This communication recalls some of the Bobylev’s definitions of support function of a fuzzy set and distance between fuzzy sets. Their equivalence with the generalized Hausdorff metric and the support function defined by of Puri and Ralescu is analyzed.

Without using the concept of Hausdorff metric, we prove some results on the existence of fixed points for generalized contractive multivalued maps with respect to u-distance. Consequently, several known fixed point results are either generalized or improved.

The fractal dimensions are very important characteristics of the fractal sets. A problem which arises in the study of the fractal sets is the determination of their dimensions. The Hausdorff dimension of this type of sets is difficult to be determined, even if the Box dimensions can be computed. In this article we present some boundedness conditions on the Hausdorff h-measure of a set, using th...

In this paper, we firstly introduce the definition of fuzzy metric sets, and discuss properties induced by Hausdorff metric. Then prove limit theorems for set-valued random variables in space; convergence is about The work an extension from classical results to space.

Recommended by Hichem Ben-El-Mechaiekh We prove some results on the existence of fixed points for multivalued generalized w-contractive maps not involving the extended Hausdorff metric. Consequently, several known fixed point results are either generalized or improved.

Finitary endofunctors of locally presentable categories are proved to have equational presentations. Special attention is paid to the Hausdorff functor of non-empty compact subsets of a complete metric space.

A natural approach to defining continuous change of shape is in terms of a metric that measures the difference between two regions. We consider four such metrics over regions: the Hausdorff distance, the dual-Hausdorff distance, the area of the symmetric difference, and the optimal-homeomorphism metric (a generalization of the Fréchet distance). Each of these gives a different criterion for con...

It is known that a real valued measure (1) on the a-ring of Baire sets of a locally compact Hausdorff space, or (2) on the Borel sets of a complete separable metric space is regular. Recently Dinculeanu and Kluvanek used regularity of non-negative Baire measures to prove that any Baire measure with values in a locally convex Hausdorff topological vector space (TVS) is regular. Subsequently a di...

We show that Rieffel’s quantum Gromov–Hausdorff distance between two compact metric spaces is not equivalent to the ordinary applied associated state spaces.