dear

The main question is that what is its advantages than the others.

At first this approach could replace the parametric analysis in some cases and secondly it can be considerd as a first step towards styding rough mathematical programming problems.

I will answer on the example of regression. The interval analysis allows to take into account errors in independent variables. An unclear method has the element of subjectivity. The known statistical methods are applicable not in all cases.

I think all interval analysis based methods are directly or indirectly have correspondence to Fuzzy Set Theory based methods. But both the models have their own advantages in their domains.

Fuzzy Sets Theory/Interval Analysis.

dear

The main question is that what is its advantages than the others.

Fuzzy(Possibility) methods are accurate when data is spread between the bounds. However, interval methods are valid in the sense of knowledge about solutions to mathematical equations.

Interval analysis, and especially interval arithmetic, makes a solid ground for assessing accuracy of results produced by computers. This is why those methods were invented in the first place more than 50 years ago. Interval results are always guaranteed to contain the exact result, no matter that its upper and lower bounds happen to be overestimated. There is no place for subjectivity here, in contrast to fuzzy-type approach where 'shapes' of fuzzy numbers are somewhat arbitrarily defined by the user. Guaranteed bounds are certainly preferred over those produced by statistics (and other uncertain methods) when human life is at stake (or very expensive equipment). Somewhat unexpectedly, interval methods can be combined with statistics, see my project https://www.researchgate.net/project/Applications-of-interval-computations .

Here we gain probably the most reliable method to deal with outliers when fitting unknown parameters to theoretical curves. Excellent tool, comparable with complex numbers in electrical engineering.

There is no place for subjectivity here, in contrast to fuzzy-type approach where 'shapes' of fuzzy numbers are somewhat arbitrarily defined by the user. Guaranteed bounds are certainly preferred over those produced by statistics (and other uncertain methods) when human life is at stake (or very expensive equipment). Somewhat unexpectedly, interval methods can be combined with statistics, see my project https://www.researchgate.net/project/Applications-of-interval-computations .