IFS on the Multi-Fuzzy Fractal Space
The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075460Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1649
 B. Forte, E.R. Vrscay. Theory of generalized fractal transforms. Fractal Image Encoding and Analysis, July, 1995.
 F.S. Fadhel. About fuzzy fixed point theorem. Ph.D. thesis, Al-Nahreen University, Baghdad, Iraq. 1998.
 G.A. Edger, J. Golds. A fractal dimension estimate for a graph-directed iterated function system of non-similarities. Indiana University Mathematics Journal, vol.48, no.2, pp. 429-447, 1999.
 G.A. Edger. Measure, topology, and fractal geometry. New York: Springer-Verlag, 1990.
 L. Zoushu, Z.Quan. Fuzzy metric spaces and fixed point theorems. J. Fuzzy Math., vol.1, no.2, 1993.
 M.F. Barnsley. Fractals everywhere. 2nd ed. Academic Press Professional, Inc., San Diego, CA, USA, 1993.
 P.E. Kloeden. Fuzzy dynamical systems. Fuzzy Sets and Systems, vol. 7, no. 3, pp. 275-296, 1982.
 V. Gregori, A. Sapena. On fixed point theorem in fuzzy metric spaces. Fuzzy Sets and Systems, vol. 125,no. 2, pp. 245-252, 1998.
 W. F. Al-Shameri. On nonlinear iterated function systems. Ph.D. thesis, Al-Mustansiriyah University, Baghdad, Iraq, 2001.
 W. Rudin. Principles of mathematical analysis. 3rd ed., McGraw-Hill Book Co., 1976.
 N. Al- Saidi. On multi fuzzy metric space. Ph.D. thesis, Al-Nahreen University, Baghdad, Iraq, 2002.
 O. Kramsil, J. Michalek. Fuzzy metric and statistical metric spaces, Kybernetika, vol. 11, pp. 326-334, pp.1975.
 M. Dorel. On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Set and Systems, vol. 158, no. 8, pp. 915-921, 2007.
 A. George. P. Veeramani. On some result in fuzzy metric spaces. Fuzzy Sets and Systems, vol.64, pp. 395-399, 1994.
 H.M. Abu-Donia. Common fixed point theorems for fuzzy mappings under ¤å-contraction condition. Chaos, Solitons and Fractals. Vol.34, pp. 538-543, Oct. 2007.
 L.A. Zadah. Fuzzy sets. Inform Control, vol. 8, pp. 338-353, 1965.
 J. Hutchinson. Fractals and self-similarity. Indiana Univ. J.Math. vol. 30, no. 5, pp. 713-747, 1981.