1. Definition of Fuzzy Sets

1.1 Introduction

1.2 Definition of Fuzzy Sets

1.3 Notations of Fuzzy Sets

Notations for Fuzzy Sets

2. Relations between and Operations on Fuzzy Sets

2.1 Relations between Fuzzy Sets

2.2 Operations on Fuzzy Sets

2.3 Examples of Operations on Fuzzy Sets

2.4 Properties of Operations on Fuzzy Sets: Part 1

2.5 Properties of Operations on Fuzzy Sets: Part 2

Operations on Fuzzy Sets

3. Lattices

3.1 Partial Ordered Sets

3.2 Hasse Diagrams

3.3 Elements with Extremal Properties

3.4 Lattices: Part 1

3.5 Lattices Part 2

3.6 Boolean Algebras Part 1

3.7 Boolean Algebras Part 2

3.8 Soft Algebras and Optimal Soft Algebras

3.9 Algebraic structure on [0,1]

3.10 Algebraic structure on the Fuzzy Power Set

Lattices

4. Fuzzy Operators

4.1 Definitions of Fuzzy Operators

4.2 Properties of Fuzzy Operators

4.3 Generalized Unions & Generalized Intersections

Fuzzy Operators

5. Cuts, Strong cuts & Scalar Multiplication

5.1 Cuts and Strong Cuts: Part 1

5.2 Cuts and Strong Cuts: Part 2

5.3 Scalar Multiplication

Cuts, Strong cuts & Scalar Multiplication

6. Resolution Principles

6.1 Resolution Principles: Part 1

6.2 Resolution Principles: Part 2

Resolution Principles

7. Representation Theorem

7.1 Nests of sets

7.2 Representation Theorem: Part 1

7.3 Representation Theorem: Part 2

Representation Theorem

8. Extension Principles

8.1 Extension Principles: Part 1

8.2 Extension Principles: Part 2

8.3 Extension Principles: Part 3

Extension Principles