A Modern Introduction to Fuzzy Mathematics 1st Edition Apostolos Syropoulos 9781119445296 1119445299

A Modern Introduction to Fuzzy Mathematics 1st Edition Apostolos Syropoulos – Ebook Instant Download/Delivery ISBN(s): 9781119445289,1119445280,9781119445296,1119445299

Product details:

• ISBN 10: 1119445299
• ISBN 13: 9781119445296 
• Author: Apostolos Syropoulos; Theophanes Grammenos
  

A Modern Introduction to Fuzzy Mathematics provides a concise presentation of fuzzy mathematics., moving from proofs of important results to more advanced topics, like fuzzy algebras, fuzzy graph theory, and fuzzy topologies.The authors take the reader through the development of the field of fuzzy mathematics, starting with the publication in 1965 of Lotfi Asker Zadeh’s seminal paper, Fuzzy Sets. The book begins with the basics of fuzzy mathematics before moving on to more complex topics. Perfect for advanced undergraduate students, graduate students, and researchers with an interest in the field of fuzzy mathematics, A Modern Introduction to Fuzzy Mathematics walks through both foundational concepts and cutting-edge, new mathematics in the field.

Table contents:

Part 1. Introduction
1.1 What Is Vagueness?
1.2 Vagueness, Ambiguity, Uncertainty, etc.
1.3 Vagueness and Fuzzy Mathematics
Part 2. Fuzzy Sets and Their Operations
2.1 Algebras of Truth Values
2.2 Zadeh’s Fuzzy Sets
2.3 ‐Cuts of Fuzzy Sets
2.4 Interval-valued and Type 2 Fuzzy Sets
2.5 Triangular Norms and Conorms
2.6 ‐fuzzy Sets
2.7 “Intuitionistic” Fuzzy Sets and Their Extensions
2.8 The Extension Principle
2.9* Boolean‐Valued Sets
2.10* Axiomatic Fuzzy Set Theory
Part 3. Fuzzy Numbers and Their Arithmetic
3.1 Fuzzy Numbers
3.2 Arithmetic of Fuzzy Numbers
3.3 Linguistic Variables
3.4 Fuzzy Equations5
3.5 Fuzzy Inequalities
3.6 Constructing Fuzzy Numbers
3.7 Applications of Fuzzy Numbers
Part 4. Fuzzy Relations
4.1 Crisp Relations
4.2 Fuzzy Relations
4.3 Cartesian Product, Projections, and Cylindrical Extension
4.4 New Fuzzy Relations from Old Ones
4.5 Fuzzy Binary Relations on a Set
4.6 Fuzzy Orders
4.7 Elements of Fuzzy Graph Theory
4.8 Fuzzy Category Theory
4.9 Fuzzy Vectors5
4.10 Applications
Part 5. Possibility Theory
5.1 Fuzzy Restrictions and Possibility Theory
5.2 Possibility and Necessity Measures
5.3 Possibility Theory
5.4 Possibility Theory and Probability Theory
5.5 An Unexpected Application of Possibility Theory
Part 6. Fuzzy Statistics
6.1 Random Variables
6.2 Fuzzy Random Variables
6.3 Point Estimation
6.4 Fuzzy Point Estimation
6.5 Interval Estimation
6.6 Interval Estimation for Fuzzy Data
6.7 Hypothesis Testing
6.8 Fuzzy Hypothesis Testing
6.9 Statistical Regression
6.10 Fuzzy Regression
Part 7. Fuzzy Logics
7.1 Mathematical Logic
7.2 Many‐Valued Logics
7.3 On Fuzzy Logics
7.4 Hájek’s Basic Many‐Valued Logic
7.5 Łukasiewicz Fuzzy Logic
7.6 Product Fuzzy Logic
7.7 Gödel Fuzzy Logic
7.8 First‐Order Fuzzy Logics
7.9 Fuzzy Quantifiers
7.10 Approximate Reasoning
7.11 Application: Fuzzy Expert Systems
7.12 A Logic of Vagueness
Part 8. Fuzzy Computation
8.1 Automata, Grammars, and Machines
8.2 Fuzzy Languages and Grammars
8.3 Fuzzy Automata
8.4 Fuzzy Turing Machines
8.5 Other Fuzzy Models of Computation
Part 9. Fuzzy Abstract Algebra
9.1 Groups, Rings, and Fields
9.2 Fuzzy Groups
9.3 Abelian Fuzzy Subgroups
9.4 Fuzzy Rings and Fuzzy Fields
9.5 Fuzzy Vector Spaces
9.6 Fuzzy Normed Spaces
9.7 Fuzzy Lie Algebras
Part 10. Fuzzy Topology
10.1 Metric and Topological Spaces1
10.2 Fuzzy Metric Spaces
10.3 Fuzzy Topological Spaces6
10.4 Fuzzy Product Spaces
10.5 Fuzzy Separation
10.6 Fuzzy Nets
10.7 Fuzzy Compactness
10.8 Fuzzy Connectedness
10.9 Smooth Fuzzy Topological Spaces
10.10 Fuzzy Banach and Fuzzy Hilbert Spaces
10.11 Fuzzy Topological Systems
Part 11. Fuzzy Geometry
11.1 Fuzzy Points and Fuzzy Distance
11.2 Fuzzy Lines and Their Properties
11.3 Fuzzy Circles
11.4 Regular Fuzzy Polygons
11.5 Applications in Theoretical Physics
Part 12. Fuzzy Calculus
12.1 Fuzzy Functions
12.2 Integrals of Fuzzy Functions
12.3 Derivatives of Fuzzy Functions
12.4 Fuzzy Limits of Sequences and Functions

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