DOUBLING PROPERTIES, DIRICHLET FORMS AND DIFFUSION PROCESSES ON THE MEASURE METRIC SPACE OF FUZZY INTERVALS

摘要: We show that the metric space fuzzy intervals holds the Doubling Metric (DP) and the Doubling Volume Property (DVP) with respect to the Hausdorf metric and measure. Several topological corollaries follow.While these results in metric topology are certainly sufficiently interesting in themselves, they open up an arsenal of ready methods of harmonic analysis to be applied in the field of fuzzy mathematics. As an example we show that fuzzy stochastic processes may be defined by Dirichlet forms.