Simulation of fuzzy random variables

8 This work deals with the simulation of fuzzy random variables, which can be used 9 to model various realistic situations, where uncertainty is not only present in form 10 of randomness but also in form of imprecision, described by means of fuzzy sets. 11 Utilizing the common arithmetics in the space of all fuzzy sets only induces a conical 12 structure. As a consequence, it is difficult to directly apply the usual simulation 13 techniques for functional data. In order to overcome this difficulty two different 14 approaches based on the concept of support functions are presented. The first one 15 makes use of techniques for simulating Hilbert space-valued random elements and 16 afterwards projects on the cone of all fuzzy sets. It is shown by empirical results that 17 the practicability of this approach is limited. The second approach imitates the re18 presentation of every element of a separable Hilbert space in terms of an orthonormal 19 basis directly on the space of fuzzy sets. In this way, a new approximation of fuzzy 20 sets useful to approximate and simulate fuzzy random variables is developed. This 21 second approach is adequate to model various realistic situations. 22