Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

A Survey of Neural Trees

Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to integrate NNs and DTs explicitly or implicitly. In this survey, these approaches are organized in a school which we term as neural trees (NTs). This survey aims to present a comprehensive review of NTs and attempts to identify how they enhance the model interpretability. We first propose a thorough taxonomy of NTs that expresses the gradual integration and co-evolution of NNs and DTs. Afterward, we analyze NTs in terms of their interpretability and performance, and suggest possible solutions to the remaining challenges. Finally, this survey concludes with a discussion about other considerations like conditional computation and promising directions towards this field. A list of papers reviewed in this survey, along with their corresponding codes, is available at: https://github.com/zju-vipa/awesome-neural-treesComment: 35 pages, 7 figures and 1 tabl

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Blind restoration of images with penalty-based decision making : a consensus approach

In this thesis we show a relationship between fuzzy decision making and image processing . Various applications for image noise reduction with consensus methodology are introduced. A new approach is introduced to deal with non-stationary Gaussian noise and spatial non-stationary noise in MRI

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers

Entwicklung eines auf Fuzzy-Regeln basierten Expertensystems zur Hochwasservorhersage im mesoskaligen Einzugsgebiet des Oberen Mains

People worldwide are faced with flood events of different magnitudes. A timely and reliable flood forecast is essential for the people to save goods and, more important, lives. The development of a fuzzy rule based flood forecast system considering extreme flood events within meso-scale catchments and with return periods of 100 years and more is the main objective of this work. Considering one river catchment extreme flood events are usually seldom. However, these data are essential for a reliable setup of warning systems. In this work the database is extended by simulations of possible flood events performing the hydrological model WaSiM-ETH (Water balance Simulation model ETH) driven by generated precipitation fields. The therefore required calibration of the hydrological model is performed applying the genetic optimization algorithm SCE (Shuffled Complex Evolution). Thereby, different SCE configuration setups are investigated and an optimization strategy for the Upper Main basin is developed in order to ensure reliable und satisfying calibration results. In this thesis the developed forecast system comprises different time horizons (3 days; 6, 12, and 48 hours) in order to ensure a reliable and continuous flood forecast at the three main gauges of the Upper Main river. Thereby, the focus of the different fuzzy inference systems lies on different discharge conditions, which together ensure a continuous flood forecast. In this work the performance of the two classical fuzzy inference systems, Mamdani and Takagi-Sugeno, is investigated considering all four forecast horizons. Thereby, a wide variety of different input features, among others Tukey data depth, is taken into consideration. For the training of the fuzzy inference systems the SA (Simulated Annealing) optimization algorithm is applied. A further performance comparison is carried out considering the 48 hour forecast behaviour of the two fuzzy inference systems and the hydrological model WaSiM-ETH. In this work the expert system ExpHo-HORIX is developed in order to combine the single, trained fuzzy inference systems to one overall flood warning system. This expert system ensures beside the fast forecast a quantification of uncertainties within a manageable, user-friendly, and transparent framework which can be easily implemented into an exiting environment.Menschen weltweit werden mit Hochwasserereignissen unterschiedlicher Stärke konfrontiert. Um Eigentum und, noch viel wichtiger, Leben zu retten, ist eine rechtzeitige und zuverlässige Hochwasserwarnung und folglich -vorhersage unerlässlich. Ziel dieser Arbeit ist es deshalb, ein auf Fuzzy-Regeln basiertes Hochwasserwarnsystem für mesoskalige Einzugsgebiete und die Vorhersage von extremen Hochwasserereignissen mit Wiederkehrperioden von 100 Jahren und mehr unter Berücksichtigung von Unsicherheiten zu entwickeln. Da extreme Hochwasserereignisse mit einer Jährlichkeit von 100 oder mehr Jahren in der Realität nicht in jedem Einzugsgebiet bereits beobachtet und aufgezeichnet wurden, ist eine Erweiterung der Datenbank auf Grund von Modellsimulationen zwingend notwendig. In dieser Arbeit werden hierzu das hydrologische Modell WaSiM-ETH (Wasserhaushalts-Simulations-Modell ETH) sowie von Bliefernicht et al. (2008) generierte Niederschlagsfelder verwendet. Die Kalibrierung des Modells erfolgt mit dem SCE (Shuffled Complex Evolution) Optimierungsalgorithmus. Um reproduzierbare Kalibrierungsergebnisse zu erzielen und die notwendige Kalibrierungszeit möglichst gering zu halten, werden unterschiedliche Optimierungskonfigurationen untersucht und eine Kalibrierungsstrategie für das mesoskalige Einzugsgebiet des Oberen Mains entwickelt. Um eine kontinuierliche und zuverlässige Vorhersage zu garantieren, ist die Idee entwickelt worden, Fuzzy-Regelsysteme für unterschiedliche Vorhersagehorizonte (3 Tage; 6, 12 und 48 Stunden) für die drei Hauptpegel des Oberen Mains aufzustellen, die im Zusammenspiel eine kontinuierliche Vorhersage sicher stellen. Der Fokus der 3-Tagesvorhersage liegt hierbei in der zuverlässigen Wiedergabe von geringen und mittleren Abflussbedingungen sowie der zuverlässigen und rechtzeitigen Vorhersage von Überschreitungen einer vordefinierten Meldestufe. Eine vorhergesagte Überschreitung der Meldestufe führt zu einem Wechsel der Vorhersagesysteme von der 3-Tages- zu der 6-, 12- und 48-Stundenvorhersage, deren Fokus auf der Vorhersage der Hochwasserganglinie liegt. In diesem Zusammenhang wird die Effizienz der beiden klassischen Regelsysteme,Mamdani und Takagi-Sugeno, sowie die Kombination unterschiedlicher Eingangsgrößen, unter anderem Tukey Tiefenfunktion, näher untersucht. Ein weiterer Effizienzvergleich wird zwischen den Mamdani Regelsystemen der 48-Stundenvorhersage und dem hydrologischen ModellWaSiM-ETH durchgeführt. Für das Training der beiden Regelsysteme wird der SA (Simulated Annealing) Optimierungsalgorithmus verwendet. Die einzelnen Fuzzy-Regelsysteme werden schließlich in dem entwickelten Hochwasserwarnsystem ExpHo-HORIX (Expertensystem Hochwasser - HORIX) zusammengefügt. Standardmäßig wird für jede Vorhersage die Niederschlagsunsicherheit auf Grund von Ensemble-Vorhersagen innerhalb ExpHo-HORIX analysiert und ausgewiesen. Im Hochwasserfall können für die stündlichen Fuzzy-RegelsystemeModellunsicherheiten des hydrologischenModells, das für die Generierung der Datenbank von Extremereignissen verwendet wurde, zusätzlich ausgewiesen werden. Hierzu müssen zusätzlich Ergebnisse der SCEM Analyse (Grundmann, 2009) vorliegen

Some mathematical aspects of fuzzy systems

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion and additive inversion, are proposed. Based on these tools, the relationship among fuzzy vectors in fuzzy space is studied. Analytical expressions of maximum and mean solutions for FREs, and an optimal algorithm for calculating minimum solutions are developed. Second, the possibility of applying functional analysis theory to Takagi-Sugeno (T-S) fuzzy systems design is investigated. Fuzzy transforms, which are based on the generalised Fourier transform in functional analysis, are proposed. It is demonstrated that, mathematically, a T-S fuzzy model is equivalent to a fuzzy transform. Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function. The functional point of view leads to an insight into the behaviour of a fuzzy system. It provides a theoretical basis for exploring improvements to the efficiency of T-S fuzzy modelling. Third, the mathematical aspects of model-based fuzzy control (MBFC) are investigated. MBFC theory is not suitable for general nonlinear systems, due to an implicit linearity assumption. This assumption limits fuzzy controller design to a special case of linear time-varying systems control. To apply MBFC in general nonlinear control, a new stability criterion for general nonlinear fuzzy system is proposed. The mathematical aspects investigated in this research, provide a systematic guidance on issues such as efficient fuzzy systems modelling, balanced "soft" and "hard" computing in fuzzy system design, and applicability of fuzzy control to general nonlinear systems. They serve as a theoretical basis for further development of fuzzy systems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Sistemas granulares evolutivos

Orientador: Fernando Antonio Campos GomideTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente tem-se observado um crescente interesse em abordagens de modelagem computacional para lidar com fluxos de dados do mundo real. Métodos e algoritmos têm sido propostos para obtenção de conhecimento a partir de conjuntos de dados muito grandes e, a princípio, sem valor aparente. Este trabalho apresenta uma plataforma computacional para modelagem granular evolutiva de fluxos de dados incertos. Sistemas granulares evolutivos abrangem uma variedade de abordagens para modelagem on-line inspiradas na forma com que os humanos lidam com a complexidade. Esses sistemas exploram o fluxo de informação em ambiente dinâmico e extrai disso modelos que podem ser linguisticamente entendidos. Particularmente, a granulação da informação é uma técnica natural para dispensar atenção a detalhes desnecessários e enfatizar transparência, interpretabilidade e escalabilidade de sistemas de informação. Dados incertos (granulares) surgem a partir de percepções ou descrições imprecisas do valor de uma variável. De maneira geral, vários fatores podem afetar a escolha da representação dos dados tal que o objeto representativo reflita o significado do conceito que ele está sendo usado para representar. Neste trabalho são considerados dados numéricos, intervalares e fuzzy; e modelos intervalares, fuzzy e neuro-fuzzy. A aprendizagem de sistemas granulares é baseada em algoritmos incrementais que constroem a estrutura do modelo sem conhecimento anterior sobre o processo e adapta os parâmetros do modelo sempre que necessário. Este paradigma de aprendizagem é particularmente importante uma vez que ele evita a reconstrução e o retreinamento do modelo quando o ambiente muda. Exemplos de aplicação em classificação, aproximação de função, predição de séries temporais e controle usando dados sintéticos e reais ilustram a utilidade das abordagens de modelagem granular propostas. O comportamento de fluxos de dados não-estacionários com mudanças graduais e abruptas de regime é também analisado dentro do paradigma de computação granular evolutiva. Realçamos o papel da computação intervalar, fuzzy e neuro-fuzzy em processar dados incertos e prover soluções aproximadas de alta qualidade e sumário de regras de conjuntos de dados de entrada e saída. As abordagens e o paradigma introduzidos constituem uma extensão natural de sistemas inteligentes evolutivos para processamento de dados numéricos a sistemas granulares evolutivos para processamento de dados granularesAbstract: In recent years there has been increasing interest in computational modeling approaches to deal with real-world data streams. Methods and algorithms have been proposed to uncover meaningful knowledge from very large (often unbounded) data sets in principle with no apparent value. This thesis introduces a framework for evolving granular modeling of uncertain data streams. Evolving granular systems comprise an array of online modeling approaches inspired by the way in which humans deal with complexity. These systems explore the information flow in dynamic environments and derive from it models that can be linguistically understood. Particularly, information granulation is a natural technique to dispense unnecessary details and emphasize transparency, interpretability and scalability of information systems. Uncertain (granular) data arise from imprecise perception or description of the value of a variable. Broadly stated, various factors can affect one's choice of data representation such that the representing object conveys the meaning of the concept it is being used to represent. Of particular concern to this work are numerical, interval, and fuzzy types of granular data; and interval, fuzzy, and neurofuzzy modeling frameworks. Learning in evolving granular systems is based on incremental algorithms that build model structure from scratch on a per-sample basis and adapt model parameters whenever necessary. This learning paradigm is meaningful once it avoids redesigning and retraining models all along if the system changes. Application examples in classification, function approximation, time-series prediction and control using real and synthetic data illustrate the usefulness of the granular approaches and framework proposed. The behavior of nonstationary data streams with gradual and abrupt regime shifts is also analyzed in the realm of evolving granular computing. We shed light upon the role of interval, fuzzy, and neurofuzzy computing in processing uncertain data and providing high-quality approximate solutions and rule summary of input-output data sets. The approaches and framework introduced constitute a natural extension of evolving intelligent systems over numeric data streams to evolving granular systems over granular data streamsDoutoradoAutomaçãoDoutor em Engenharia Elétric