vagueness in the knowledge elicited from managers and the approximate nature of their reasoning, the system is built around fuzzy IF-THEN rules and uses fuzzy logic for decision inference. IS-JFK supports two methods for forecast adjustments: 1) a direct approach and 2) an approach based on fuzzy intervention analysis. Actual data from a hotel property are used in some case-scenario simulations to illustrate the merits of the intelligent support system.