Simulations of Fuzzy Dynamical Systems using the LU Representation of Fuzzy Numbers

We suggest the use of the parametric LU-representation of the fuzzy numbers, introduced in Guerra and Stefanini [Guerra ML, Stefanini L. Approximate fuzzy arithmetic operations using monotonic interpolations. Fuzzy Sets System2005;150:5–33] and improved in Stefanini et al. [Stefanini L, Sorini L, Guerra ML. Parametric representations of fuzzy numbers and applications. Working Paper Series EMS, 95, University of Urbino, 2004], in the simulation of fuzzy dynamical systems or fuzzy iterated maps. We show the computational advantages of the LU-representation in extending some well known standard maps to the fuzzy context, allowing the simulation by the Zadeh s extension principle in the general case of fuzzy parameters