# A Short Course for Fuzzy Set Theory

Part of the Computer Science Workbench book series (WORKBENCH)

## Abstract

Intuitively, a set is any collection of objects. Many examples are found in the real world and in mathematical theories. There are two main ways of defining a set. One is to list up objects that constitutes a set. For example, {John, Mary, Thomas} is a set of the three objects: John, Mary, and Thomas. We can think that these three objects are mere words or names indicating three real persons. Usually we give a name, say X, to the collection: X = {John, Mary, Thomas}, and we refer to X instead of listing up all the objects after we have given the name. Thus, in an abstract manner a set X = {x;1, x 2, … ,x n x is the collection of χ1, x 2,… ,x n.

## Keywords

Membership Function Fuzzy Number Modal Logic Fuzzy Relation Possibility Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. [1]
D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
2. [2]
D. Dubois and H. Prade, “Fuzzy numbers: an overview,” in Analysis of Fuzzy Information, Vol.1, J.C. Bezdek, (Ed.), CRC Press, pp.3–39, 1987.Google Scholar
3. [3]
D. Dubois and H. Prade, Possibility Theory, Plenum, New York, 1988.
4. [4]
V. Novák, Fuzzy Sets and Their Applications, Adam Hilger, Bristol, 1989.Google Scholar
5. [5]
Z. Pawlak, Rough Sets, Kluwer, Dordrecht, 1991.
6. [6]
G. Takeuti and S. Titani, “Intuitionistic fuzzy logic and intuitionistic fuzzy set theory,” J. Symbolic Logic, Vol.49, pp.851–866, 1984.
7. [7]
L. A. Zadeh, Fuzzy sets, Information and Control, Vol.8, pp.338–353, 1965.
8. [8]
L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, Vol.1, pp.3–28, 1978.