Let us consider two-sorted intuitionistic set theory ZFI2 with sort 0 for natural numbers and sort 1 for sets. We shall show that well-known Church rule with parameters of sort 1 is admissible in ZFI2 in some rather strong sense, and get from this point the admissibility of Markov rule with all parameters in ZFI2, and also DP and numerical EP with set parameters for it in the same sense.

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and...

In this paper, a new intuitionistic fuzzy model for images based on the HSV color histogram is proposed. The image can be treated as an Attanassov’s intuitionistic fuzzy set (IFS) with this new model. A new and simple calculation of similarity measurement called IFSL1 based on similarity measurement of intuitionistic fuzzy set L1 is presented. Unlike general fuzzy similarity measure that consid...

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X,R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approxima...

Introduction Clustering is one of the unsupervised segmentation methods for the partitioning of image into different parts having some homogeneous features. Uncertain information is presented in medical images due impreciseness and fuzziness of pixels and edges [1]. However, due to the uncertainty and complexity of images, clustering is commonly used to segment the images into different cluster...

In this paper the concept of interval valued intuitionistic fuzzy soft set relations (IVIFSS-relations for short) is proposed. Our relations on interval valued intuitionistic fuzzy soft sets is an extension of the relations on intuitionistic fuzzy soft sets, introduced by Mukherjee and Chakraborty in 2009. The basic properties of the IVIFSS-relations are also presented and discussed. It is seen...

In this paper, three new operations are introduced on intuitionistic fuzzy soft sets .They are based on concentration, dilatation and normalization of intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.