Fuzzy measures in inductive reasoning

The authors address: (1) the problem of optimal recording, i.e. the problem of an optimal selection of landmarks (the borderlines between neighboring domains in the discretization of continuous-time variables); and (2) the problem of reconstructing the continuous variables following the class behavior forecast. A modified inductive-reasoning technique is considered which makes it possible to reconstruct the continuous signals from the forecast discrete signals with very good accuracy. For this purpose, the previously used probabilistic quality measures are exchanged for fuzzy quality measures, and, together with the discrete states, fuzzy membership functions of the forecast signals are predicted. From these membership functions, one can then regenerate the continuous signals. The technique has been tested by means of a third-order continuous-time linear system and has given promising results