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           

#### Contents (PDF format)

1. Definition of Membership Function and Fuzzy Set
2. Intersection, Union and Complement
3. Empty Fuzzy Set and Universal Fuzzy Set
4. Exclusive Sum, Absolute Difference

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