Simulation of fuzzy random variables

• Published in: Information sciences Vol. 179; no. 5; pp. 642 - 653
• Main Authors: González-Rodríguez, Gil, Colubi, Ana, Trutschnig, Wolfgang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.2009
• Subjects: Fuzzy random variables; Hilbert spaces; Imprecise data; Simulation; Support functions; Fuzzy random variables; Hilbert spaces; Simulation; Support functions; Imprecise data
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2008.10.018

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