69 research outputs found
The Stratic Defuzzifier for Discretised General Type-2 Fuzzy Sets
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Stratification is a feature of the type-reduced set of the general type-2 fuzzy set, from which a new technique for general type-2 defuzzification, Stratic Defuzzification, may be derived. Existing defuzzification strategies are summarised. The stratified structure is described, after which the Stratic Defuzzifier is presented and contrasted experimentally for accuracy and efficiency with both the Exhaustive Method of Defuzzification (to benchmark accuracy) and the alpha-Planes/Karnik–Mendel Iterative Procedure strategy, employing 5, 11, 21, 51 and 101 alpha-planes. The Stratic Defuzzifier is shown to be much faster than the Exhaustive Defuzzifier. In fact the Stratic Defuzzifier and the alpha-Planes/Karnik–Mendel Iterative Procedure Method are comparably speedy; the speed of execution correlates with the number of planes participating in the defuzzification process. The accuracy of the Stratic Defuzzifier is shown to be excellent. It is demonstrated to be more accurate than the alpha-Planes/Karnik–Mendel Iterative Procedure Method in four of six test cases, regardless of the number of -planes employed. In one test case, it is less accurate than the alpha-Planes/Karnik–Mendel Iterative Procedure Method, regardless of the number of alpha-planes employed. In the remaining test case, the alpha-Planes/Karnik–Mendel Iterative Procedure Method with 11 alpha-Planes gives the most accurate result, with the Stratic Defuzzifier coming second
Learning of Type-2 Fuzzy Logic Systems using Simulated Annealing.
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
Fuzzy Logic in Decision Support: Methods, Applications and Future Trends
During the last decades, the art and science of fuzzy logic have witnessed significant developments and have found applications in many active areas, such as pattern recognition, classification, control systems, etc. A lot of research has demonstrated the ability of fuzzy logic in dealing with vague and uncertain linguistic information. For the purpose of representing human perception, fuzzy logic has been employed as an effective tool in intelligent decision making. Due to the emergence of various studies on fuzzy logic-based decision-making methods, it is necessary to make a comprehensive overview of published papers in this field and their applications. This paper covers a wide range of both theoretical and practical applications of fuzzy logic in decision making. It has been grouped into five parts: to explain the role of fuzzy logic in decision making, we first present some basic ideas underlying different types of fuzzy logic and the structure of the fuzzy logic system. Then, we make a review of evaluation methods, prediction methods, decision support algorithms, group decision-making methods based on fuzzy logic. Applications of these methods are further reviewed. Finally, some challenges and future trends are given from different perspectives. This paper illustrates that the combination of fuzzy logic and decision making method has an extensive research prospect. It can help researchers to identify the frontiers of fuzzy logic in the field of decision making
Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set.
Other research group involved: Centre for Computational Intelligence (CCI).The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised interval type-2 fuzzy sets. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this bottleneck. In this paper we survey four alternative strategies for defuzzifying an interval type-2 fuzzy set: 1. The Karnik-Mendel Iterative Procedure, 2. the Wu-Mendel Approximation, 3. the Greenfield-Chiclana Collapsing Defuzzifier, and 4. the Nie-Tan Method.
We evaluated the different methods experimentally for accuracy, by means of a comparative study using six representative test sets with varied characteristics, using the exhaustive method as the standard. A preliminary ranking of the methods was achieved using a multi-criteria decision making methodology based on the assignment of weights according to performance. The ranking produced, in order of decreasing accuracy, is 1. the Collapsing Defuzzifier, 2. the Nie-Tan Method, 3. the Karnik-Mendel Iterative Procedure, and 4. the Wu-Mendel Approximation.
Following that, a more rigorous analysis was undertaken by means of the Wilcoxon Nonparametric Test, in order to validate the preliminary test conclusions. It was found that there was no evidence of a significant difference between the accuracy of the Collapsing and Nie-Tan Methods, and between that of the Karnik-Mendel Iterative Procedure and the Wu-Mendel Approximation. However, there was evidence to suggest that the collapsing and Nie-Tan Methods are more accurate than the Karnik-Mendel Iterative Procedure and the Wu-Mendel Approximation.
In relation to efficiency, each method’s computational complexity was analysed, resulting in a ranking (from least computationally complex to most computationally complex) as follows: 1. the Nie-Tan Method, 2. the Karnik-Mendel Iterative Procedure (lowest complexity possible), 3. the Greenfield-Chiclana Collapsing Defuzzifier, 4. the Karnik-Mendel Iterative Procedure (highest complexity possible), and 5. the Wu-Mendel Approximation
Geometric Fuzzy Logic Systems
There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems
Uncertainty and Interpretability Studies in Soft Computing with an Application to Complex Manufacturing Systems
In systems modelling and control theory, the benefits of applying neural networks have been extensively studied. Particularly in manufacturing processes, such as the prediction of mechanical properties of heat treated steels. However, modern industrial processes usually involve large amounts of data and a range of non-linear effects and interactions that might hinder their model interpretation. For example, in steel manufacturing the understanding of complex mechanisms that lead to the mechanical properties which are generated by the heat treatment process is vital. This knowledge is not available via numerical models, therefore an experienced metallurgist estimates the model parameters to obtain the required properties. This human knowledge and perception sometimes can be imprecise leading to a kind of cognitive uncertainty such as vagueness and ambiguity when making decisions. In system classification, this may be translated into a system deficiency - for example, small input changes in system attributes may result in a sudden and inappropriate change for class assignation.
In order to address this issue, practitioners and researches have developed systems that are functional equivalent to fuzzy systems and neural networks. Such systems provide a morphology that mimics the human ability of reasoning via the qualitative aspects of fuzzy information rather by its quantitative analysis. Furthermore, these models are able to learn from data sets and to describe the associated interactions and non-linearities in the data. However, in a like-manner to neural networks, a neural fuzzy system may suffer from a lost of interpretability and transparency when making decisions. This is mainly due to the application of adaptive approaches for its parameter identification.
Since the RBF-NN can be treated as a fuzzy inference engine, this thesis presents several methodologies that quantify different types of uncertainty and its influence on the model interpretability and transparency of the RBF-NN during its parameter identification. Particularly, three kind of uncertainty sources in relation to the RBF-NN are studied, namely: entropy, fuzziness and ambiguity.
First, a methodology based on Granular Computing (GrC), neutrosophic sets and the RBF-NN is presented. The objective of this methodology is to quantify the hesitation produced during the granular compression at the low level of interpretability of the RBF-NN via the use of neutrosophic sets. This study also aims to enhance the disitnguishability and hence the transparency of the initial fuzzy partition. The effectiveness of the proposed methodology is tested against a real case study for the prediction of the properties of heat-treated steels.
Secondly, a new Interval Type-2 Radial Basis Function Neural Network (IT2-RBF-NN) is introduced as a new modelling framework. The IT2-RBF-NN takes advantage of the functional equivalence between FLSs of type-1 and the RBF-NN so as to construct an Interval Type-2 Fuzzy Logic System (IT2-FLS) that is able to deal with linguistic uncertainty and perceptions in the RBF-NN rule base. This gave raise to different combinations when optimising the IT2-RBF-NN parameters.
Finally, a twofold study for uncertainty assessment at the high-level of interpretability of the RBF-NN is provided. On the one hand, the first study proposes a new methodology to quantify the a) fuzziness and the b) ambiguity at each RU, and during the formation of the rule base via the use of neutrosophic sets theory. The aim of this methodology is to calculate the associated fuzziness of each rule and then the ambiguity related to each normalised consequence of the fuzzy rules that result from the overlapping and to the choice with one-to-many decisions respectively. On the other hand, a second study proposes a new methodology to quantify the entropy and the fuzziness that come out from the redundancy phenomenon during the parameter identification.
To conclude this work, the experimental results obtained through the application of the proposed methodologies for modelling two well-known benchmark data sets and for the prediction of mechanical properties of heat-treated steels conducted to publication of three articles in two peer-reviewed journals and one international conference
Higher order fuzzy logic in controlling selective catalytic reduction systems
This paper presents research on applications of fuzzy logic and higher-order fuzzy logic systems to control filters reducing air pollution [1]. The filters use Selective Catalytic Reduction (SCR) method and, as for now, this process is controlled manually by a human expert. The goal of the research is to control an SCR system responsible for emission of nitrogen oxide (NO) and nitrogen dioxide (NO2) to the air, using SCR with ammonia (NH3). There are two higher-order fuzzy logic systems presented, applying interval-valued fuzzy sets and type-2 fuzzy sets, respectively. Fuzzy sets and higher order fuzzy sets describe linguistically levels of nitrogen oxides as the input, and settings of ammonia valve in the air filter as the output. The obtained results are consistent with data provided by experts. Besides, we show that the type-2 fuzzy logic controllers allows us to obtain results much closer to desired parameters of the ammonia valve, than traditional FLS
Modelação e controlo de sistemas com incertezas baseados em lógica difusa de tipo-2
Doutoramento em Engenharia EletrotécnicaA última fronteira da Inteligência Artificial será o desenvolvimento de
um sistema computacional autónomo capaz de "rivalizar" com a capacidade
de aprendizagem e de entendimento humana. Ainda que tal
objetivo não tenha sido até hoje atingido, da sua demanda resultam
importantes contribuições para o estado-da-arte tecnológico atual. A
Lógica Difusa é uma delas que, influenciada pelos princípios fundamentais
da lógica proposicional do raciocínio humano, está na base
de alguns dos sistemas computacionais "inteligentes" mais usados da
atualidade.
A teoria da Lógica Difusa é uma ferramenta fundamental na suplantação
de algumas das limitações inerentes à representação de informação
incerta em sistemas computacionais. No entanto esta apresenta
ainda algumas lacunas, pelo que diversos melhoramentos à teoria
original têm sido introduzidos ao longo dos anos, sendo a Lógica
Difusa de Tipo-2 uma das mais recentes propostas. Os novos graus de
liberdade introduzidos por esta teoria têm-se demonstrado vantajosos,
particularmente em aplicações de modelação de sistemas não-lineares
complexos. Uma das principais vantagens prende-se com o aumento
da robustez dos modelos assim desenvolvidos comparativamente àqueles
baseados nos princípios da Lógica Difusa de Tipo-1 sem implicar
necessariamente um aumento da sua dimensão. Tal propriedade é particularmente
vantajosa considerando que muitas vezes estes modelos
são utilizados como suporte ao desenvolvimento de sistemas de controlo
que deverão ser capazes de assegurar o comportamento ótimo
de um processo em condições de operação variáveis. No entanto, o
estado-da-arte da teoria de controlo de sistemas baseada em modelos
não tem integrado todos os melhoramentos proporcionados pelo desenvolvimento
de modelos baseados nos princípios da Lógica Difusa de
Tipo-2.
Por essa razão, a presente tese propõe-se a abordar este tópico desenvolvendo
uma metodologia de síntese de Controladores Preditivos
baseados em modelos Takagi-Sugeno seguindo os princípios da Lógica
Difusa de Tipo-2. De modo a cumprir este objetivo, quatro linhas de
investigação serão debatidas neste trabalho.Primeiramente proceder-se-á ao desenvolvimento de uma metodologia
de treino de Modelos Difusos de Tipo-2 simplificada, focada em dois
paradigmas: manter a clareza dos intervalos de incerteza introduzidos
sobre um Modelo Difuso de Tipo-1; assegurar a validade dos diversos
modelos localmente lineares que constituem a estrutura Takagi-
Sugeno, de modo a torná-los adequados a métodos de síntese de controladores
baseados em modelos.
O modelo desenvolvido é tipicamente utilizado para extrapolar o comportamento
do sistema numa janela temporal futura. No entanto,
quando usados em aproximações de sistemas não lineares, os modelos
do tipo Takagi-Sugeno estabelecem um compromisso entre exatidão e
complexidade computacional. Assim, é proposta a utilização dos princípios
da Lógica Difusa de Tipo-2 para reduzir a influência dos erros de
modelação nas estimações obtidas através do ajuste dos intervalos de
incerteza dos parâmetros do modelo.
Com base na estrutura Takagi-Sugeno, um método de linearização local
de modelos não-lineares será utilizado em cada ponto de funcionamento
do sistema de modo a obter os parâmetros necessários para a
síntese de um controlador otimizado numa janela temporal futura de
acordo com os princípios da teoria de Controlo Preditivo Generalizado -
um dos algoritmos de Controlo Preditivo mais utilizado na indústria. A
qualidade da resposta do sistema em malha fechada e a sua robustez a
perturbações serão então comparadas com implementações do mesmo
algoritmo baseadas em métodos de modelação mais simples.
Para concluir, o controlador proposto será implementado num
System-on-Chip baseado no core ARM Cortex-M4. Com o propósito
de facilitar a realização de testes de implementação de algoritmos
de controlo em sistemas embutidos, será apresentada também uma
plataforma baseada numa arquitetura Processor-In-the-Loop, que permitirá
avaliar a execução do algoritmo proposto em sistemas computacionais
com recursos limitados, aferindo a existência de possíveis
limitações antes da sua aplicação em cenários reais.
A validade do novo método proposto é avaliada em dois cenários de
simulação comummente utilizados em testes de sistemas de controlo
não-lineares: no Controlo da Temperatura de uma Cuba de Fermentação
e no Controlo do Nível de Líquidos num Sistema de Tanques
Acoplados. É demonstrado que o algoritmo de controlo desenvolvido
permite uma melhoria da performance dos processos supramencionados,
particularmente em casos de mudança rápida dos regimes de funcionamento
e na presença de perturbações ao processo não medidas.The development of an autonomous system capable of matching
human knowledge and learning capabilities embedded in a compact
yet transparent way has been one of the most sought milestones of
Artificial Intelligence since the invention of the first mechanical general
purpose computers. Such accomplishment is yet to come but, in its
pursuit, important contributions to the state-of-the-art of current technology
have been made. Fuzzy Logic is one of such, supporting some
of the most used frameworks for embedding human-like knowledge in
computational systems.
The theory of Fuzzy Logic overcame some of the difficulties that the
inherent uncertainty in information representations poses to the development
of computational systems. However, it does present some
limitations so, aiming to further extend its capabilities, several improvements
over its original formalization have been proposed over the
years such as Type-2 Fuzzy Logic - one of its most recent advances.
The additional degrees of freedom of Type-2 Fuzzy Logic are showing
greater potential to supplant its original counterpart, especially in
complex non-linear modeling tasks. One of its main outcomes is its
capability of improving the developed model’s robustness without necessarily
increasing its dimensionality comparatively to a Type-1 Fuzzy
Model counterpart. Such feature is particularly advantageous if one
considers these model as a support for developing control systems capable
of maintaining a process’s optimal performance over changing
operating conditions. However, state-of-the art model-based control
theory does not seem to be taking full advantage of the improvements
achieved with the development of Type-2 Fuzzy Logic based models.
Therefore, this thesis proposes to address this problem by developing a
Model Predictive Control system supported by Interval Type-2 Takagi-
Sugeno Fuzzy Models. To accomplish this goal, four main research
directions are covered in this work.Firstly, a simpler method for training a Type-2 Takagi-Sugeno Fuzzy
Model focused on two main paradigms is proposed: maintaining a
meaningful interpretation of the uncertainty intervals embedded over
an estimated Type-1 Fuzzy Model; ensuring the validity of several locally
linear models that constitute the Takagi-Sugeno structure in order
to make them suitable for model-based control approaches.
Based on the developed model, a multi-step ahead estimation of the
process behavior is extrapolated. However, as Takagi-Sugeno Fuzzy
Models establish a trade-off between accuracy and computational complexity
when used as a non-linear process approximation, it is proposed
to apply the principles of Type-2 Fuzzy Logic to reduce the influence
of modeling uncertainties on the obtained estimations by adjusting the
model parameters’ uncertainty intervals.
Supported by the developed Type-2 Takagi-Sugeno Fuzzy Model, a
locally linear approximation of each current operation point is used to
obtain the optimal control law over a prediction horizon according to
the principles of Generalized Predictive Control - one of the most used
Model Predictive Control algorithms in Industry. The improvements in
terms of closed loop tracking performance and robustness to unmodeled
operation conditions are then assessed comparatively to Generalized
Predictive Control implementations based on simpler modeling
approaches.
Ultimately, the proposed control system is implemented in a general
purpose System-on-a-Chip based on a ARM Cortex-M4 core. A
Processor-In-the-Loop testing framework, developed to support the implementation
of control loops in embedded systems, is used to evaluate
the algorithm’s turnaround time when executed in such computationally
constrained platform, assessing its possible limitations before deployment
in real application scenarios.
The applicability of the new methods introduced in this thesis is illustrated
in two simulated processes commonly used in non-linear control
benchmarking: the Temperature Control of a Fermentation Reactor
and the Liquid Level Control of a Coupled Tanks System. It is shown
that the developed control system achieves an improved closed loop
performance of the above mentioned processes, particularly in the cases
of quick changes in the operation regime and in presence of unmeasured
external disturbances
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