The concept of fuzzy relation, two-dimensional fuzzy sets, fuzzy extension principle, fuzzy projection, binary and n-ary fuzzy relations is discussed in this chapter. Representing verbal terms and expressions as fuzzy relations are also introduced in this chapter.

Chapter Contents:

• 4.1 Introduction
• 4.2 Fuzzy relation
• 4.3 Operation with fuzzy relations
• 4.3.1 Intersection of two fuzzy relations
• 4.3.2 Union of two fuzzy relations
• 4.3.3 Negation of a fuzzy relation
• 4.3.4 Inverse of a fuzzy relation
• 4.3.5 Composition of fuzzy relations
• 4.3.6 Compositional rule of inference
• 4.3.7 The relational joint
• 4.4 Binary relations
• 4.5 The extension principle
• 4.5.1 The cylindrical extension
• 4.6 Fuzzy mapping
• 4.7 Problems
• References

Inspec keywords: fuzzy set theory

Other keywords: n-ary fuzzy relations; two-dimensional fuzzy sets; fuzzy extension principle; fuzzy projection

Subjects: Combinatorial mathematics; Combinatorial mathematics; Algebra, set theory, and graph theory; Combinatorial mathematics