After the successful applications of fuzzy sets theory on the controller systems,
this theory have applied in other areas. In the most these applications fuzzy
numbers are one way to describe the data vagueness and imprecision. They can be
regarded as an extension of the real numbers. In the literature of fuzzy sets there is
some shortcoming in the definition of fuzzy number. Frankly some authors do not
distinguish between positive and nonnegative fuzzy numbers. Here, we focus on
the triangular fuzzy number and give two different definitions for nonnegative and
positive triangular fuzzy numbers to eliminate this shortcoming.