Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000
Association of Mizar Users
The Concept of Fuzzy Relation and Basic Properties of its Operation

Takashi Mitsuishi

Shinshu University, Nagano

Katsumi Wasaki

Shinshu University, Nagano

Yasunari Shidama

Shinshu University, Nagano
Summary.

This article introduces the fuzzy relation. This is the expansion of
usual relation, and the value is given at the fuzzy value. At
first, the definition of the fuzzy relation characterized by membership
function is described. Next, the definitions of the zero relation and
universe relation and basic operations of these relations are
shown.
MML Identifier:
FUZZY_3
The terminology and notation used in this paper have been
introduced in the following articles
[2]
[5]
[6]
[1]
[3]
[4]

Definition of Fuzzy Relation

Zero Relation and Universe Relation
Bibliography
 [1]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Jaroslaw Kotowicz.
Partial functions from a domain to the set of real numbers.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Takashi Mitsuishi, Noboru Endou, and Yasunari Shidama.
The concept of fuzzy set and membership function and basic properties of fuzzy set operation.
Journal of Formalized Mathematics,
12, 2000.
 [5]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received September 15, 2000
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