Discrete Frechet fuzzy metric
Анотація
The Fr\'echet distance between curves in metric spaces is known to have its fuzzy counterpart. In the present note we consider the fuzzy discrete distance between sequences of points in fuzzy metric spaces. Also, discrete curves in non-Archimedean fuzzy metric spaces are considered.
It is proved that the Fr\'echet distance between piecewise linear curves in the fuzzy normed spaces equals the discrete Fr\'echet distance between discrete curves consisting of their vertices.
The fuzzy distance between two points can be interpreted as a function of the parameter $t>0$. We prove that the fuzzy distance between continuous curves is approximated by the distances between their close discrete curves in the topology of convergence on compact sets.
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