An Essential Guide to Fuzzy Systems

Michael Gr. Voskoglou, PhD (Editor)
Professor Emeritus of Mathematical Sciences, Graduate Technological Educational Institute (T.E.I.) of Western Greece, School of Technological Applications, Patras, Greece

Series: Computational Mathematics and Analysis
BISAC: MAT018000

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The recent development of the fuzzy set theory has given scientists the opportunity to model under conditions which are vague or not precisely defined, thus succeeding to solve mathematically problems whose statements are expressed in our natural language. Since Zadeh introduced the concept of fuzzy set in 1965, many efforts have been made by specialists for improving its effectiveness to deal with uncertain, ambiguous and vague situations. As a result a series of extensions and generalizations of the ordinary fuzzy set followed and several theories have been proposed as alternatives to the fuzzy set theory. The spectre of applications of those theories has been rapidly expanded during the last years covering physical sciences, economics and management, expert systems like financial planners, diagnostic, meteorological, information-retrieval, control systems, etc, industry, robotics, decision making, programming, medicine, biology, humanities, education and almost all the other sectors of the human activity, including human reasoning itself.

The target of the present book is to become an essential guide to fuzzy sets and systems and to related theories. The whole book consists of ten chapters and a shorter commentary. It starts from the history and an introduction to fuzzy sets and logic and from a brief exposition of related theories. The management of the uncertainty in fuzzy environment as well as the evaluation of fuzzy data, frequently appearing nowadays in science and technology, are also studied. Assessment methods are presented using tools such as triangular fuzzy numbers, fuzzy relation equations and the grey system theory. An introduction to the theory of fuzzy graphs, a review of the hybrids of neural networks and fuzzy logic and an introduction to single valued neutrosophic numbers and the granular calculus of single valued neutrosophic functions are also contained among the topics of the book. More specialized topics include the controllability of non linear fuzzy fractional differential systems, the use of fuzzy probability and fuzzy possibility theory for integrating the voltage sag type detection of electrical networks, the presentation of an algorithm to highlight the importance of using statistical methods in pattern recognition, the study of the known from Physics Goursat problem for a fuzzy hyperbolic equation under the fractional Caputo g-derivative for fuzzy-valued multivariable functions an a hybrid fuzzy potential field method for the navigation of Sumo robots.

It is hoped that all the above information can provide a framework to the readers of the book that enables them to proceed to a deeper study of fuzzy systems and the related to them theories.
(Imprint: Nova)

Preface

Chapter 1. Fuzzy Sets, Grey System Theory and Computational Thinking
(Michael Gr. Voskoglou, Graduate Technological Educational Institute of Western Greece, Koukouli, Patras, Greece)

Chapter 2. Evaluation of Fuzzy Data and Fuzzy Relation Equations
(Michael Gr. Voskoglou, Graduate Technological Educational Institute of Western Greece, Koukouli, Patras, Greece)

Chapter 3. An Introduction to Fuzzy Graph Theory
(Madhumangal Pal, Department of Applied Mathematics with Oceanology and Computer Programming,
Vidyasagar University, Midnapore, India)

Chapter 4. Controllability of Fuzzy Fractional Stochastic Differential Systems
(P. Balasubramaniam and J. Priyadharsini, Department of Mathematics, Gandhigram Rural Institute, Gandhigram, Dindigul, Tamil Nadu, India)

Chapter 5. Deep Fuzzy Neural Network: An Evolving Perspective
(Amir Samadi and M. Foad Samadi, Department of Electrical Engineering, Center of Excellence on Soft Computing and Intelligent Information Processing, Ferdowsi University of Mashhad, Mashhad, Iran, and others)

Chapter 6. Fuzzy Possibility Theory-An Integration of Voltage Sag Type Detection and Its Impact on Equipment Behavior
(Rituparna Mitra, Arup Kumar Goswami and Prashant Kumar Tiwari, Electrical Engineering Department, National Institute of Technology Silchar, Assam, India)

Chapter 7. Feature Selection Using a Bhattacharyya Distance
(Iuliana-Florentina Iatan, Department of Mathematics and Computer Science, Technical University of Civil Engineering, Bucharest, Romania)

Chapter 8. Fuzzy Goursat Problems of Fractional Order with Generalized Hukuhara Derivatives
(Nguyen Thi Kim Son, Ha Thi Thanh Tam and Hoang Viet Long, Faculty of Natural Science, Hanoi Metropolitan University, Hanoi, Vietnam)

Chapter 9. A Foundation on Neutrosophic Calculus
(Nguyen Thi Kim Son, Nguyen Phuong Dong, Hoang Viet Long, Faculty of Natural Science, Hanoi Metropolitan University, Hanoi, Vietnam)

Chapter 10. Application of Hybrid Fuzzy Potential Field for Navigation of Sumo Robots
(Carlos Erlan Olival Lima, Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi, Aichi, Japan)

Chapter 11. Generalizations of Fuzzy Sets and Relative Theories
(Michael Gr. Voskoglou, Graduate Technological Educational Institute of Western Greece, Koukouli, Patras, Greece)

Index

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