Asymptotic results for the entropy of a random fuzzy partition. (English. Ukrainian original) Zbl 0998.60049

Yurachkivs’kyj, A. P.

Theory Probab. Math. Stat. 64, 179-192 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 152-163 (2001).

The author discusses a generalization of the “entropy of space partition” notion in the case when partition is created by fuzzy sets. The asymptotic behaviour of the entropy is studied under the additional assumption that fuzzy sets are uniformly small. Martingale approach is an essential moment in proving the limit results.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60G57	Random measures
60D05	Geometric probability and stochastic geometry

Keywords:

space division; fuzzy sets; entropy; asymptotic behaviour; weak convergence; convergence in probability; martingales