Indian Journal of Science and Technology, Vol 10(28), DOI: 10.17485/ijst/2017/v10i28/90453, July 2017 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 * Author for correspondence Abstract Objectives: To study the iterated multi-function systems in the framework of fuzziness. Methods/Statistical Analysis: The concept of fuzziness is used to define a new class of superfractals as attractors of fuzzy super iterated function systems. Findings: The fuzzy super iterated function systems are defined and some existence theorems on fractals in fuzzy metric spaces are established. Applications/Improvements: Our results extend and generalize some of the recent results reported in the literature in fuzzy settings. Keywords: Fractal Space, Fuzzy Metric Space, Fuzzy Contraction, Fuzzy Hutchinson-Barnsley Operator, Fuzzy Superfractal The Attractors of Fuzzy Super Iterated Function Systems Bhagwati Prasad * and Kuldip Katiyar Department of Mathematics, Jaypee Institute of Information Technology, A–10, Sector–62, Noida – 201309, Uttar Pradesh, India; b_prasad10@yahoo.com, kuldipkatiyar.jiitn@gmail.com 1. Introduction Te notion of fuzzy set was introduced in 1965 1 as a mathematical way to represent the imprecision in everyday life. Tereafer, most of the domains of knowledge were explored in the framework of fuzzy sets. Kramosil and Machalek introduced the concept of fuzzy metric space to measure the uncertainty in computing the distance between two objects or sets 2 . Teir concept was modifed by defning a Hausdorf and countable topology on the space 3,4 . Grabiec extended the celebrated Banach contraction principle in fuzzy metric spaces 5 . Several important properties of Hausdorf fuzzy metric on compact sets are studied in 6 . Tis has enthused the researcher for the fuzzifcation of fxed point theory and subsequently a number of results appeared in the literature regarding fxed points of maps satisfying some more general contractive conditions in fuzzy and more generalized spaces (see for example 5,7–15 and several references therein). Te concept of fuzziness is also extended to fractals 10 , a new frontier of science, initiated by Mandelbrot. He observed that many of the real world objects are very complex and irregular in nature and thus cannot be described fully by the traditional Euclidean geometry and felt the need of fractal geometry as a powerful mathematical tool for handling such complex systems. Te non-integer dimension, self-similarity and iterative formulation are the prime characterizations of the fractals. Afer Mandelbrot, fractals are extensively studied in the literature by various authors. Te advancement of the computational tools further enriched the domain of the theory and analysis of fractals with diverse applications in almost all branches of sciences and engineering, for details on fractals and its applications, one can refer 16–27 . An exciting idea of Iterated Function System (IFS) is presented to defne and construct fractals as compact invariant subsets of an IFS with respect to the union of contractions in 16,23,28 . Generally fractals are generated by two approaches, namely, deterministic and random. A deterministic fractal is obtained by deterministic approach while the random fractal is the result of random approach or chaos game. Many objects in the nature exhibit both the patterns. For modeling such objects the concept of superfractals were proposed 19,20 . Recently, Hutchinson-Barnsley (HB) operators on fuzzy metric spaces are studied and an analysis on fractals in such spaces is presented 29,30 . More recently V-variable fractals in metric spaces 19 are invented. Te purpose of this paper is to defne and study fuzzy super IFS and obtain some existence results on superfractals in the settings of fuzzy metric.