Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000
Association of Mizar Users
Basic Properties of Fuzzy Set Operation and Membership Function

Takashi Mitsuishi

Shinshu University, Nagano

Katsumi Wasaki

Shinshu University, Nagano

Yasunari Shidama

Shinshu University, Nagano
Summary.

This article introduces the fuzzy theory.
The definition of the difference set, algebraic product and algebraic sum
of fuzzy set is shown. In addition, basic properties of those operations
are described. Basic properties of fuzzy set are a~little different
from those of crisp set.
MML Identifier:
FUZZY_2
The terminology and notation used in this paper have been
introduced in the following articles
[5]
[1]
[8]
[6]
[7]
[2]
[9]
[3]
[4]

Basic Properties of Membership Function and Difference Set

Algebraic Product and Algebraic Sum
Bibliography
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 [2]
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 [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]
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 [6]
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1, 1989.
 [9]
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Journal of Formalized Mathematics,
1, 1989.
Received May 22, 2000
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