Continuity properties of attractors for iterated fuzzy set systems

Continuity Properties of Fuzzy Set Multifunctions

In this paper, we study continuity properties in Hausdorff topology for different special set multifunctions. Key–words: set multifunction, multi(sub)measure, regular, exhaustive, increasing/decreasing convergent, order continuity, probability.

Attractors of Iterated Function Systems

In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric X , there is a Cantor set C such that the disjoint union of C and X is an attractor. In the process, it is proved that every such X is the Lipschitz image of a Cantor set.

Stability results for set solution of fuzzy integro-differential systems

Attractors of Sequences of Iterated Function Systems

If F and G are iterated function systems, then any infinite word W in the symbols F and G induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single C iterated function system H. We prove that under certain assumptions on F and G, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.

Expectations over Attractors of Iterated Function Systems

Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of th...