Properties of Fuzzy Relation

Noboru Endou

Gifu National College of Technology

Takashi Mitsuishi

Miyagi University

Keiji Ohkubo

Shinshu University, Nagano

Summary.

In this article, we introduce four fuzzy relations and the composition, and some useful properties are shown by them. In section 2, the definition of converse relation $R^{-1}$ of fuzzy relation $R$ and properties concerning it are described. In the next section, we define the composition of the fuzzy relation and show some properties. In the final section we describe the identity relation, the universe relation and the zero relation.

MML Identifier: FUZZY_4

Contents (PDF format)

1. Basic Properties of the Membership Function
2. Definition of Converse Fuzzy Relation and some Properties
3. Definition of the Composition and some Properties
4. Definition of Identity Relation and Properties of Universe and Zero Relation

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