Syropoulos A. Fuzzy Mathematics. A Fundamental Introduction 2025

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Syropoulos A. Fuzzy Mathematics. A Fundamental Introduction 2025

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Textbook in PDF format 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