Hi, you can have a look to the following PhD thesis in which different models are compared (deterministic, stochastic and Fuzzy). In the first sections you will find a description of the different theories behind.

Fuzzy - boundaries vary, relating to a form of set theory and logic in which predicates may have degrees of applicability, rather than simply being true or false

Stochastic - having a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely

Fuzzy refers to the uncertinity in the concepts. Sctochastics considers rendomness.

Fuzzy can add human knowlege into the modeling process

@Erik Cuevas I find in literature fuzzy and stochastic is being used inter-changeably for uncertainty. Stochastic LP model is being referred as LP under uncertainty. Fuzzy AHP is being referred as MCDM model under uncertainty. But the approach to solution are different. Can we have Fuzzy Stochastic Model such as Fuzzy TOPSIS where ratings are done in linguistic terms to which FTN values assigned but ratings by group of decision makers are random and have variance. Can we apply stochastic modeling as done in Stochastic LP model ?

I think stochastic is more dynamic.

Fuzziness describes event ambiguity. It measures the degree to which an event occurs, not whether it occurs. Randomness describes the uncertainty of event occurrence. An event occurs or not, and one can bet on it. Whether an event occurs is "random" and to what degree it occurs is "fuzzy".

Randomness is an objective form of indeterminacy whose distribution function of random variables are deduced by application of statistical methods and fuzziness to be subjective form of indeterminacy which is distinguished by degree of belongingness to a set.

Difference is in the fact that there are fuzzy stochastic numbers.

For example, in a foodball match there is some probability for penalty. At such case every player has his own possibility or membership function to reach the goal.

In stochastic mathematics, the arithmetic mean and standard deviation are important. In fuzzy mathematics and interval reasoning, the arithmetic mean and standard deviation are not always important.

Fuzzy is a tool to tackle the proboms which may be solved by other methods, fuzzy could afford more free space in control problems which presnets many unknown factors, such as disturbance, ummodeled dynamics, or parasmatic uncertainties, et al.

Stochastic more like concentrate on data or process itself, to profile the data or model with unchange resluts.