Syropoulos A. Fuzzy Mathematics. A Fundamental Introduction 2025
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Syropoulos A. Fuzzy Mathematics. A Fundamental Introduction 2025
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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.
Preface
On Vagueness
What Is Vagueness?
Vagueness, Uncertainty, Imprecision…
Measuring Vagueness
``Continuous'' Sorites Paradox
A Précis of Basic Set Theory
What Is a Set?
Sets and Their Elements
The Empty Set
Unions and Intersections of Sets
Set Difference and Symmetric Difference
Cartesian Product of Sets
Fuzzy Subsets
Alternative Mathematics
What Is a Fuzzy Subset?
α-Cuts of Fuzzy Subsets
How Do We Assign Membership Degrees?
New Fuzzy Subsets from Old Ones
Triangular Norms and Conorms
``Intuitionistic'' Fuzzy Subsets
Pythagorean Fuzzy Subsets
Neutrosophic Fuzzy Subsets
Bipolar Fuzzy Subsets
Interval Valued Fuzzy Subsets
Fuzzy Multisets
The Extension Principle
Fuzzy Numbers and Linguistic Variables
What Is a Fuzzy Number?
Shapes of Fuzzy Numbers
Triangular Fuzzy Numbers
Trapezoidal Fuzzy Numbers
Gaussian Fuzzy Numbers
Quadratic Fuzzy Numbers
Exponential Fuzzy Numbers
LR Fuzzy Numbers
Generalized Fuzzy Numbers
Arithmetic of Fuzzy Numbers
Interval Arithmetic
Interval Arithmetic and α-Cuts
Fuzzy Arithmetic and the Extension Principle
Linguistic Variables
Linguistic Hedges
Bibliography
Index