Fuzzy numbers are fuzzy subsets of the real line. They have a peak or plateau with membership grade 1, over which the members of the universe are completely in the set. The membership function is increasing towards the peak and decreasing away from it.

Fuzzy numbers are used very widely in fuzzy control applications. A typical case is the triangular fuzzy number

1.0 +                   +
    |                  / \
    |                 /   \
0.5 +                /     \
    |               /       \
    |              /         \
0.0 +-------------+-----+-----+--------------
                  |     |     |
                 5.0   7.0   9.0

which is one form of the fuzzy number 7. Slope and trapezoidal functions are also used, as are exponential curves similar to Gaussian probability densities.

For more information, see:

Dubois, Didier, and Prade, Henri, "Fuzzy Numbers: An Overview", in Analysis of Fuzzy Information 1:3-39, CRC Press, Boca Raton, 1987.

Dubois, Didier, and Prade, Henri, "Mean Value of a Fuzzy Number", Fuzzy Sets and Systems 24(3):279-300, 1987.

Kaufmann, A., and Gupta, M.M., "Introduction to Fuzzy Arithmetic", Reinhold, New York, 1985.