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

Takashi Mitsuishi

Shinshu University, Nagano

Noboru Endou

Shinshu University, Nagano

Yasunari Shidama

Shinshu University, Nagano
Summary.

This article introduces the fuzzy theory. At first, the definition of
fuzzy set characterized by membership function is described.
Next, definitions of empty fuzzy set and universal fuzzy set and
basic operations of these fuzzy sets are shown. At last, exclusive
sum and absolute difference which are special operation are
introduced.
MML Identifier:
FUZZY_1
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[1]
[10]
[8]
[9]
[2]
[5]
[11]
[3]
[4]
[6]

Definition of Membership Function and Fuzzy Set

Intersection, Union and Complement

Empty Fuzzy Set and Universal Fuzzy Set

Exclusive Sum, Absolute Difference
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 [11]
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1, 1989.
Received May 18, 2000
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