Tofigh Allahviranloo

This book identifies the important uncertainties to use in real-world problem modeling. Having information about several types of ambiguities, vagueness, and uncertainties is vital in modeling problems that involve linguistic variables, parameters, and word computing. Today, since most of our real-world problems are related to decision-making at the right time, we need to apply intelligent decision science. Clearly, in order to have an appropriate and flexible mathematical model, every intelligent system requires real data on our environment. Presenting problems that can be represented using mathematical models to create a system of linear equations, this book discusses the latest insights into uncertain information.

Soft Numerical Computing in Uncertain Dynamic Systems is intended for system specialists interested in dynamic systems that operate at different time scales. The book discusses several types of errors and their propagation, covering numerical methods—including convergence and consistence properties and characteristics—and proving of related theorems within the setting of soft computing. Several types of uncertainty representation like interval, fuzzy, type 2 fuzzy, granular, and combined uncertain sets are discussed in detail. The book can be used by engineering students in control and finite element fields, as well as all engineering, applied mathematics, economics, and computer science students. One of the important topics in applied science is dynamic systems and their applications. The authors develop these models and deliver solutions with the aid of numerical methods. Since they are inherently uncertain, soft computations are of high relevance here. This is the reason behind investigating soft numerical computing in dynamic systems. If these systems are involved with complex-uncertain data, they will be more practical and important. Real-life problems work with this type of data and most of them cannot be solved exactly and easily—sometimes they are impossible to solve. Clearly, all the numerical methods need to consider error of approximation. Other important applied topics involving uncertain dynamic systems include image processing and pattern recognition, which can benefit from uncertain dynamic systems as well. In fact, the main objective is to determine the coefficients of a matrix that acts as the frame in the image. One of the effective methods exhibiting high accuracy is to use finite differences to fill the cells of the matrix.

This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.

This book identifies the important uncertainties to use in real-world problem modeling. Having information about several types of ambiguities, vagueness, and uncertainties is vital in modeling problems that involve linguistic variables, parameters, and word computing. Today, since most of our real-world problems are related to decision-making at the right time, we need to apply intelligent decision science. Clearly, in order to have an appropriate and flexible mathematical model, every intelligent system requires real data on our environment. Presenting problems that can be represented using mathematical models to create a system of linear equations, this book discusses the latest insights into uncertain information.