Название: Fuzzy Mathematics: A Fundamental IntroductionАвтор: Apostolos Syropoulos
Издательство: Springer
Серия: Synthesis Lectures on Mathematics & Statistics
Год: 2025
Страниц: 109
Язык: английский
Формат: pdf (true), epub
Размер: 10.1 MB
This book aims to introduce readers without a strong mathematical background to the basic ideas of fuzzy set theory and logic. Fuzzy mathematics is the mathematics of vagueness, a universal property of this world. There are many objects that are called vague because they cannot be precisely defined. Since vagueness is so common, a tool is needed to describe it and to effectively deal with it. Fuzzy mathematics is such a tool, and it is used by most researchers and scholars. As such, this book provides a short overview of the field written for non-specialists. This book allows readers to delve into the theory of fuzzy sets and introduces core mathematical ideas without using the usual formalities of books in mathematics, i.e. theorems, proofs, etc.
The book has been designed for anyone who has a very basic background in mathematics and wants to learn what are these weird mathematical objects that are called fuzzy sets. Anyone who wants to learn about fuzzy sets needs to know what is a set and what are the properties and operations between sets. Thus, this book introduces all these notions and ideas. In different words, it is a self-contained introduction to the basics of fuzzy mathematics. However, fuzzy sets are a mathematical model of vagueness and Chap. 1 of the book is an introduction to vagueness and related ideas. This chapter presents the various concepts and ideas from a philosophical and a practical point of view. Since fuzzy sets are sets, it is necessary to have a basic understanding of sets and the operations between them. This is the subject of Chap. 2. Chapter 3 introduces fuzzy sets, their operations, their representations, and some of their most common extensions. Chapter 4 is about fuzzy numbers and their operations. Fuzzy numbers have found many applications and, naturally, most people working on practical problems using fuzzy sets, use fuzzy numbers. Certainly, this book could have more about fuzzy sets and their mathematics, but this was not my initial intention. The reader who will read this book and get an understanding of fuzzy sets and their operations can continue studying fuzzy sets and their mathematics—there are many good books on the subject.
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