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Continuity properties of attractors for iterated fuzzy set systems

Published online by Cambridge University Press:  17 February 2009

B. Forte ,
M. Lo Schiavo  and
E. R. Vrscay
B. Forte
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1.
M. Lo Schiavo
Affiliation:
Metodi e Mod. Mat. Sc. Appl., Universita' di Roma “La Sapienza”, 00161 Rome, Italy.
E. R. Vrscay
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1.
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Abstract

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An N-map Iterated Fuzzy Set System (IFZS), introduced in [4] and to be denoted as (w, Φ), is a system of N contraction maps wi: X → X over a compact metric space (X, d), with associated “grey level” maps øi: [0, 1] → [0, 1]. Associated with an IFZS (w, Φ) is a fixed point u ∈ f*(X), the class of normalized fuzzy sets on X, u: X → [0, 1]. We are concerned with the continuity properties of u with respect to changes in the wi, and the φi. Establishing continuity for the fixed points of IFZS is more complicated than for traditional Iterated Function Systems (IFS) with probabilities since a composition of functions is involved. Continuity at each specific attractor u may be established over a suitably restricted domain of φi maps. Two applications are (i) animation of images and (ii) the inverse problem of fractal construction.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 2 , October 1994 , pp. 175 - 193
Copyright
Copyright © Australian Mathematical Society 1994

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