This thesis reports the work of using simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of type-1 and type-2 fuzzy logic systems to maximise their modelling ability. Therefore, it presents the combination of simulated annealing with three models, type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and general type-2 fuzzy logic systems to model four bench-mark problems including real-world problems. These problems are: noise-free Mackey-Glass time series forecasting, noisy Mackey-Glass time series forecasting and two real world problems which are: the estimation of the low voltage electrical line length in rural towns and the estimation of the medium voltage electrical line maintenance cost. The type-1 and type-2 fuzzy logic systems models are compared in their abilities to model uncertainties associated with these problems. Also, issues related to this combination between simulated annealing and fuzzy logic systems including type-2 fuzzy logic systems are discussed. The thesis contributes to knowledge by presenting novel contributions. The first is a novel approach to design interval type-2 fuzzy logic systems using the simulated annealing algorithm. Another novelty is related to the first automatic design of general type-2 fuzzy logic system using the vertical slice representation and a novel method to overcome some parametrisation difficulties when learning general type-2 fuzzy logic systems. The work shows that interval type-2 fuzzy logic systems added more abilities to modelling information and handling uncertainties than type-1 fuzzy logic systems but with a cost of more computations and time. For general type-2 fuzzy logic systems, the clear conclusion that learning the third dimension can add more abilities to modelling is an important advance in type-2 fuzzy logic systems research and should open the doors for more promising research and practical works on using general type-2 fuzzy logic systems to modelling applications despite the more computations associated with it.

Le travail de la thèse traite le problème de suivi de trajectoires des systèmes non linéaires incertains,dont le modèle nominal est construit à l’aide d’un système flou TS (Takagi-Sugeno) de type-2. Cedernier, exploite les modèles locaux du système obtenus par linéarisation autour de certains pointsde fonctionnement. La commande développée est basée sur les modes glissants d’ordre deux avecSuper-Twisting. Nous avons proposé deux systèmes flous type-2 adaptatifs, qui ont comme uniqueentrée la surface de glissement, pour résoudre le problème du calcul de la valeur optimale des gainsde la commande. Des résultats de simulation ont permis de comparer les performances de l’approcheproposée avec la méthode classique. Ensuite, nous avons introduit le concept de l’intégral sliding modepour imposer à priori le temps d’arrivée sur la surface de glissement. Les approches proposées sontgénéralisées aux cas des systèmes multivariables. Plusieurs résultats par simulation et implémentationen temps réel sont présentés pour illustrer les performances des approches développées / This work deals with a fuzzy tracking control design for uncertain nonlinear dynamic system withexternal disturbances and using a TS (Takagi-Sugeno) fuzzy model description. The control is basedon the Super-Twisting algorithm, which is among of second order sliding mode control. Moreover, twoadaptive fuzzy type-2 systems have been introduced to generate the two Super-Twisting signals toavoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upperbounds. These adaptive fuzzy type-2 systems has only one input : the sliding surface, and one output :the optimale values of the control gains, which are hard to compute with the original algorithm.Simulation results are obtained in order to compare the performances of the proposed method tothat given by Levant. Then, we have introduced the integral sliding mode concept to impose inadvance the convergence time and the arrival on the sliding surface. The proposed approaches aregeneralized to the case of multivariable systems. Several results in simulation and in real time usinga benchmark are obtained to validate and to confirm the performances of our contributions.

Finding a product with high quality and reasonable price online is a difficult task due to the fuzzy nature of data and queries. In order to handle the fuzzy problem, a new type-2 fuzzy reasoning based decision support system, the Web Shopping Expert for online users is proposed. In the Web Shopping Expert, an interval type-2 fuzzy logic system is used and a fuzzy output can be obtained using the up-low limit technique, which offers an opportunity to directly employ all the rules and methods of the type-1 fuzzy sets onto the type-2 fuzzy sets. To achieve the best performance the fuzzy inference system is optimized by the least square and numerical method. The key advantages of the least square method are the efficient use of samples and the simplicity of the implementation. The Web Shopping Expert based on the interval type-2 fuzzy inference system provides more reasonable conclusions for online users.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-10T12:31:18Z No. of bitstreams: 1 eduardopestanadeaguiar.pdf: 7884545 bytes, checksum: 182caace21281f7afce6554505811116 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-13T17:18:31Z (GMT) No. of bitstreams: 1 eduardopestanadeaguiar.pdf: 7884545 bytes, checksum: 182caace21281f7afce6554505811116 (MD5) / Made available in DSpace on 2017-03-13T17:18:31Z (GMT). No. of bitstreams: 1 eduardopestanadeaguiar.pdf: 7884545 bytes, checksum: 182caace21281f7afce6554505811116 (MD5) Previous issue date: 2016-09-26 / - / This thesis presents new fuzzy models applied to classification problems. With this regards, we introduce the use of set-membership concept, derived from the adaptive filter theory, into the training procedure of type-1 and singleton/non-singleton fuzzy logic systems, in order to reduce computational complexity and to increase convergence speed. Also, we present different criteria for using together with set-membership. Furthermore, we discuss the usefulness of delta rule delta, local Lipschitz estimation, variable step size and variable step size adaptive algorithms to yield additional improvement in terms of computational complexity reduction and convergence speed. Another important contribution of this thesis is to address the height type-reduction and to propose a modified version of interval singleton type-2 fuzzy logic system, so−called upper and lower singleton type-2 fuzzy logic system. The obtained results are compared with other models reported in the literature, demonstrating the effectiveness of the proposed classifiers and revealing that the proposals are able to properly handle with uncertainties associated with the measurements and with the data that are used to tune the parameters of the model. Based on data set provided by a Brazilian railway company, the models outlined above are applied in the classification of three possible faults and the normal condition of the switch machine, which is an equipment used for handling railroad switches. Finally, this thesis discusses the use of set-membership concept into the training procedure of an interval and singleton type-2 fuzzy logic system and of an upper and lower singleton type-2 fuzzy logic system, aiming to reduce computational complexity and to increase the convergence speed and the classification ratio. Also, we discuss the adoption of different criteria together with set-membership based-techniques. The performance is based on the data set composed of images provided by the same Brazilian railway company, which covers the four possible rail head defects and the normal condition of the rail head. The reported results show that the proposed models result in improved convergence speed, slightly higher classification ratio and remarkable computation complexity reduction when we limit the number of epochs for training, which may be required due to real time constraint or low computational resource availability.

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and a new probability type reduced reasoning method for the interval-valued fuzzy logic system are proposed in this thesis. In order to optimize this particle system’s performance, we adopt genetic algorithm (GA) to adjust parameters. The applications for the new system are performed and results have shown that the developed method is more accurate and robust to design a reliable fuzzy logic system than type-1 method and the computation of our proposed method is more efficient.

Fuzzy logic systems (FLSs) are well known in the literature for their ability to model linguistics and system uncertainties. Due to this ability, FLSs have been successfully used in modeling and control applications such as medicine, finance, communications, and operations research. Moreover, the ability of higher order fuzzy systems to handle system uncertainty has become an interesting topic of research in the field. In particular, type-2 FLSs (T2 FLSs), systems consisting of fuzzy sets with fuzzy grades of membership, a feature that type-1 (T1) does not offer, are most well-known for this capability. The structure of T2 FLSs allows for the incorporation of uncertainty in the input membership grades, a common situation in reasoning with physical systems. General T2 FLSs have a complex structure, thus making them difficult to adopt on a large scale. As a result, interval T2 FLSs (IT2 FLSs), a special class of T2 FLSs, have recently shown great potential in various applications with input-output (I/O) system uncertainties. Due to the sophisticated mathematical structure of IT2 FLSs, little to no systematic analysis has been reported in the literature to use such systems in control design. Moreover, to date, designers have distanced themselves from adopting such systems on a wide scale because of their design complexity. Furthermore, the very few existing control methods utilizing IT2 fuzzy logic control systems (IT2 FLCSs) do not guarantee the stability of their system. Therefore, this thesis presents a systematic method for designing stable IT2 Takagi-Sugeno-Kang (IT2 TSK) fuzzy systems when antecedents are T2 fuzzy sets and consequents are crisp numbers (A2-C0). Five new inference mechanisms are proposed that have closed-form I/O mappings, making them more feasible for FLCS stability analysis. The thesis focuses on control applications for when (a) both plant and controller use A2-C0 TSK models, and (b) the plant uses T1 Takagi-Sugeno (T1 TS) and the controller uses IT2 TS models. In both cases, sufficient stability conditions for the stability of the closed-loop system are derived. Furthermore, novel linear matrix inequality-based algorithms are developed for satisfying the stability conditions. Numerical analyses are included to validate the effectiveness of the new inference methods. Case studies reveal that a well-tuned IT2 TS FLCS using the proposed inference engine can potentially outperform its T1 TSK counterpart, a result of IT2 having greater structural flexibility than T1. Moreover, due to the simple nature of the proposed inference engine, it is easy to implement in real-time control systems. In addition, a novel design methodology is proposed for IT2 TSK FLC for modular and reconfigurable robot (MRR) manipulators with uncertain dynamic parameters. A mathematical framework for the design of IT2 TSK FLCs is developed for tracking purposes that can be effectively used in real-time applications. To verify the effectiveness of the proposed controller, experiments are performed on an MRR with two degrees of freedom which exhibits dynamic coupling behavior. Results show that the developed controller can outperform some well-known linear and nonlinear controllers for different configurations. Therefore, the proposed structure can be adopted for the position control of MRRs with unknown dynamic parameters in trajectory-tracking applications. Finally, a rigorous mathematical analysis of the robustness of FLSs (both T1 and IT2) is presented in the thesis and entails a formulation of the robustness of FLSs as a constraint multi-objective optimization problem. Consequently, a procedure is proposed for the design of robust IT2 FLSs. Several examples are presented to demonstrate the effectiveness of the proposed methodologies. It was concluded that both T1 and IT2 FLSs can be designed to achieve robust behavior in various applications. IT2 FLSs, having a more flexible structure than T1 FLSs, exhibited relatively small approximation errors in the several examples investigated. The rigorous methodologies presented in this thesis lay the mathematical foundations for analyzing the stability and facilitating the design of stabilizing IT2 FLCSs. In addition, the proposed control technique for tracking purposes of MRRs will provide control engineers with tools to control dynamic systems with uncertainty and changing parameters. Finally, the systematic approach developed for the analysis and design of robust T1 and IT2 FLSs is of great practical value in various modeling and control applications.

Fuzzy logic systems (FLSs) are well known in the literature for their ability to model linguistics and system uncertainties. Due to this ability, FLSs have been successfully used in modeling and control applications such as medicine, finance, communications, and operations research. Moreover, the ability of higher order fuzzy systems to handle system uncertainty has become an interesting topic of research in the field. In particular, type-2 FLSs (T2 FLSs), systems consisting of fuzzy sets with fuzzy grades of membership, a feature that type-1 (T1) does not offer, are most well-known for this capability. The structure of T2 FLSs allows for the incorporation of uncertainty in the input membership grades, a common situation in reasoning with physical systems. General T2 FLSs have a complex structure, thus making them difficult to adopt on a large scale. As a result, interval T2 FLSs (IT2 FLSs), a special class of T2 FLSs, have recently shown great potential in various applications with input-output (I/O) system uncertainties. Due to the sophisticated mathematical structure of IT2 FLSs, little to no systematic analysis has been reported in the literature to use such systems in control design. Moreover, to date, designers have distanced themselves from adopting such systems on a wide scale because of their design complexity. Furthermore, the very few existing control methods utilizing IT2 fuzzy logic control systems (IT2 FLCSs) do not guarantee the stability of their system. Therefore, this thesis presents a systematic method for designing stable IT2 Takagi-Sugeno-Kang (IT2 TSK) fuzzy systems when antecedents are T2 fuzzy sets and consequents are crisp numbers (A2-C0). Five new inference mechanisms are proposed that have closed-form I/O mappings, making them more feasible for FLCS stability analysis. The thesis focuses on control applications for when (a) both plant and controller use A2-C0 TSK models, and (b) the plant uses T1 Takagi-Sugeno (T1 TS) and the controller uses IT2 TS models. In both cases, sufficient stability conditions for the stability of the closed-loop system are derived. Furthermore, novel linear matrix inequality-based algorithms are developed for satisfying the stability conditions. Numerical analyses are included to validate the effectiveness of the new inference methods. Case studies reveal that a well-tuned IT2 TS FLCS using the proposed inference engine can potentially outperform its T1 TSK counterpart, a result of IT2 having greater structural flexibility than T1. Moreover, due to the simple nature of the proposed inference engine, it is easy to implement in real-time control systems. In addition, a novel design methodology is proposed for IT2 TSK FLC for modular and reconfigurable robot (MRR) manipulators with uncertain dynamic parameters. A mathematical framework for the design of IT2 TSK FLCs is developed for tracking purposes that can be effectively used in real-time applications. To verify the effectiveness of the proposed controller, experiments are performed on an MRR with two degrees of freedom which exhibits dynamic coupling behavior. Results show that the developed controller can outperform some well-known linear and nonlinear controllers for different configurations. Therefore, the proposed structure can be adopted for the position control of MRRs with unknown dynamic parameters in trajectory-tracking applications. Finally, a rigorous mathematical analysis of the robustness of FLSs (both T1 and IT2) is presented in the thesis and entails a formulation of the robustness of FLSs as a constraint multi-objective optimization problem. Consequently, a procedure is proposed for the design of robust IT2 FLSs. Several examples are presented to demonstrate the effectiveness of the proposed methodologies. It was concluded that both T1 and IT2 FLSs can be designed to achieve robust behavior in various applications. IT2 FLSs, having a more flexible structure than T1 FLSs, exhibited relatively small approximation errors in the several examples investigated. The rigorous methodologies presented in this thesis lay the mathematical foundations for analyzing the stability and facilitating the design of stabilizing IT2 FLCSs. In addition, the proposed control technique for tracking purposes of MRRs will provide control engineers with tools to control dynamic systems with uncertainty and changing parameters. Finally, the systematic approach developed for the analysis and design of robust T1 and IT2 FLSs is of great practical value in various modeling and control applications.

The generalization abilities of machine learning algorithms often depend on the algorithms’ initialization, parameter settings, training sets, or feature selections. For instance, SVM classifier performance largely relies on whether the selected kernel functions are suitable for real application data. To enhance the performance of individual classifiers, this dissertation proposes classifier fusion models using computational intelligence knowledge to combine different classifiers. The first fusion model called T1FFSVM combines multiple SVM classifiers through constructing a fuzzy logic system. T1FFSVM can be improved by tuning the fuzzy membership functions of linguistic variables using genetic algorithms. The improved model is called GFFSVM. To better handle uncertainties existing in fuzzy MFs and in classification data, T1FFSVM can also be improved by applying type-2 fuzzy logic to construct a type-2 fuzzy classifier fusion model (T2FFSVM). T1FFSVM, GFFSVM, and T2FFSVM use accuracy as a classifier performance measure. AUC (the area under an ROC curve) is proved to be a better classifier performance metric. As a comparison study, AUC-based classifier fusion models are also proposed in the dissertation. The experiments on biomedical datasets demonstrate promising performance of the proposed classifier fusion models comparing with the individual composing classifiers. The proposed classifier fusion models also demonstrate better performance than many existing classifier fusion methods. The dissertation also studies one interesting phenomena in biology domain using machine learning and classifier fusion methods. That is, how protein structures and sequences are related each other. The experiments show that protein segments with similar structures also share similar sequences, which add new insights into the existing knowledge on the relation between protein sequences and structures: similar sequences share high structure similarity, but similar structures may not share high sequence similarity.

[pt] Os sistemas de inferência fuzzy são técnicas de aprendizado de máquina que possuem a capacidade de modelar incertezas matematicamente. Eles são divididos em sistemas de inferências fuzzy tipo-1 e fuzzy tipo-2. O sistema de inferência fuzzy tipo-1 vem sendo amplamente aplicado na solução de diversos problemas referentes ao aprendizado de máquina, tais como, controle, classificação, clusterização, previsão, dentre outros. No entanto, por apresentar uma melhor modelagem matemática das incertezas, o sistema de inferência fuzzy tipo-2 vem ganhando destaque ao longo dos anos. Esta melhora modelagem vem também acompanhada de um aumento do esforço matemático e computacional. Visando reduzir tais pontos para solucionar problemas de classificação, este trabalho apresenta o desenvolvimento e a comparação de duas funções de pertinência Gaussiana para um sistema de inferência fuzzy tipo-2 intervalar usando o método superior e inferior. São utilizadas as funções de pertinência Gaussiana com incerteza na média e com incerteza no desvio padrão. Ambos os modelos fuzzy abordados neste trabalho são treinados por algoritmos baseados em informações de primeira ordem. Além disso, este trabalho propõe a extensão dos modelos fuzzy tipo-2 intervalar para apresentarem múltiplas saídas, reduzindo significativamente o custo computacional na solução de problemas de classificação multiclasse. Finalmente, visando contextualizar a utilização desses modelos em aplicações de engenharia mecânica, este trabalho apresenta a solução de um problema de detecção de falhas em turbinas a gás, utilizadas em aeronaves. / [en] Fuzzy logic systems are machine learning techniques that can model mathematically uncertainties. They are divided into type-1 fuzzy, and type-2 fuzzy logic systems. The type-1 fuzzy logic system has been widely applied to solve several problems related to machine learning, such as control, classification, clustering, prediction, among others. However, as it presents a better mathematical modeling of uncertainties, the type-2 fuzzy logic system has received much attention over the years. This modeling improvement is also accompanied by an increase in mathematical and computational effort. Aiming to reduce these issues to solve classification problems, this work presents the development and comparison of two Gaussian membership functions for a type-2 interval fuzzy logic system using the upper and lower method. Gaussian membership functions with uncertainty in the mean and with uncertainty in the standard deviation are used. Both fuzzy models covered in this work are trained by algorithms based on first order information. Furthermore, this work proposes the extension of interval type-2 fuzzy models to present multiple outputs, significantly reducing the computational cost in solving multiclass classification problems. Finally, aiming to contextualize the use of these models in mechanical engineering applications, this work presents the solution of a problem of fault detection in aircraft gas turbines.

Dans le cadre du transport de marchandises par voie ferroviaire, un certain nombre de verrous limitent les efforts consentis pour un fret plus "propre". Des améliorations doivent être faites afin de limiter le nombre de locotracteurs assurant les charges/décharges de marchandises en bout de ligne. Dans cette perspective, FEMTO-ST et Alstom Transport ont pour objectif de concevoir et développer un système de gestion d'énergie pour locomotive électrique hybride. Composée d'un groupe électrogène couplé à des accumulateurs électrochimiques et des super-condensateurs, la locomotive électrique hybride permet d'accroître la souplesse et l'efficacité du transport ferroviaire électrique, tout en réduisant encore son impact environnemental. Cette étude a consisté dans un premier temps à développer une modélisation macroscopique de la chaîne de traction électrique hybride et à proposer une structuration de la commande avec l'identification des capteurs matériels et logiciels nécessaires au contrôle optimal de la chaîne de traction. La caractérisation expérimentale des moyens de stockage a permis l'amélioration comportementale et dynamique des modèles correspondant. Dans un second temps, le contrôle de la tension de sortie d'un hacheur dévolteur a permis d'étudier l'application de la logique floue de type-2 (intervalle et générale) dans le cas d'applications industrielles (relativement simples). Enfin, une gestion innovante des flux d'énergie au sein d'un système plus complexe: locomotive électrique hybride, a été développée. Mettant en œuvre la logique floue de type-2 et des algorithmes s'inspirant de la théorie de l'évolution, cette gestion d'énergie optimale opère en temps réel et sans connaissance à priori du cycle de conduite. La gestion fréquentielle ainsi que le contrôle des états de charge des sources secondaires du véhicule contribuent également à leur bon fonctionnement. / To achieve a "greener" freight transport, efforts are still needed to overcome some technological barriers. New improvements must be carried at to limit the shunting locomotives' use intended for the goods' load/unload. Considering this aim, FEMTO-ST and Alstom Transport decided to conceive and develop an energy management strategy system for hybrid electric locomotives. Such locomotives include a diesel driven generator set which is coupled with batteries and ultra-capacitors. The architecture aims at improving the flexibility, the effectiveness of the electrical railway transport and at reducing the environmental impact of these activities again. Firstly, the study consists in implementing a macroscopic modelling of the hybrid electric powertrain. Then, the control is optimally designed by identifying the hardware and software sensors of the powertrain. The dynamics and the behavior of the secondary sources' models are improved thanks to their experimental characterizations. Secondly, the use of Type-2 Fuzzy Logic (interval and general) controllers permits to study their efficiency in the control of a very simple industrial system: the output voltage of a buck converter. Lastly, based on the obtained results, an innovative management of the system's energy flows is developed in the case of the hybrid electrical locomotive. The use of the type-2 fuzzy logic and evolutionary algorithms permit to optimally perform a real time energy management strategy without a priori knowledge of the duty cycle. The frequency approach and the secondary sources' state of charge control contribute to their efficient use.