A New Region Growing Medical Image Segmentation Algorithm Based on Interval Type-2 Fuzzy Sets

In this paper, an interval type-2 Takagi-Sugeno fuzzy classification system (IT2T-SFCS) learned by particle swarm optimization (PSO) and support vector machine (SVM) for antecedent and consequent parameters optimization is proposed. The IT2T-SFCS is constructed by fuzzy if-then rules whose antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The antecedents of IT2T-SFCS use the fuzzy iterative self-organizing data analysis technique (ISODATA) and PSO to learn and calculate the optimal centers and the uncertain widths of the Gaussian membership functions. Consequent parameters in IT2T-SFCS are learned through SVM for the purpose of achieving higher generalization ability. The proposed IT2T-SFCS is able to directly handle uncertainties, minimize the effects of uncertainties and get the better generalization performance, which inherits the benefits of interval type-2 T-S fuzzy system and SVM. For demonstration, IT2T-SFCS is used as a classifier in gender recognition. The experimental results show that the performance of the proposed IT2T-SFCS is superior to that of the previous mainstream classifiers.

This paper deals with the serious problems of a ventilation system in a large road tunnel. Higher visibility and lower concentration of carbon monoxide are the key issues concerning the ventilation system. Prior to designing the fuzzy control model, a configuration layout of the ventilation system including sensing, control and traffic prediction as well is conceptually constructed. Based on the layout that offers assignments of sensors and control elements, a fuzzy logic control model is developed. Membership functions of sensor errors and control increments are physically submitted in order to set up the fuzzy logic rules. Timing and spacing filtering in terms of weighting approaches is employed in the fuzzy logic rules. A dynamic equation describing the concentration of air pollution is also given so as to cooperate with the fuzzy logic rules and to play roles in the computer simulation. The result of computer simulation reveals that the structure can be an observer to work off line with real road tunnels.

A self-tuning robust fuzzy controller

In the past several years, research results on type- 2 fuzzy control have started to emerge in the literature. None of them, however, are concerned with mathematical input-output relationship of a type-2 fuzzy controller. Establishing such relationship is important as it will deepen our understanding of type- 2 fuzzy controller structures, how they function, and their advantages and drawbacks as compared to type-1 fuzzy controllers and conventional controllers (e.g., the PID controller). The availability of such structure will also lay a foundation for more rigorous theoretical analysis and design of type-2 fuzzy control systems. In this paper, we derive the mathematical input-output relation of a type-2 fuzzy PD (or PI) controller that has one of the simplest possible configurations - only two interval type-2 fuzzy sets for each input variables, four fuzzy rules with Zadeh AND operator, and four interval type-2 output fuzzy sets. We relate the resulting structure to conventional control theory and show that it actually is a PD (or PI) controller with the proportional and derivative (or integral) gains changing as the input variable values vary.

In this paper mathematical models of Mamdani type fuzzy PI or PD controllers via Center of Gravity (CoG) defuzzification are obtained. These controllers are called the simplest fuzzy PI or PD controllers as minimal number of fuzzy sets (two fuzzy sets on each of the two-input variables and three fuzzy sets on the output variable) are employed. The basic components of these models are L-type and Y-type membership functions on each input variable, trapezoidal or triangular membership functions on output variable, minimum / algebraic product t-norm, maximum OR operator, three linear fuzzy control rules, minimum / algebraic product inference and CoG defuzzification. Mathematical models of fuzzy controller via CoG defuzzification were not reported in the literature and are therefore presented for the first time in this paper.

This book presents a systematic framework targeting at fuzzy modeling and fuzzy control of nonlinear systems with uncertainties. The book is organized into three major parts incorporating 13 chapters. The first part contains four chapters focusing on the modeling of nonlinear dynamical systems by using fuzzy logic. The second part includes five chapters in which fuzzy inference and control techniques are addressed. The final part consists of four chapters, which covers several advanced topics in fuzzy control ranging from controller and filter design to chaotification of fuzzy systems and feedforward fuzzy control of nonlinear systems via Fourier integrals. One of the major contributions of this book is that it presents the latest original research developments in the field. It provides rich examples and references, too. It is a valuable resource for those researchers and practitioners interested in expanding their knowledge from fuzzy logic and applications to nonlinear dynamical systems.

We apply the fuzzy control method to the temperature control system with moisture analyzer because of its uncertainty and variation in the parameters and nonlinear lag. Fuzzy control has fast response speed, short regulation time and strong robustness. But it has a steady-state error mainly because the fuzzy control rules are based on the designers' experience in the operation process and fuzzy information. The non-linearity and time-variation of the controlled process result in imperfectness of the fuzzy control rules and these will affect the result of the control from varying degrees. To make up the imperfectness, we designed the self-adjusting parameter fuzzy controller composed of basic fuzzy controller and self-adjusting parameter models. The task of self-adjusting parameter model is to regulate the quantification factor and scale factor on-line and optimize the basic fuzzy controller in order to largely perfect the response performance of the system. We have successfully controlled the temperature control system with infrared moisture analyzer with controller using this algorithm.

Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview.- Regaining comprehensibility of approximative fuzzy models via the use of linguistic hedges.- Identifying flexible structured premises for mining concise fuzzy knowledge.- A multiobjective genetic learning process for joint feature selection and granularity and contexts learning in fuzzy rule-based classification systems.- Extracting linguistic fuzzy models from numerical data-AFRELI algorithm.- Constrained optimization of fuzzy decision trees.- A new method for inducing a set of interpretable fuzzy partitions and fuzzy inference systems from data.- A Feature Ranking Algorithm for Fuzzy Modelling Problems.- Interpretability in multidimensional classification.- Interpretable semi-mechanistic fuzzy models by clustering, OLS and FIS model reduction.- Trade-off between approximation accuracy and complexity: TS controller design via HOSVD based complexity minimization.- Simplification and reduction of fuzzy rules.- Effect of rule representation in rule base reduction.- Singular value-based fuzzy reduction with relaxed normalization condition.- Interpretability, complexity, and modular structure of fuzzy systems.- Hierarchical genetic fuzzy systems: accuracy, interpretability and design autonomy.- About the trade-off between accuracy and interpretability of Takagi-Sugeno models in the context of nonlinear time series forecasting.- Accurate, transparent and compact fuzzy models by multi-objective evolutionary algorithms.- Transparent fuzzy systems in modeling and control.- Uniform fuzzy partitions with cardinal splines and wavelets: getting interpretable linguistic fuzzy models.- Relating the theory of partitions in MV-logic to the design of interpretable fuzzy systems.- A formal model of interpretability of linguistic variables.- Expressing relevance and interpretability of rule-based systems.- Conciseness of fuzzy models.- Exact trade-off between approximation accuracy and interpretability: solving the saturation problem for certain FRBSs.- Interpretability improvement of RBF-based neurofuzzy systems using regularized learning.- Extracting fuzzy classification rules from fuzzy clusters on the basis of separating hyperplanes.

This paper presents the stability analysis of fuzzy-model-based control systems. Stepwise membership functions are introduced to facilitate the stability analysis. Through the stepwise membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability analysis approach offers a nice property to include the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated fuzzy-model-based control system. Furthermore, the proposed stability analysis approach can be applied to the fuzzy-model-based control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed by choosing the membership functions during the design of fuzzy controllers. By employing membership functions with simple structure, it is possible to lower the structural complexity and the implementation cost. Simulation example is given to illustrate the merits of the proposed approach.

Type-2 fuzzy model based controller design for neutralization processes

This paper proposes a hybrid evolutionary functional link and interval type-2 fuzzy neural system (EFLIT2FNS) to predict the currency exchange rate data for six different time horizons starting from one day to one year. The antecedent part of each fuzzy rule of EFLIT2FNS model is an interval type-2 fuzzy set and the fuzzy rules are of the Takagi-Sugano-Kang (TSK) and the consequent part comprises a functional link artificial neural network (FLANN). The parameters of both the antecedent and consequent part of the fuzzy rules are optimised by the gradient descent algorithm. Further, to overcome the limitations of the above said algorithm, two evolutionary algorithms, i.e., genetic algorithm (GA) and differential evolution (DE) are used to optimise all the parameters used in the model. Five different currency exchange time series data are considered for evaluating the performance of the proposed algorithm. The simulation results reveal that the prediction accuracy of the EFLIT2FNS model is significantly better than other models used for comparison.

Oxygen excess ratio control is closely related to the performance and safety of a Proton Exchange Membrane fuel cell system. Some control strategies should be used to regulate the oxygen excess ratio at the suitable value in order to avoid stack starvation and damage. And in this paper, a simple fuzzy double model control has been proposed to adjust the oxygen excess ratio under variation load currents. The double model controller combines a PID controller and a fuzzy logic controller which can be switched based on the fuzzy inference rules during the regulation process. The simulation results demonstrate that the fuzzy double model control can adjust the oxygen excess ratio at the setting point when the current is changed, and improve the dynamic performance of oxygen excess ratio than fuzzy PID control.KeywordsPEM fuel celloxygen excess ratiofuzzy controlPID controlsoft switching

An energy-saving fuzzy control system for highway tunnel lighting

We examine the performance of compact fuzzy rule-based classification systems that consist of a small number of simple fuzzy rules with high comprehensibility. Those fuzzy systems are designed in a heuristic manner using rule selection criteria. We first describe fuzzy rule-based classification. Next we describe heuristic rule selection criteria using the terminology in data mining: confidence and support. A small number of fuzzy rules are extracted from numerical data based on each rule selection criterion. Then we examine the classification performance of extracted fuzzy rules through computational experiments on a number of benchmark data sets from the UCI ML Repository. Our results should be viewed as the lowest benchmark performance of fuzzy rule-based classification systems because fuzzy rules are extracted using a simple heuristic method with no optimization or tuning procedures. Nevertheless our results on some data sets are comparable to reported results by the C4.5 algorithm in the literature.

The central point in designing a fuzzy system for modeling and control is the generation of a set of efficient and effective fuzzy rules. Generally, fuzzy rules can be generated either from heuristics or from experimental data. Heuristic fuzzy rule generation, as discussed in Chapter 1, consists of the following main steps: Determination of the structure of the fuzzy systems. This includes mainly the selection of the inputs and outputs. Usually, a multi-input multi-output fuzzy systems can be decomposed into a number of multi-input single-output fuzzy systems. Definition of linguistic terms and their fuzzy membership function for each fuzzy variables. If a Mamdani fuzzy system is designed, each input and output can be seen as a linguistic variable. Therefore, it is necessary to define the linguistic terms (e.g., Small, Medium, Large etc.) and their fuzzy membership function. Details about the definition of a linguistic variable is presented in Section 1.2.1. Determination of fuzzy inference method. For example, for fuzzy mapping rules, the fuzzy Cartesian product can be used to define the fuzzy relation. Refer to Section 1.2.2. Defuzzification. If the Mamdani type fuzzy rules are used, the fuzzy output derived from the fuzzy rule base should be defuzzified. Refer also to Section 1.2.2 for different defuzzification methods. If the Takagi-Sugeno fuzzy rules are used, the defuzzification is included in the fuzzy inference and a crisp output is obtained directly.