**5. Conclusion**

Neural net in identification sense, considered the adaptation process requiring adjust the weights dynamically using the common proportional condition. But in many cases, these applications generate convergence problems because the gain in all cases increase the neural net weights positive or negatively without converge to desired value. In the black box traditional scheme the internal weights are known, but in real conditions it is impossible and only has a desired or objective answer. But, the neural nets help jumping weights estimation adjusting dynamically their internal weights, needing adaptation process with smooth movements as a function of identification error (function generated by the difference between the filter answer with respect to desired answer.). An option considered was the fuzzy logic in where its natural actions based on distribution function error allowing built the adjustable membership functions and mobile inference limits. Therefore, the neural weights are adjusted dynamically considering the fussy logic adaptable properties applied in the law actions, shown in figure 7. Stable weights conditions were exposed in section 3, with movements bounded in (8). In the results section, the figure 13, illustrated the Neuro-Fuzzy Digital Filter advantages without lost the stability with respect to desired system answer observed in distribution sense, observing the Hausdorff condition approximating the filter to desired system answer in distribution sense.
