Effect of noise on chaotic fuzzy mappings

摘要

Chaotic mappings in the space of fuzzy sets induced by mappings of the underlying reference set are investigated. Different fuzzification schemes are considered and their impact on the resultant iterated fuzzy set, under a quadratic mapping, is studied numerically. The fuzzy set mapping is described in terms of the mapping of level cuts, resulting from the resolution theorem for fuzzy sets. In the two-dimensional case, a generalized notion, given as a fuzzy set, of the Hausdorff dimension is formulated. An example, based on the Henon Mapping, is provided.