Predominantly in the faltering atmosphere, the precise value of some factors is difficult to measure. Though, it can be easily approximated by intuitionistic fuzzy linguistic term in the real-life world problem. To deal with such situations, in this paper two information measures based on trigonometric function for intuitionistic fuzzy sets, which are a generalized version of the fuzzy informat...

We survey some of the topological properties of the attractors of iterated function systems such as connectedness, arcwise connectedness and locally arcwise connectedness. We give necessary and sufficient conditions for the attractors of finite iterated function system (IFS) to be a connected sets and in the case when infinite iterated function systems (IIFS) are considered we give only some su...

Abstract: In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of nature or outcomes of scientific experiments that reveal one or more structures embedded in to another. In the construction of SFIF, an IFS is chosen from a pool of several IFSs at each level of iteration leading to implementation of the desired randomnes...

During the last few years, more and more researchers have been applying IFSs to multi-attribute decision making under various different situations, and a lot of work has been done (Chen and Tan 1994; Hong and Choi 2000; Xu and Yager 2006; Boran et al. 2009; Xu 2010a, c; Zhao 2009; Zhao et al. 2010; Tan and Chen 2010; Wei 2010a; Xu and Xia 2012a; Xu and Cai 2010; Wu and Chen 2011, etc.). The con...

We consider a class of iterated function systems (IFSs) of contracting similarities of Rn, introduced by Hutchinson, for which the invariant set possesses a natural Hölder continuous parameterization by the unit interval. When such an invariant set is homeomorphic to an interval, we give necessary conditions in terms of the similarities alone for it to possess a quasisymmetric (and as a corolla...

Abstract The classical TODIM considers the crisp numbers to handle information. However, in a real-world applicative context, this information is bounded by noise and vagueness hence uncertain. There are wide range of works literature which utilizes fuzzy sets uncertainty various dimensions. there constraint hesitancy such decision-making problems due involvement decision-makers. Also, method, ...

Srivastava and Maheshwari (Iranian Journal of Fuzzy Systems 13(1)(2016) 25-44) introduced a new divergence measure for intuitionisticfuzzy sets (IFSs). The properties of the proposed divergence measurewere studied and the efficiency of the proposed divergence measurein the context of medical diagnosis was also demonstrated. In thisnote, we point out some errors in ...

Self-similar fractals arise as the unique attractors of iterated function systems (IFSs) consisting of finitely many contracting similarities satisfying an open set condition. Each point x in such a fractal F arising from an IFS S is naturally regarded as the “outcome” of an infinite coding sequence T (which need not be unique) over the alphabet Σk = {0, . . . , k − 1}, where k is the number of...

The fractal necklaces in R^d (d>1) introduced this paper are a class of connected sets generated by the so-called necklace IFSs, for which lot basic topology questions interesting. We give two subclasses and prove that every these classes has no cut points. Also, we stable self-similar R^2 points, whilst an analog self-affine is false.

Iterated function systems (IFSs) were conceived in the present form by John Hutchinson [4] and popularized by Michael Barnsley [1] and are one of the most common and most general ways to generate fractals. Many of the important examples of sets and functions with special and unusual properties in analysis turn out to be fractal sets or functions whose graph are a fractal sets and a great part o...