Guaranteed fuzzy function approximation using interval analysis

Usually, fuzzy systems approximate functions by covering their graphs with fuzzy patches in the input-output state space. Each fuzzy rule defines a fuzzy patch. The approximation increases in accuracy as the fuzzy patches increase in number and decrease in size. We propose an other approach in which the estimation of the fuzzy parameters from experimental data is viewed as one of set inversion, which is solved in an approximate but guaranteed way with the tools of interval analysis. Any prior knowledge, that can be expressed as a series of inequalities to be satisfied by the fuzzy parameters, can be taken into account.