3.6 Fuzzy valued functions
Fuzzy valued functions f*(·) are functions whose range of values are fuzzy intervals, i.e.
Let f*(·) be a fuzzy valued function with domain M, and x ∈ M.
Denoting the δ-cuts of f *(x) by
for variable x the real valued functions and are called δ-level functions.
In the case M = the δ-level functions are called δ-level curves.
Fuzzy valued functions can be graphically displayed by depicting some δ-level curves. An example is given in Figure 3.4.
Fuzzy valued functions are important in environmetrics when modeling emissions to the environment. For calculations concerning total amounts of emissions integration of emission rates are necessary. Therefore a calculus of generalized integration is needed. This is possible based on δ-level functions with existing integrals.