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Fuzzy Decision Analysis: Multi Attribute Decision Making Approach (Studies in Computational Intelligence #1121)
by Farhad Hosseinzadeh Lotfi Somayeh Razipour GhalehJough Tofigh Allahviranloo Witold Pedrycz Mohammadreza Shahriari Hamid SharafiAuthored by a leading expert in the field, this book introduces an innovative methodology that harnesses the power of fuzzy logic to enhance decision-making in multi-attribute scenarios. In a world of complexity and uncertainty, effective decision-making is paramount. Springer proudly presents a cutting-edge publication that revolutionizes decision analysis: "Fuzzy Decision Analysis: Multi-attribute Decision-Making Approach." This book stands at the forefront of decision analysis, introducing the integration of fuzzy logic into multi-attribute decision-making. It is a transformative journey into the realm of advanced decision analysis. It book not only equips you with the knowledge to comprehend the theoretical underpinnings but also empowers you to apply these insights in practical scenarios. This book serves as your indispensable companion. Its comprehensive coverage serves as a beacon, guiding you through the intricate maze of fuzzy logic and multi-attribute decision-making, ultimately empowering you to embrace innovation and master the art of making well-informed decisions in an ever-changing world.
Fuzzy Graph Theory with Applications to Human Trafficking (Studies in Fuzziness and Soft Computing #365)
by Davender S. Malik Sunil Mathew John N. MordesonThis book reports on advanced concepts in fuzzy graph theory, showing a set of tools that can be successfully applied to understanding and modeling illegal human trafficking. Building on the previous book on fuzzy graph by the same authors, which set the fundamentals for readers to understand this developing field of research, this second book gives a special emphasis to applications of the theory. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs, the concept of independence and domination in fuzzy graphs, as well as directed fuzzy networks, incidence graphs and many more.
Fuzzy Hierarchical Model for Risk Assessment
by Xiaojun Wang Hing Kai ChanRisk management is often complicated by situational uncertainties and the subjective preferences of decision makers. Fuzzy Hierarchical Model for Risk Assessment introduces a fuzzy-based hierarchical approach to solve risk management problems considering both qualitative and quantitative criteria to tackle imprecise information. This approach is illustrated through number of case studies using examples from the food, fashion and electronics sectors to cover a range of applications including supply chain management, green product design and green initiatives. These practical examples explore how this method can be adapted and fine tuned to fit other industries as well. Supported by an extensive literature review, Fuzzy Hierarchical Model for Risk Assessment comprehensively introduces a new method for project managers across all industries as well as researchers in risk management. this area.
Fuzzy Humanist: Trilogie Teil III: Von der Fuzzy-Logik zum Computing with Words (essentials)
by Edy PortmannAuch mit Worten, Phrasen, Präpositionen, Fragen sowie anderen semantischen Einheiten der natürlichen Sprache ist es möglich, zu rechnen. Daher ist diese Methode für einen Einsatz im Sinne des Humanismus prädestiniert. Edy Portmann erläutert den Zusammenhang von Fuzzy-Logik und dem Rechnen mit Worten und zeigt daran den Unterschied zwischen heutigen Suchmaschinen sowie zukünftigen Frage-Antwort-Systemen auf. Er legt dar, wie das Rechnen mit Worten als Grundlage einer Mensch-Maschine-Symbiose dient, die in kollektiver (urbaner) Intelligenz mündet. Als Ausblick weist der Autor darauf hin, wie Computing with Words zur Schaffung von kollektiver Intelligenz beitragen kann.Der Autor:Prof. Dr. Edy Portmann ist Swiss Post Professor of Computer Science am Human-IST Institut der Universität Fribourg, Schweiz. In seiner Forschung beschäftigt er sich mit Fragen rund um Informationssysteme, -verarbeitung und -beschaffung.
Fuzzy Hypergraphs and Related Extensions (Studies in Fuzziness and Soft Computing #390)
by Muhammad Akram Anam LuqmanThis book presents the fundamental and technical concepts of fuzzy hypergraphs and explains their extensions and applications. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, m-polar fuzzy, Pythagorean, complex Pythagorean, and q-rung orthopair hypergraphs, as well as single-valued neutrosophic, complex neutrosophic and bipolar neutrosophic hypergraphs. In addition, the book also sheds light on real-world applications of these hypergraphs, making it a valuable resource for students and researchers in the field of mathematics, as well as computer and social scientists.
Fuzzy Information and Engineering-2019 (Advances in Intelligent Systems and Computing #1094)
by Bing-Yuan CaoThis book includes 70 selected papers from the Ninth International Conference on Fuzzy Information and Engineering (ICFIE) Satellite, which was held on December 26–30, 2018; and from the 9th International Conference on Fuzzy Information and Engineering (ICFIAE), which was held on February 13–15, 2019. The two conferences presented the latest research in the areas of fuzzy information and engineering, operational research and management, and their applications.
Fuzzy Information & Engineering and Operations Research & Management
by Bing-Yuan Cao Hadi NasseriFuzzy Information & Engineering and Operations Research & Management is the monograph from submissions by the 6th International Conference on Fuzzy Information and Engineering (ICFIE2012, Iran) and by the 6th academic conference from Fuzzy Information Engineering Branch of Operation Research Society of China (FIEBORSC2012, Shenzhen,China). It is published by Advances in Intelligent and Soft Computing (AISC). We have received more than 300 submissions. Each paper of it has undergone a rigorous review process. Only high-quality papers are included in it containing papers as follows: I Programming and Optimization. II Lattice and Measures. III Algebras and Equation. IV Forecasting, Clustering and Recognition. V Systems and Algorithm. VI Graph and Network. VII Others.
Fuzzy Information Processing: 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Fortaleza, Brazil, July 4-6, 2018, Proceedings (Communications in Computer and Information Science #831)
by Guilherme A. Barreto Ricardo CoelhoThis book constitutes the thoroughly refereed proceedings of the 37th IFSA Conference, NAFIPS 2018, held in Fortaleza, Brazil, in July 2018. The 55 full papers presented were carefully reviewed and selected from 73 submissions. The papers deal with a large spectrum of topics, including theory and applications of fuzzy numbers and sets, fuzzy logic, fuzzy inference systems, fuzzy clustering, fuzzy pattern classification, neuro-fuzzy systems, fuzzy control systems, fuzzy modeling, fuzzy mathematical morphology, fuzzy dynamical systems, time series forecasting, and making decision under uncertainty.
Fuzzy Information Processing 2020: Proceedings of the 2020 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2020 (Advances in Intelligent Systems and Computing #1337)
by Vladik Kreinovich Barnabás Bede Martine Ceberio Martine De CockThis book describes how to use expert knowledge—which is often formulated by using imprecise (fuzzy) words from a natural language. In the 1960s, Zadeh designed special "fuzzy" techniques for such use. In the 1980s, fuzzy techniques started controlling trains, elevators, video cameras, rice cookers, car transmissions, etc. Now, combining fuzzy with neural, genetic, and other intelligent methods leads to new state-of-the-art results: in aerospace industry (from drones to space flights), in mobile robotics, in finances (predicting the value of crypto-currencies), and even in law enforcement (detecting counterfeit banknotes, detecting online child predators and in creating explainable AI systems). The book describes these (and other) applications—as well as foundations and logistics of fuzzy techniques. This book can be recommended to specialists—both in fuzzy and in various application areas—who will learn latest techniques and their applications, and to students interested in innovative ideas.
Fuzzy Information Processing 2023 (Lecture Notes in Networks and Systems #751)
by Kelly Cohen Nicholas Ernest Barnabas Bede Vladik KreinovichThis book is an overview of latest successes and applications of fuzzy techniques—techniques that use expert knowledge formulated by natural-language words like "small". Engineering applications deal with aerospace (control of spacecrafts and unmanned aerial vehicles, air traffic control, airport passenger flow predictions), materials (designing gold nano-structures for medicine, catalysis, and sensors), and robot navigation and manipulation. Other application areas include cosmology, demographics, finances, wine production, medicine (diagnostics, epidemics control), and predicting human behavior. In many cases, fuzzy techniques are combined with machine learning AI. Due to natural-language origin of fuzzy techniques, such combination adds explainability (X) to AI. This book is recommended to students and practitioners interested in the state-of-the-art fuzzy-related XAI and to researchers willing to take on numerous remaining challenges.
Fuzzy Intelligent Systems: Methodologies, Techniques, and Applications (Artificial Intelligence and Soft Computing for Industrial Transformation)
by E. Chandrasekaran R. Anandan G. Suseendran S. Balamurugan Hanaa HachimiFuzzy Intelligent Systems: Methodologies, Techniques and Applications comprises state-of-the-art chapters detailing how expert systems are built and the fuzzy logic resembling human reasoning powering them. Hybrid and neuro-fuzzy intelligent systems are discussed along with Evolutionary and, in particular, Genetic Algorithms. This approach has been extended by using Multiobjective Evolutionary Algorithms, which can consider multiple conflicting objectives instead of a single one. The book also discusses the hybridization between Multiobjective Evolutionary Algorithms and Fuzzy Systems which is known as Multiobjective Evolutionary Fuzzy Systems.
Fuzzy Leadership: Trilogie Teil I: Von den Wurzeln der Fuzzy-Logik bis zur smarten Gesellschaft (essentials)
by Edy Portmann Andreas MeierDie unscharfe Logik (Fuzzy Logic) erweitert die klassische Logik, indem neben den beiden Wahrheitswerten 1 für ‚wahr’ und 0 für ‚falsch’ alle Werte des Einheitsintervalls zugelassen sind. Die unscharfe Logik entspricht der menschlichen Wahrnehmung, da sie unsichere Sachverhalte oder vage Aussagen in einem Entscheidungsprozess mitberücksichtigt. Edy Portmann und Andreas Meier geben in diesem essential über Fuzzy Leadership einen Überblick zu Grundlagen der unscharfen Logik und zeigen das Potenzial in unterschiedlichen Anwendungen der digitalen Wirtschaft sowie in der Informations- und Wissensgesellschaft auf. Die Autoren:Prof. Dr. Edy Portmann ist Swiss Post Professor of Computer Science am Human-IST Institut der Universität Fribourg, Schweiz. In seiner Forschung beschäftigt er sich mit Fragen rund um Informationssysteme, -verarbeitung und -beschaffung. Prof. Dr. Andreas Meier leitete in den Jahren 1999 bis 2018 den Lehrstuhl für Wirtschaftsinformatik an der Universität Fribourg, Schweiz. Seine Forschungsgebiete waren eBusiness, eGovernment und Informationsmanagement.
Fuzzy Learning and Applications (International Series on Computational Intelligence)
by Marco RussoWith low computational complexity and relatively short development time, Fuzzy Logic is an indispensable tool for engineering applications. The field is growing at an unprecedented rate, and there is a need for a book that describes essential tools, applications, examples, and perspectives in the field of fuzzy learning. The editors of Fuzzy Learni
Fuzzy Linear Programming: Solution Techniques and Applications (Studies in Fuzziness and Soft Computing #379)
by Seyed Hadi Nasseri Ali Ebrahimnejad Bing-Yuan CaoThis book presents the necessary and essential backgrounds of fuzzy set theory and linear programming, particularly a broad range of common Fuzzy Linear Programming (FLP) models and related, convenient solution techniques. These models and methods belong to three common classes of fuzzy linear programming, namely: (i) FLP problems in which all coefficients are fuzzy numbers, (ii) FLP problems in which the right-hand-side vectors and the decision variables are fuzzy numbers, and (iii) FLP problems in which the cost coefficients, the right-hand-side vectors and the decision variables are fuzzy numbers. The book essentially generalizes the well-known solution algorithms used in linear programming to the fuzzy environment. Accordingly, it can be used not only as a textbook, teaching material or reference book for undergraduate and graduate students in courses on applied mathematics, computer science, management science, industrial engineering, artificial intelligence, fuzzy information processes, and operations research, but can also serve as a reference book for researchers in these fields, especially those engaged in optimization and soft computing. For textbook purposes, it also includes simple and illustrative examples to help readers who are new to the field.
Fuzzy Logic: Recent Applications and Developments
by Jenny Carter Francisco Chiclana Arjab Singh Khuman Tianhua ChenSince its inception, fuzzy logic has attracted an incredible amount of interest, and this interest continues to grow at an exponential rate. As such, scientists, researchers, educators and practitioners of fuzzy logic continue to expand on the applicability of what and how fuzzy can be utilised in the real-world. In this book, the authors present key application areas where fuzzy has had significant success. The chapters cover a plethora of application domains, proving credence to the versatility and robustness of a fuzzy approach. A better understanding of fuzzy will ultimately allow for a better appreciation of fuzzy. This book provides the reader with a varied range of examples to illustrate what fuzzy logic can be capable of and how it can be applied. The text will be ideal for individuals new to the notion of fuzzy, as well as for early career academics who wish to further expand on their knowledge of fuzzy applications. The book is also suitable as a supporting text for advanced undergraduate and graduate-level modules on fuzzy logic, soft computing, and applications of AI.
Fuzzy Logic and Neural Networks for Hybrid Intelligent System Design (Studies in Computational Intelligence #1061)
by Oscar Castillo Patricia MelinThis book covers recent developments on fuzzy logic, neural networks and optimization algorithms, as well as their hybrid combinations. In addition, the above-mentioned methods are applied to areas such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction and optimization of complex problems. Nowadays, the main topic of the book is highly relevant, as most current intelligent systems and devices in use utilize some form of intelligent feature to enhance their performance. In addition, on the theoretical side, new and advanced models and algorithms of type-2 and type-3 fuzzy logic are presented, which are of great interest to researchers working on these areas. Also, new nature-inspired optimization algorithms and innovative neural models are put forward in the manuscript, which are very popular subjects, at this moment. There are contributions on theoretical aspects as well as applications, which make the book very appealing to a wide audience, ranging from researchers to professors and graduate students.
Fuzzy Logic and Soft Computing Applications
by Alfredo Petrosino Vincenzo Loia Witold PedryczThis book comprises a selection of papers from the IFSA 2007 World Congress on theoretical advances and applications of fuzzy logic and soft computing. These papers were selected from over 400 submissions and constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies. Soft Computing consists of several computing paradigms, including fuzzy logic, neural networks, genetic algorithms, and other techniques, which can be used to produce powerful intelligent systems for solving real-world problems. Applications range from pattern recognition to intelligent control and sow the advantages of using soft computing theory and methods. The papers of IFSA 2007 also make a contribution to this goal.
Fuzzy Logic and Technology, and Aggregation Operators: 13th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2023, and 12th International Summer School on Aggregation Operators, AGOP 2023, Palma de Mallorca, Spain, September 4–8, 2023, Proceedings (Lecture Notes in Computer Science #14069)
by Sebastia Massanet Susana Montes Daniel Ruiz-Aguilera Manuel González-HidalgoThis book constitutes the proceedings of the 13th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2023, and 12th International Summer School on Aggregation Operators, AGOP 2023, jointly held in Palma de Mallorca, Spain, during September 4–8, 2023. The 71 full papers presented in this book were carefully reviewed and selected from 161 submissions. The papers are divided into special sessions on: Interval uncertainty; information fusion techniques based on aggregation functions, preaggregation functions and their generalizations; evaluative linguistic expressions, generalized quantifiers and applications; neural networks under uncertainty and imperfect information; imprecision modeling and management in XAI systems; recent trends in mathematical fuzzy logics; fuzzy graph-based models: theory and application; new frontiers of computational intelligence for pervasive healthcare systems; fuzzy implication functions; and new challenges and ideas in statistical inference and data analysis.
Fuzzy Logic Augmentation of Nature-Inspired Optimization Metaheuristics
by Oscar Castillo Patricia MelinThis book describes recent advances on fuzzy logic augmentation of nature-inspired optimization metaheuristics and their application in areas such as intelligent control and robotics, pattern recognition, time series prediction and optimization of complex problems. The book is organized in two main parts, which contain a group of papers around a similar subject. The first part consists of papers with the main theme of theoretical aspects of fuzzy logic augmentation of nature-inspired optimization metaheuristics, which basically consists of papers that propose new optimization algorithms enhanced using fuzzy systems. The second part contains papers with the main theme of application of optimization algorithms, which are basically papers using nature-inspired techniques to achieve optimization of complex optimization problems in diverse areas of application.
Fuzzy Logic-Based Software Systems (Learning and Analytics in Intelligent Systems #34)
by Konstantina ChrysafiadiThis book aims to provide information about significant advances of Fuzzy Logic in software systems to researchers, scientists, educators, students, software engineers and developers. In particular, this book explains how Fuzzy Logic, can be used in software systems to automatically predict, model, decide, diagnose, recommend etc.. In more details, Fuzzy Logic is an artificial intelligent technique that is ideal for successfully addressing, , the uncertainty, imprecision and vagueness that exist in many diverse scientific and technological areas. It was introduced by Lotfi A. Zadeh of the University of California at Berkeley, as a methodology for computing with words. This ability of Fuzzy Logic allows the representation of imprecise and vague data in a more realistic way. Therefore, Fuzzy Logic-based systems can simulate the human reasoning and decision-making processes, addressing the human subjectivity. Fuzzy Logic-based software systems are referred to any software that concerns an automated program or process that is used in everyday life, like heating or air-conditioning system, or in the scientific world, like a medical diagnostic system, which uses Fuzzy Logic in order to perform reasoning. A Fuzzy Logic-based system consists of three basic modules: Fuzzifier, Inference Engine and Defuzzifier. The Fuzzifier accepts as input numerical data and assigns them to fuzzy sets with some degree of membership, converting crisp data to fuzzy sets. The Inference Engine applies fuzzy rules over the defined fuzzy sets and produces outputs based on linguistic information. The Defuzzifier, converts fuzzy values into crisp values. The use of Fuzzy Logic in software systems constitutes a compelling and active research area in recent years, especially due to the increased interest in artificial intelligence. In the view of the above, this book presents thoroughly the Fuzzy Logic theory and the structure and operation of a Fuzzy Logic-based system. It also explains the role of Fuzzy Logic in artificial intelligence and smart applications, presenting how it can improve the efficiency and effectiveness of automatic processes and tasks. Furthermore, the book describes techniques of artificial intelligence with which the fuzzy logic is combined and how. Furthermore, this book presents several Fuzzy Logic-based software systems in the discipline of medicine, education, decision making and recommendation, natural language processing, automotive engineering and industry, heating, ventilation and air-conditioning, navigation, scheduling, network traffic and security. Thereby, this book can provide deep insights and valuable information not only to readers of computer science-related disciplines, but also to readers, who come from a variety of disciplines and are interesting in systems that perform tasks related to their discipline, in a more efficient way.
Fuzzy Logic Hybrid Extensions of Neural and Optimization Algorithms: Theory and Applications (Studies in Computational Intelligence #940)
by Oscar Castillo Patricia MelinWe describe in this book, recent developments on fuzzy logic, neural networks and optimization algorithms, as well as their hybrid combinations, and their application in areas such as, intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction and optimization of complex problems. The book contains a collection of papers focused on hybrid intelligent systems based on soft computing. There are some papers with the main theme of type-1 and type-2 fuzzy logic, which basically consists of papers that propose new concepts and algorithms based on type-1 and type-2 fuzzy logic and their applications. There also some papers that presents theory and practice of meta-heuristics in different areas of application. Another group of papers describe diverse applications of fuzzy logic, neural networks and hybrid intelligent systems in medical applications. There are also some papers that present theory and practice of neural networks in different areas of application. In addition, there are papers that present theory and practice of optimization and evolutionary algorithms in different areas of application. Finally, there are some papers describing applications of fuzzy logic, neural networks and meta-heuristics in pattern recognition problems.
Fuzzy Machine Learning Algorithms for Remote Sensing Image Classification
by Anil Kumar A. Senthil Kumar Priyadarshi UpadhyayThis book covers the state-of-art image classification methods for discrimination of earth objects from remote sensing satellite data with an emphasis on fuzzy machine learning and deep learning algorithms. Both types of algorithms are described in such details that these can be implemented directly for thematic mapping of multiple-class or specific-class landcover from multispectral optical remote sensing data. These algorithms along with multi-date, multi-sensor remote sensing are capable to monitor specific stage (for e.g., phenology of growing crop) of a particular class also included. With these capabilities fuzzy machine learning algorithms have strong applications in areas like crop insurance, forest fire mapping, stubble burning, post disaster damage mapping etc. It also provides details about the temporal indices database using proposed Class Based Sensor Independent (CBSI) approach supported by practical examples. As well, this book addresses other related algorithms based on distance, kernel based as well as spatial information through Markov Random Field (MRF)/Local convolution methods to handle mixed pixels, non-linearity and noisy pixels. Further, this book covers about techniques for quantiative assessment of soft classified fraction outputs from soft classification and supported by in-house developed tool called sub-pixel multi-spectral image classifier (SMIC). It is aimed at graduate, postgraduate, research scholars and working professionals of different branches such as Geoinformation sciences, Geography, Electrical, Electronics and Computer Sciences etc., working in the fields of earth observation and satellite image processing. Learning algorithms discussed in this book may also be useful in other related fields, for example, in medical imaging. Overall, this book aims to: exclusive focus on using large range of fuzzy classification algorithms for remote sensing images; discuss ANN, CNN, RNN, and hybrid learning classifiers application on remote sensing images; describe sub-pixel multi-spectral image classifier tool (SMIC) to support discussed fuzzy and learning algorithms; explain how to assess soft classified outputs as fraction images using fuzzy error matrix (FERM) and its advance versions with FERM tool, Entropy, Correlation Coefficient, Root Mean Square Error and Receiver Operating Characteristic (ROC) methods and; combines explanation of the algorithms with case studies and practical applications.
Fuzzy Management: A Fuzzy Grassroots Ontology For Online Reputation Management (essentials)
by Andreas Meier Edy PortmannAndreas Meier und Edy Portmann verwenden in diesem essential über Fuzzy Management die unscharfe Logik zur Lösung betriebswirtschaftlicher Probleme in der digitalen Wirtschaft. Die unscharfe Logik erweitert die klassische Logik mit den beiden Werten „wahr“ und „falsch“ und führt zu differenzierteren Beurteilungen. Neben Portfolio Management, Performance Measurement, Service Level Engineering und Reputationsmanagement wird die Business Intelligence mit weichen Faktoren angereichert, um den Entscheidungsprozess zu verbessern.
Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets
by Cengiz Kahraman İrem OtayThis book offers a comprehensive guide to the use of neutrosophic sets in multiple criteria decision making problems. It shows how neutrosophic sets, which have been developed as an extension of fuzzy and paraconsistent logic, can help in dealing with certain types of uncertainty that classical methods could not cope with. The chapters, written by well-known researchers, report on cutting-edge methodologies they have been developing and testing on a variety of engineering problems. The book is unique in its kind as it reports for the first time and in a comprehensive manner on the joint use of neutrosophic sets together with existing decision making methods to solve multi-criteria decision-making problems, as well as other engineering problems that are complex, hard to model and/or include incomplete and vague data. By providing new ideas, suggestions and directions for the solution of complex problems in engineering and decision making, it represents an excellent guide for researchers, lecturers and postgraduate students pursuing research on neutrosophic decision making, and more in general in the area of industrial and management engineering.
Fuzzy Neural Intelligent Systems: Mathematical Foundation and the Applications in Engineering
by Hongxing Li C.L. Philip Chen Han-Pang HuangAlthough fuzzy systems and neural networks are central to the field of soft computing, most research work has focused on the development of the theories, algorithms, and designs of systems for specific applications. There has been little theoretical support for fuzzy neural systems, especially their mathematical foundations. Fuzzy Neural Intelligent Systems fills this gap. It develops a mathematical basis for fuzzy neural networks, offers a better way of combining fuzzy logic systems with neural networks, and explores some of their engineering applications. Dividing their focus into three main areas of interest, the authors give a systematic, comprehensive treatment of the relevant concepts and modern practical applications:Fundamental concepts and theories for fuzzy systems and neural networks.Foundation for fuzzy neural networks and important related topicsCase examples for neuro-fuzzy systems, fuzzy systems, neural network systems, and fuzzy-neural systemsSuitable for self-study, as a reference, and ideal as a textbook, Fuzzy Neural Intelligent Systems is accessible to students with a basic background in linear algebra and engineering mathematics. Mastering the material in this textbook will prepare students to better understand, design, and implement fuzzy neural systems, develop new applications, and further advance the field.