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This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.
This book provides an overview of the state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. Covering topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods for differential equations, it discusses applications such as fuzzy real-time scheduling, intelligent control, diagnostics and time series prediction. The book features selected contributions presented at the 6th international congress of the Moroccan Applied Mathematics Society, which took place at Sultan Moulay Slimane University Beni Mellal, Morocco, from 7 to 9 November 2019.
This book "Advanced Applications of Computational Mathematics" covers multidisciplinary studies containing advanced research in the field of computational and applied mathematics. The book includes research methodology, techniques, applications, and algorithms. The book will be very useful to advanced students, researchers and practitioners who are involved in the areas of computational and applied mathematics and engineering.
Modelling Invasive Alien Plant Species: Fuzzy Based Uncertainty presents the application of different fuzzy set theory techniques in developing risk assessment models for invasive plant species- those whose introduction and spread outside their natural range threatens local biodiversity. Invasion risk of species is expressed by biological traits which would be considered as the risk factors accompanied with uncertainty and imprecision. The book considers both quantitative and qualitative inputs in modelling the invasive risk by incorporating different mathematical models based on fuzzy set theory operators, interval methods, and fuzzy linguistic operators. The proposed models can be applied for investigating risk of invasive alien plant species in various regions and conditions. Features: Uniquely merges mathematical models with biological expressions. Presents different factor-based models as a case study on the risk of invasive alien plant species. Explains how users can perform primary-level risk assessment through fuzzy modeling techniques. Appropriate for upper-level students, researchers, and practicing professionals, this book shows how conventional approaches such as probability theory can be of limited use to solve issues of uncertainty, and how they fuzzy set theory plays a better role in understanding uncertain system dynamics, such invasive plant modelling.
Since 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.
This book gathers selected papers presented at the conference of the Forum for Interdisciplinary Mathematics (FIM), held at Palau Macaya, Barcelona, on 18 to 20 November, 2015. The event was co-organized by the University of Barcelona (Spain), the Spanish Royal Academy of Economic and Financial Sciences (Spain) and the Forum for Interdisciplinary Mathematics (India). This instalment of the conference was presented with the title “Applied Mathematics and Computational Intelligence” and particularly focused on the use of Mathematics and Computational Intelligence techniques in a diverse range of scientific disciplines, as well as their applications in real-world problems. The book presents thirty peer-reviewed research papers, organised into four topical sections: on Mathematical Foundations; Computational Intelligence and Optimization Techniques; Modelling and Simulation Techniques; and Applications in Business and Engineering. This book will be of great interest to anyone working in the area of applied mathematics and computational intelligence and will be especially useful for scientists and graduate students pursuing research in these fields.
This volume is a comprehensive collection of extended contributions from the Workshop on Computational Optimization 2015. It presents recent advances in computational optimization. The volume includes important real life problems like parameter settings for controlling processes in bioreactor, control of ethanol production, minimal convex hill with application in routing algorithms, graph coloring, flow design in photonic data transport system, predicting indoor temperature, crisis control center monitoring, fuel consumption of helicopters, portfolio selection, GPS surveying and so on. It shows how to develop algorithms for them based on new metaheuristic methods like evolutionary computation, ant colony optimization, constrain programming and others. This research demonstrates how some real-world problems arising in engineering, economics, medicine and other domains can be formulated as optimization problems.
This book meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of soft computing on the other. Soft computing is the recent development about the computing methods which include fuzzy set theory/logic, evolutionary computation (EC), probabilistic reasoning, artificial neural networks, machine learning, expert systems, etc. Soft computing refers to a partnership of computational techniques in computer science, artificial intelligence, machine learning, and some other engineering disciplines, which attempt to study, model, and analyze complex problems from different interdisciplinary problems. This, as opposed to traditional computing, deals with approximate models and gives solutions to complex real-life problems. Unlike hard computing, soft computing is tolerant of imprecision, uncertainty, partial truth, and approximations. Interdisciplinary sciences include various challenging problems of science and engineering. Recent developments in soft computing are the bridge to handle different interdisciplinary science and engineering problems. In recent years, the correspondingly increased dialog between these disciplines has led to this new book. This is done, firstly, by encouraging the ways that soft computing may be applied in traditional areas, as well as point towards new and innovative areas of applications and secondly, by encouraging other scientific disciplines to engage in a dialog with the above computation algorithms outlining their problems to both access new methods as well as to suggest innovative developments within itself.
Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.
Digital systems that bring together the computing capacity for processing large bodies of information with the human cognitive capability are called intelligent systems. Building these systems has become one of the great goals of modem technology. This goal has both intellectual and economic incentives. The need for such intelligent systems has become more intense in the face of the global connectivity of the internet. There has become an almost insatiable requirement for instantaneous information and decision brought about by this confluence of computing and communication. This requirement can only be satisfied by the construction of innovative intelligent systems. A second and perhaps an even more significant development is the great advances being made in genetics and related areas of biotechnology. Future developments in biotechnology may open the possibility for the development of a true human-silicon interaction at the micro level, neural and cellular, bringing about a need for "intelligent" systems. What is needed to further the development of intelligent systems are tools to enable the representation of human cognition in a manner that allows formal manipulation. The idea of developing such an algebra goes back to Leibniz in the 17th century with his dream of a calculus ratiocinator. It wasn't until two hundred years later beginning with the work of Boole, Cantor and Frege that a formal mathematical logic for modeling human reasoning was developed. The introduction of the modem digital computer during the Second World War by von Neumann and others was a culmination of this intellectual trend.