Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

## 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

The terminology and notation used in this paper have been introduced in the following articles [9] [2] [12] [1] [10] [11] [13] [5] [4] [3] [6] [7] [8]

#### 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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