Fuzzy classifiers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scientific and business applications. Fuzzy classifiers use fuzzy rules and do not require assumptions common to statistical classification. Rough set theory is useful when data sets are incomplete. It defines a formal approximation of crisp sets by providing the lower and the upper approximation of the original set. Systems based on rough sets have natural ability to work on such data and incomplete vectors do not have to be preprocessed before classification. To achieve better performance than existing machine learning systems, fuzzy classifiers and rough sets can be combined in ensembles. Such ensembles consist of a finite set of learning models, usually weak learners. The present book discusses the three aforementioned fields - fuzzy systems, rough sets and ensemble techniques. As the trained ensemble should represent a single hypothesis, a lot of attention is placed on the possibility to combine fuzzy rules from fuzzy systems being members of classification ensemble. Furthermore, an emphasis is placed on ensembles that can work on incomplete data, thanks to rough set theory. .

This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors' past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.

This book is the second enlarged and revised edition of the first successful monograph on complex-valued neural networks (CVNNs) published in 2006, which lends itself to graduate and undergraduate courses in electrical engineering, informatics, control engineering, mechanics, robotics, bioengineering, and other relevant fields.

In the second edition the recent trends in CVNNs research are included, resulting in e.g. almost a doubled number of references. The parametron invented in 1954 is also referred to with discussion on analogy and disparity. Also various additional arguments on the advantages of the complex-valued neural networks enhancing the difference to real-valued neural networks are given in various sections.

The book is useful for those beginning their studies, for instance, in adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, robotics inspired by human neural systems, and brain-like information processing, as well as interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas.

The book is useful for those beginning their studies, for instance, in adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, robotics inspired by human neural systems, and brain-like information processing, as well as interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas.

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The purpose of this book is to present an up to date account of fuzzy ideals of a semiring. The book concentrates on theoretical aspects and consists of eleven chapters including three invited chapters. Among the invited chapters, two are devoted to applications of Semirings to automata theory, and one deals with some generalizations of Semirings. This volume may serve as a useful hand book for graduate students and researchers in the areas of Mathematics and Theoretical Computer Science.

This book constitutes the refereed proceedings of the 8th International Conference on Neural Networks and Artificial Intelligence, ICNNAI 2014, held in Brest, Belarus, in June 2014. The 19 revised full papers presented were carefully reviewed and selected from 27 submissions. The papers are organized in topical sections on forest resource management; artificial intelligence by neural networks; optimization; classification; fuzzy approach; machine intelligence; analytical approach; mobile robot; real world application.

This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.

This volume presents examples of how ANNs are applied in biological sciences and related areas. Chapters focus on the analysis of intracellular sorting information, prediction of the behavior of bacterial communities, biometric authentication, studies of Tuberculosis, gene signatures in breast cancer classification, use of mass spectrometry in metabolite identification, visual navigation, and computer diagnosis. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, application details for both the expert and non-expert reader, and tips on troubleshooting and avoiding known pitfalls. Authoritative and practical, Artificial Neural Networks: Second Edition aids scientists in continuing to study Artificial Neural Networks (ANNs).

Frontiers of Higher Order Fuzzy Sets, provides a unified representation theorem for higher order fuzzy sets. The book elaborates on the concept of gradual elements and their integration with the higher order fuzzy sets. This book also is devoted to the introduction of new frameworks based on general T2FSs, IT2FSs, Gradual elements, Shadowed sets and rough sets. Such new frameworks will provide more capable frameworks for real applications. Applications of higher order fuzzy sets in various fields will be discussed. In particular, the properties and characteristics of the new proposed frameworks would be studied. Such frameworks that are the result of the integration of general T2FSs, IT2FSs, gradual elements, shadowed sets and rough sets will be shown to be suitable to be applied in the fields of bioinformatics, business, management, ambient intelligence, medicine, cloud computing and smart grids.

This book deals with the theory, design principles, and application of hybrid intelligent systems using type-2 fuzzy sets in combination with other paradigms of Soft Computing technology such as Neuro-Computing and Evolutionary Computing. It provides a self-contained exposition of the foundation of type-2 fuzzy neural networks and presents a vast compendium of its applications to control, forecasting, decision making, system identification and other real problems. Type-2 Fuzzy Neural Networks and Their Applications is helpful for teachers and students of universities and colleges, for scientists and practitioners from various fields such as control, decision analysis, pattern recognition and similar fields.

The book reports on the latest theories on artificial neural networks, with a special emphasis on bio-neuroinformatics methods. It includes twenty-three papers selected from among the best contributions on bio-neuroinformatics-related issues, which were presented at the International Conference on Artificial Neural Networks, held in Sofia, Bulgaria, on September 10-13, 2013 (ICANN 2013). The book covers a broad range of topics concerning the theory and applications of artificial neural networks, including recurrent neural networks, super-Turing computation and reservoir computing, double-layer vector perceptrons, nonnegative matrix factorization, bio-inspired models of cell communities, Gestalt laws, embodied theory of language understanding, saccadic gaze shifts and memory formation, and new training algorithms for Deep Boltzmann Machines, as well as dynamic neural networks and kernel machines. It also reports on new approaches to reinforcement learning, optimal control of discrete time-delay systems, new algorithms for prototype selection, and group structure discovering. Moreover, the book discusses one-class support vector machines for pattern recognition, handwritten digit recognition, time series forecasting and classification, and anomaly identification in data analytics and automated data analysis. By presenting the state-of-the-art and discussing the current challenges in the fields of artificial neural networks, bioinformatics and neuroinformatics, the book is intended to promote the implementation of new methods and improvement of existing ones, and to support advanced students, researchers and professionals in their daily efforts to identify, understand and solve a number of open questions in these fields.

The three volume set LNCS 8226, LNCS 8227 and LNCS 8228 constitutes the proceedings of the 20th International Conference on Neural Information Processing, ICONIP 2013, held in Daegu, Korea, in November 2013. The 180 full and 75 poster papers presented together with 4 extended abstracts were carefully reviewed and selected from numerous submissions. These papers cover all major topics of theoretical research, empirical study and applications of neural information processing research. The specific topics covered are as follows: cognitive science and artificial intelligence; learning theory, algorithms and architectures; computational neuroscience and brain imaging; vision, speech and signal processing; control, robotics and hardware technologies and novel approaches and applications.

It's time to dispel the myth that machine learning is difficult. Grokking Machine Learning teaches you how to apply ML to your projects using only standard Python code and high school-level math. No specialist knowledge is required to tackle the hands-on exercises using readily available machine learning tools! In Grokking Machine Learning, expert machine learning engineer Luis Serrano introduces the most valuable ML techniques and teaches you how to make them work for you. Practical examples illustrate each new concept to ensure you're grokking as you go. You'll build models for spam detection, language analysis, and image recognition as you lock in each carefully-selected skill. Packed with easy-to-follow Python-based exercises and mini-projects, this book sets you on the path to becoming a machine learning expert. Key Features * Different types of machine learning, including supervised and unsupervised learning * Algorithms for simplifying, classifying, and splitting data * Machine learning packages and tools * Hands-on exercises with fully-explained Python code samples For readers with intermediate programming knowledge in Python or a similar language. About the technology Machine learning is a collection of mathematically-based techniques and algorithms that enable computers to identify patterns and generate predictions from data. This revolutionary data analysis approach is behind everything from recommendation systems to self-driving cars, and is transforming industries from finance to art. Luis G. Serrano has worked as the Head of Content for Artificial Intelligence at Udacity and as a Machine Learning Engineer at Google, where he worked on the YouTube recommendations system. He holds a PhD in mathematics from the University of Michigan, a Bachelor and Masters from the University of Waterloo, and worked as a postdoctoral researcher at the University of Quebec at Montreal. He shares his machine learning expertise on a YouTube channel with over 2 million views and 35 thousand subscribers, and is a frequent speaker at artificial intelligence and data science conferences.

The pursuit of artificial intelligence has been a highly active domain of research for decades, yielding exciting scientific insights and productive new technologies. In terms of generating intelligence, however, this pursuit has yielded only limited success. This book explores the hypothesis that adaptive growth is a means of moving forward. By emulating the biological process of development, we can incorporate desirable characteristics of natural neural systems into engineered designs and thus move closer towards the creation of brain-like systems. The particular focus is on how to design artificial neural networks for engineering tasks.

The book consists of contributions from 18 researchers, ranging from detailed reviews of recent domains by senior scientists, to exciting new contributions representing the state of the art in machine learning research. The book begins with broad overviews of artificial neurogenesis and bio-inspired machine learning, suitable both as an introduction to the domains and as a reference for experts. Several contributions provide perspectives and future hypotheses on recent highly successful trains of research, including deep learning, the Hyper NEAT model of developmental neural network design, and a simulation of the visual cortex. Other contributions cover recent advances in the design of bio-inspired artificial neural networks, including the creation of machines for classification, the behavioural control of virtual agents, the design of virtual multi-component robots and morphologies and the creation of flexible intelligence. Throughout, the contributors share their vast expertise on the means and benefits of creating brain-like machines.

This book is appropriate for advanced students and practitioners of artificial intelligence and machine learning.

This monograph puts the reader in touch with a decade s worth of new developments in the field of fuzzy control specifically those of the popular Takagi Sugeno (T S) type. New techniques for stabilizing control analysis and design of arebased on multiple Lyapunov functions and linear matrix inequalities (LMIs). All the results are illustrated with numerical examples and figures and a rich bibliography is provided for further investigation.
Control saturations are taken into account within the fuzzy model. The concept of positive invariance is used to obtain sufficient conditions of asymptotic stability for the global fuzzy system with constrained control inside a subset of the state space.
The authors also consider the non-negativity of the states. This is of practical importance in many chemical, physical and biological processes that involve quantities that have intrinsically constant and non-negative sign: concentration of substances, level of liquids, etc. Results for linear systems are then extended to systems with delay. It is shown that LMI techniques can usually only handle the new constraint of non-negativity of the states when care is taken to use an adequate Lyapunov function. From these foundations, the following further problems are also treated: asymptotic stabilization of uncertain T-S fuzzy systems with time-varying delay, focusing on delay-dependent stabilization synthesis based on parallel distribution control;asymptotic stabilization of uncertain T-S fuzzy systems with multiple delays, focusing on delay-dependent stabilization synthesis based on parallel distribution control with results obtained under linear programming;design of delay-independent, observer-based, H-infinity control for T S fuzzy systems with time varying delay; andasymptotic stabilization of 2-d T S fuzzy systems.

"Advanced Takagi Sugeno Fuzzy Systems "provides researchers and graduate students interested in fuzzy control systems with further reliable means for maintaining stability and performance even when a sensor and/or actuator malfunctions."

The word consensus has been frequently used for centuries, perhaps millenia. People have always deemed it important that decisions having a long lasting impact on groups, countries or even civilizations be arrived at in a consensual manner. Undoubtedly the complexity of modern world in all its social, technological, economic and cultural dimensions has created new environments where consensus is regarded desirable. Consensus typically denotes a state of agreement prevailing in a group of agents, human or software. In the strict sense of the term, consensus means that the agreement be unanimous. Since such a state is often unreachable or even unnecessary, other less demanding consensus-related notions have been introduced. These typically involve some graded, partial or imprecise concepts. The contributions to this volume define and utilize such less demanding - and thus at the same time more general - notions of consensus. However, consensus can also refer to a process whereby the state of agreement is reached. Again this state can be something less stringent than a complete unanimity of all agents regarding all options. The process may involve modifications, resolutions and /or mitigations of the views or inputs of individuals or software agents in order to achieve the state of consensus understood in the more general sense. The consensus reaching processes call for some soft computational approaches, methods and techniques, notably fuzzy and possibilistic ones. These are needed to accommodate the imprecision in the very meaning of some basic concepts utilized in the definition of consensus as a state of agreement and as a process whereby this state is to be reached. The overall aim of this volume is to provide a comprehensive overview and analysis of the issues related to consensus states and consensual processes.

Flexible Neuro-Fuzzy Systems is the first professional literature about the new class of powerful, flexible fuzzy systems. The author incorporates various flexibility parameters to the construction of neuro-fuzzy systems. This approach dramatically improves their performance, allowing the systems to perfectly represent the pattern encoded in data. Flexible Neuro-Fuzzy Systems is the only book that proposes a flexible approach to fuzzy modeling and fills the gap in existing literature. This book introduces new fuzzy systems which outperform previous approaches to system modeling and classification, and has the following features: -Provides a framework for unification, construction and development of neuro-fuzzy systems; -Presents complete algorithms in a systematic and structured fashion, facilitating understanding and implementation, -Covers not only advanced topics but also fundamentals of fuzzy sets, -Includes problems and exercises following each chapter, -Illustrates the results on a wide variety of simulations, -Provides tools for possible applications in business and economics, medicine and bioengineering, automatic control, robotics and civil engineering.

This book deals with expert evaluation models in the form of semantic spaces with completeness and orthogonality properties (complete orthogonal semantic spaces). Theoretical and practical studies of some researchers have shown that these spaces describe expert evaluations most adequately, and as a result they were often included in more sophisticated models of intellectual systems for decision making and data analysis. Methods for constructing expert evaluation models of characteristics, comparative analysis of these models, studies of structural composition of their sets and constructing of generalized models are described. Models to obtain rating points for objects and groups of objects with qualitative and quantitative characteristics are presented. A number of regression models combining elements of classical and fuzzy regressions are presented. All methods and models developed by the authors and described in the book are illustrated with examples from various fields of human activities. This book meant for scientists in the field of computer science, expert systems, artificial intelligence and decision making; and also for engineers, post-graduate students and students who study the fuzzy set theory and its applications.

The three volume set LNCS 8226, LNCS 8227, and LNCS 8228 constitutes the proceedings of the 20th International Conference on Neural Information Processing, ICONIP 2013, held in Daegu, Korea, in November 2013. The 180 full and 75 poster papers presented together with 4 extended abstracts were carefully reviewed and selected from numerous submissions. These papers cover all major topics of theoretical research, empirical study and applications of neural information processing research. The specific topics covered are as follows: cognitive science and artificial intelligence; learning theory, algorithms and architectures; computational neuroscience and brain imaging; vision, speech and signal processing; control, robotics and hardware technologies and novel approaches and applications.

The book constitutes the refereed proceedings of the 11th International Conference on Adaptive and Natural Computing Algorithms, ICANNGA 2013, held in Lausanne, Switzerland, in April 2013. The 51 revised full papers presented were carefully reviewed and selected from a total of 91 submissions. The papers are organized in topical sections on neural networks, evolutionary computation, soft computing, bioinformatics and computational biology, advanced computing, and applications.

The intensity of global competition and ever-increasing economic uncertainties has led organizations to search for more efficient and effective ways to manage their business operations. Data envelopment analysis (DEA) has been widely used as a conceptually simple yet powerful tool for evaluating organizational productivity and performance. Fuzzy DEA (FDEA) is a promising extension of the conventional DEA proposed for dealing with imprecise and ambiguous data in performance measurement problems. This book is the first volume in the literature to present the state-of-the-art developments and applications of FDEA. It is designed for students, educators, researchers, consultants and practicing managers in business, industry, and government with a basic understanding of the DEA and fuzzy logic concepts.

The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to using the intuitionistic fuzzy set expressed with membership and non-membership functions. This book is addressed to all those involved in theoretical research and practical applications from a variety of fields/disciplines: decision science, game theory, management science, fuzzy sets, operational research, applied mathematics, systems engineering, industrial engineering, economics, etc.

The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. Ideas for future research and explorations are also provided. Students and researchers in computer science and mathematics will benefit from this work.

This book goes to great depth concerning the fast growing topic of technologies and approaches of fuzzy logic in the Semantic Web. The topics of this book include fuzzy description logics and fuzzy ontologies, queries of fuzzy description logics and fuzzy ontology knowledge bases, extraction of fuzzy description logics and ontologies from fuzzy data models, storage of fuzzy ontology knowledge bases in fuzzy databases, fuzzy Semantic Web ontology mapping, and fuzzy rules and their interchange in the Semantic Web. The book aims to provide a single record of current research in the fuzzy knowledge representation and reasoning for the Semantic Web. The objective of the book is to provide the state of the art information to researchers, practitioners and graduate students of the Web intelligence and at the same time serve the knowledge and data engineering professional faced with non-traditional applications that make the application of conventional approaches difficult or impossible.

This book offers an in-depth and comprehensive introduction to the priority methods of intuitionistic preference relations, the consistency and consensus improving procedures for intuitionistic preference relations, the approaches to group decision making based on intuitionistic preference relations, the approaches and models for interactive decision making with intuitionistic fuzzy information, and the extended results in interval-valued intuitionistic fuzzy environments.

Approximate reasoning is a key motivation in fuzzy sets and possibility theory. This volume provides a coherent view of this field, and its impact on database research and information retrieval. First, the semantic foundations of approximate reasoning are presented. Special emphasis is given to the representation of fuzzy rules and specialized types of approximate reasoning. Then syntactic aspects of approximate reasoning are surveyed and the algebraic underpinnings of fuzzy consequence relations are presented and explained. The second part of the book is devoted to inductive and neuro-fuzzy methods for learning fuzzy rules. It also contains new material on the application of possibility theory to data fusion. The last part of the book surveys the growing literature on fuzzy information systems. Each chapter contains extensive bibliographical material. Fuzzy Sets in Approximate Reasoning and Information Systems is a major source of information for research scholars and graduate students in computer science and artificial intelligence, interested in human information processing.