Fuzzy modelling with tolerances

We consider the problem of the resolution of fuzzy equation systems: A certain number of fuzzy inputs and outputs is given. How can we determine a fuzzy relation which describes the behaviour of the object under consideration? When attributing this problem to fuzzy equations in the classical sense it may happen that a solution does not exist. Therefore we introduce fuzzy tolerances as an extension of the solvability conception. For this problem we get the whole solution set by means of posets. Moreover, we consider the inverse problem: How to determine tolerances to get consistency (i.e. at least one solution) for the arising equation system.