Nowadays, voluminous textbooks and monographs in fuzzy logic are devoted only to separate or some combination of separate facets of fuzzy logic. There is a lack of a single book that presents a comprehensive and self-contained theory of fuzzy logic and its applications.Written by world renowned authors, Lofti Zadeh, also known as the Father of Fuzzy Logic, and Rafik Aliev, who are pioneers in fuzzy logic and fuzzy sets, this unique compendium includes all the principal facets of fuzzy logic such as logical, fuzzy-set-theoretic, epistemic and relational. Theoretical problems are prominently illustrated and illuminated by numerous carefully worked-out and thought-through examples.This invaluable volume will be a useful reference guide for academics, practitioners, graduates and undergraduates in fuzzy logic and its applications.

A significant amount of effort in neural modeling is directed towards understanding the representation of information in various parts of the brain, such as cortical maps [6], and the paths along which sensory information is processed. Though the time domain is integral an integral aspect of the functioning of biological systems, it has proven very challenging to incorporate the time domain effectively in neural network models. A promising path that is being explored is to study the importance of synchronization in biological systems. Synchronization plays a critical role in the interactions between neurons in the brain, giving rise to perceptual phenomena, and explaining multiple effects such as visual contour integration, and the separation of superposed inputs. The purpose of this book is to provide a unified view of how the time domain can be effectively employed in neural network models. A first direction to consider is to deploy oscillators that model temporal firing patterns of a neuron or a group of neurons. There is a growing body of research on the use of oscillatory neural networks, and their ability to synchronize under the right conditions. Such networks of synchronizing elements have been shown to be effective in image processing and segmentation tasks, and also in solving the binding problem, which is of great significance in the field of neuroscience. The oscillatory neural models can be employed at multiple scales of abstraction, ranging from individual neurons, to groups of neurons using Wilson-Cowan modeling techniques and eventually to the behavior of entire brain regions as revealed in oscillations observed in EEG recordings. A second interesting direction to consider is to understand the effect of different neural network topologies on their ability to create the desired synchronization. A third direction of interest is the extraction of temporal signaling patterns from brain imaging data such as EEG and fMRI. Hence this Special Session is of emerging interest in the brain sciences, as imaging techniques are able to resolve sufficient temporal detail to provide an insight into how the time domain is deployed in cognitive function. The following broad topics will be covered in the book: Synchronization, phase-locking behavior, image processing, image segmentation, temporal pattern analysis, EEG analysis, fMRI analyis, network topology and synchronizability, cortical interactions involving synchronization, and oscillatory neural networks. This book will benefit readers interested in the topics of computational neuroscience, applying neural network models to understand brain function, extracting temporal information from brain imaging data, and emerging techniques for image segmentation using oscillatory networks

This excellent reference for all those involved in neural networks research and application presents, in a single text, the necessary aspects of parallel implementation for all major artificial neural network models. The book details implementations on varoius processor architectures (ring, torus, etc.) built on different hardware platforms, ranging from large general purpose parallel computers to custom built MIMD machines using transputers and DSPs.
Experts who performed the implementations author the chapters and research results are covered in each chapter. These results are divided into three parts.
Theoretical analysis of parallel implementation schemes on MIMD message passing machines.
Details of parallel implementation of BP neural networks on a general purpose, large, parallel computer.
Four chapters each describing a specific purpose parallel neural computer configuration.
This book is aimed at graduate students and researchers working in artificial neural networks and parallel computing. Graduate level educators can use it to illustrate the methods of parallel computing for ANN simulation. The text is an ideal reference providing lucid mathematical analyses for practitioners in the field.

This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.

This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.

This volume constitutes the proceedings of two collocated international conferences: EUSFLAT-2017 - the 10th edition of the flagship Conference of the European Society for Fuzzy Logic and Technology held in Warsaw, Poland, on September 11-15, 2017, and IWIFSGN'2017 - The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, held in Warsaw on September 13-15, 2017. The conferences were organized by the Systems Research Institute, Polish Academy of Sciences, Department IV of Engineering Sciences, Polish Academy of Sciences, and the Polish Operational and Systems Research Society in collaboration with the European Society for Fuzzy Logic and Technology (EUSFLAT), the Bulgarian Academy of Sciences and various European universities. The aim of the EUSFLAT-2017 was t o bring together theoreticians and practitioners working on fuzzy logic, fuzzy systems, soft computing and related areas and to provide a platform for exchanging ideas and discussing the latest trends and ideas, while the aim of IWIFSGN'2017 was to discuss new developments in extensions of the concept of a fuzzy set, such as an intuitionistic fuzzy set, as well as other concepts, like that of a generalized net. The papers included, written by leading international experts, as well as the special sessions and panel discussions contribute to the development the field, strengthen collaborations and intensify networking.

It is necessary to practice methodological doubt, like Descartes, in - der to loosen the hold of mental habits; and it is necessary to cultivate logical imagination, in order to have a number of hypotheses at c- mand, and not to be the slave of the one which common sense has r- dered easy to imagine. These two processes, of doubting the familiar and imagining the unfamiliar, are corrective, and form the chief part of the mental training required for a philosopher. Bertrand Russell At every stage and in all circumstances knowledge is incomplete and provisional, conditioned and limited by the historical circumstances under which it was acquired, including the means and methods used for gaining it and the historically conditioned assumptions and categories used in the formulation of ideas and conclusions. Maurice Cornforth This monograph is the second in the series of meta-theoretic analysis of fuzzy paradigm and its contribution and possible contribution to formal reasoning in order to free the knowledge production process from the ridge frame of the classical paradigm that makes its application to soft and inexact sciences d- ficult or irrelevant. The work in the previous monograph was strictly devoted to problems of theory of knowledge and critique of classical, bounded and other rationalities in decision-choice processes regarding the principles of verification, falsification or corroboration in knowledge production. This monograph deals mostly with epistemic decision-choice models and theories and how they are related to both the classical and fuzzy paradigms.

This book contains the articles from the international conference 11th Workshop on Self-Organizing Maps 2016 (WSOM 2016), held at Rice University in Houston, Texas, 6-8 January 2016. WSOM is a biennial international conference series starting with WSOM'97 in Helsinki, Finland, under the guidance and direction of Professor Tuevo Kohonen (Emeritus Professor, Academy of Finland). WSOM brings together the state-of-the-art theory and applications in Competitive Learning Neural Networks: SOMs, LVQs and related paradigms of unsupervised and supervised vector quantization.The current proceedings present the expert body of knowledge of 93 authors from 15 countries in 31 peer reviewed contributions. It includes papers and abstracts from the WSOM 2016 invited speakers representing leading researchers in the theory and real-world applications of Self-Organizing Maps and Learning Vector Quantization: Professor Marie Cottrell (Universite Paris 1 Pantheon Sorbonne, France), Professor Pablo Estevez (University of Chile and Millennium Instituteof Astrophysics, Chile), and Professor Risto Miikkulainen (University of Texas at Austin, USA). The book comprises a diverse set of theoretical works on Self-Organizing Maps, Neural Gas, Learning Vector Quantization and related topics, and an excellent variety of applications to data visualization, clustering, classification, language processing, robotic control, planning, and to the analysis of astronomical data, brain images, clinical data, time series, and agricultural data.

A comprehensive reference book for detailed explanations for every algorithm and techniques related to the transformers. 60+ transformer architectures covered in a comprehensive manner. A book for understanding how to apply the transformer techniques in speech, text, time series, and computer vision. Practical tips and tricks for each architecture and how to use it in the real world. Hands-on case studies and code snippets for theory and practical real-world analysis using the tools and libraries, all ready to run in Google Colab.

This book constitutes the refereed proceedings of the 16th International Conference on Engineering Applications of Neural Networks, EANN 2015, held in Rhodes, Greece, in September 2015. The 36 revised full papers presented together with the abstracts of three invited talks and two tutorials were carefully reviewed and selected from 84 submissions. The papers are organized in topical sections on industrial-engineering applications of ANN; bioinformatics; intelligent medical modeling; life-earth sciences intelligent modeling; learning-algorithms; intelligent telecommunications modeling; fuzzy modeling; robotics and control; smart cameras; pattern recognition-facial mapping; classification; financial intelligent modeling; echo state networks.

On the basis of fuzzy sets and some of their relevant generalizations, this book systematically presents the fundamental principles and applications of group decision making under different scenarios of preference relations. By using intuitionistic knowledge as the field of discourse, this work investigates by utilizing innovative research means the fundamental principles and methods of group decision making with various different intuitionistic preferences: Mathematical reasoning is employed to study the consistency of group decision making; Methods of fusing information are applied to look at the aggregation of multiple preferences; Techniques of soft computing and optimization are utilized to search for satisfactory decision alternatives. Each chapter follows the following structurally clear format of presentation: literature review, development of basic theory, verification and reasoning of principles , construction of models and computational schemes, and numerical examples, which cover such areas as technology, enterprise competitiveness, selection of airlines, experts decision making in weather-sensitive enterprises, etc. In terms of theoretical principles, this book can be used as a reference for researchers in the areas of management science, information science, systems engineering, operations research, and other relevant fields. It can also be employed as textbook for upper level undergraduate students and graduate students. In terms of applications, this book will be a good companion for all those decision makers in government, business, and technology areas.

In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering time as a source of fuzzy uncertainty in dynamic systems. It begins with a thorough introduction, where the general research domain, the problems, and ways of their solutions are discussed. The book then progresses systematically by first covering the theoretical aspects before tackling the applications. In the application section, a software library is described, which contains discrete EFDS identification methods elaborated during fundamental research of the book. Extremal Fuzzy Dynamic Systems will be of interest to theoreticians interested in modeling fuzzy processes, to researchers who use fuzzy statistics, as well as practitioners from different disciplines whose research interests include abnormal, extreme and monotone processes in nature and society. Graduate students could also find this book useful.

This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet. The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.

Micromechanical manufacturing based on microequipment creates new possibi- ties in goods production. If microequipment sizes are comparable to the sizes of the microdevices to be produced, it is possible to decrease the cost of production drastically. The main components of the production cost - material, energy, space consumption, equipment, and maintenance - decrease with the scaling down of equipment sizes. To obtain really inexpensive production, labor costs must be reduced to almost zero. For this purpose, fully automated microfactories will be developed. To create fully automated microfactories, we propose using arti?cial neural networks having different structures. The simplest perceptron-like neural network can be used at the lowest levels of microfactory control systems. Adaptive Critic Design, based on neural network models of the microfactory objects, can be used for manufacturing process optimization, while associative-projective neural n- works and networks like ART could be used for the highest levels of control systems. We have examined the performance of different neural networks in traditional image recognition tasks and in problems that appear in micromechanical manufacturing. We and our colleagues also have developed an approach to mic- equipment creation in the form of sequential generations. Each subsequent gene- tion must be of a smaller size than the previous ones and must be made by previous generations. Prototypes of ?rst-generation microequipment have been developed and assessed.

The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space is defective from the simple principles of acquaintances and the limitations of cognitive agents operating in the epistemological space. How then do we arrive and claim exactness in our knowledge-production system? The general conclusion of this book is that the conditions of the fuzzy paradigm with its laws of thought and mathematics present a methodological unity of exact and inexact sciences where every zone of thought has fuzzy covering.

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. .

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 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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This book includes results of the seventh International Conference on Fuzzy Information and Engineering (ICFIE'2014) and the 1st International Conference of Operations Research and Management (ICORM'2014) on November 7-11, 2014 in ZhuHai, China. The book, contains 35 selected high-quality papers, and is divided into five main parts: Part I focuses on ``Fuzzy Systems and Its Applications", Part II on ``Fuzzy Mathematics and Its Applications", Part III discusses ``Fuzzy Information and Computer", Part IV is devoted to ``Operations Research and Management and Its Applications" and Part V includes various other topics.

This volume collects a selection of contributions which has been presented at the 22nd Italian Workshop on Neural Networks, the yearly meeting of the Italian Society for Neural Networks (SIREN). The conference was held in Italy, Vietri sul Mare (Salerno), during May 17-19, 2012. The annual meeting of SIREN is sponsored by International Neural Network Society (INNS), European Neural Network Society (ENNS) and IEEE Computational Intelligence Society (CIS). The book - as well as the workshop- is organized in three main components, two special sessions and a group of regular sessions featuring different aspects and point of views of artificial neural networks and natural intelligence, also including applications of present compelling interest.

This book offers a systematic introduction to the clustering algorithms for intuitionistic fuzzy values, the latest research results in intuitionistic fuzzy aggregation techniques, the extended results in interval-valued intuitionistic fuzzy environments, and their applications in multi-attribute decision making, such as supply chain management, military system performance evaluation, project management, venture capital, information system selection, building materials classification, and operational plan assessment, etc.

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 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 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.

The three volume set LNCS 8834, LNCS 8835, and LNCS 8836 constitutes the proceedings of the 21st International Conference on Neural Information Processing, ICONIP 2014, held in Kuching, Malaysia, in November 2014. The 231 full papers presented were carefully reviewed and selected from 375 submissions. The selected papers cover major topics of theoretical research, empirical study, and applications of neural information processing research. The 3 volumes represent topical sections containing articles on cognitive science, neural networks and learning systems, theory and design, applications, kernel and statistical methods, evolutionary computation and hybrid intelligent systems, signal and image processing, and special sessions intelligent systems for supporting decision, making processes, theories and applications, cognitive robotics, and learning systems for social network and web mining.