A generating IFS of a Cantor set F is an IFS whose attractor is F . For a given Cantor set such as the middle-3rd Cantor set we consider the set of its generating IFSs. We examine the existence of a minimal generating IFS, i.e. every other generating IFS of F is an iterating of that IFS. We also study the structures of the semi-group of homogeneous generating IFSs of a Cantor set F in R under t...

A comparison between type-1 fuzzy sets (T1FSs) and intuitionistic fuzzy sets (IFSs) is made. The operators defined over IFSs that do not have analogues in T1FSs are shown, and such analogues are introduced whenever possible.

The importance of suitable distance measures between intuitionistic fuzzy sets (IFSs) arises because of the role they play in the inference problem. A concept closely related to one of distance measures is a divergence measure based on the idea of information-theoretic entropy that was first introduced in communication theory by Shannon (1949). It is known that Jdivergence is an important famil...

One of the core tasks of Knowledge Discovery in Databases (KDD) is the mining of association rules. In this paper, truth values of association rules are discussed. Firstly, two knowledge bases of association rules are fixed, i.e., information system A and a fixed association rule (it’s confidence is 1), then based on Intuitionistic fuzzy special sets (IFSS) Representation of Rough Set, IFSS rep...

A new concept of the inclusion measure for intuitionistic fuzzy sets is proposed by the axiomatic definition. Also, the distance measures, similarity measures and information entropy are recalled and summarized. Most of important, some relationships among distance measure, information entropy, and inclusion measure of IFSs are then investigated. Finally, we obtain some important theorems by whi...

This paper presents a new method for similarity measures between intuitionistic fuzzy sets (IFSs). We will present a method to calculate the distance between IFSs on the basis of the Hausdorff distance. We will then use this distance to generate a new similarity measure to calculate the degree of similarity between IFSs. Finally we will prove some properties of the proposed similarity measure a...

This paper presents a genetic algorithm used to infer Iterated Function Systems (IFSs) for approximation of 1D and 2D data sets. First, we give an introduction to IFSs. Secondly, we discuss the encoding of 1D and 2D IFSs in the form of chromosomes, and present genetic operators to work upon these representations. The performance of the genetic algorithm is evaluated on four 1D and two 2D test s...

In this paper, we propose new method to calculate the distance between intuitionistic fuzzy sets (IFSs) based on three dimensional representation of IFSs and analyze relations similarity measure IFSs. Finally, apply proposed measures pattern recognitions.

In 1965, Zadeh introduced the concept of fuzzy subsets. Latter many authors defined different directions of fuzzy subsets. Turksen (1986) generalized the concept of fuzzy set in terms of interval-valued fuzzy set (IVFS). Several researchers present a number of results using IVFSs. Using these concept of (IVFS) Pal and Shyamal (2006) introduced interval-valued fuzzy matrices and shown several pr...