Measuring the Spread of Fuzzy Variable by L-S Integral

In credibility theory, variance is usually used as a measure of the variation of a possibility distribution about the expected value. Since the variance is defined via nonlinear fuzzy integral, its computation is difficult for general fuzzy variables. To avoid this difficulty, this paper defines the spread of a fuzzy variable based on Lebesgue-Stieltjes (L-S) integral. Our approach is to find an "average distance" from the expected value to the possible values of the fuzzy variable. For discrete and several common continuous fuzzy variables such as triangular and normal ones, we present their computation formulas about spread. The relationships between spread and variance are also discussed for common fuzzy variables. The established formulas are useful that can be employed to model practical fuzzy optimization problems.