in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

Environmental Performance Index (EPI) has been introduced since 2006 to depict the environmental performance for most of the countries in the world. The index considers ten policy categories associated with environmental public health and ecosystem sustainability. The main mathematics operation in establishing EPI is arithmetic mean of all ten policy categories. However, this operation carries ...

In this paper, we investigate the multiple attribute decision making (MADM) problems for for evaluating the computer network security with interval-valued intuitionistic fuzzy information. To determine the attribute weights, a model based on the information entropy, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted ave...

This paper presents a comparison of the three fuzzy based image segmentation methods namely Fuzzy C-Means (FCM), TYPE-II Fuzzy C-Means (T2FCM), and Intuitionistic Fuzzy C-Means (IFCM) for digital images with varied levels of noise. Apart from qualitative performance, the paper also presents quantitative analysis of these three algorithms using four validity functions-Partition coefficient (Vpc)...

A conventional fuzzy cmeans (FCM) clustering algorithm did not use the spatial information of the data and is very much sensitive to noise. To improve the noise sensitivity of FCM, Spatial FCM (SFCM) incorporates the spatial information to improve the results. Intuitionistic fuzzy sets introduce hesitation factor in the fuzzy sets to enhance the performance of fuzzy sets and also added entropy ...

In this paper, we propose new methods to represent interdependence among alternative attributes and experts’ opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interva...

We propose a new measure of entropy for intuitionistic fuzzy sets. This paper is in a sense a continuation of our previous paper on entropy of intuitionistic fuzzy sets — the inferences are based on the same two types of distances as previously — to the farer and to the nearer crisp elements. But now we propose the formulas easier to calculate. Next, we show that the same result can be obtained...

In this paper, we proposed an algorithm to find the optimal threshold value for denoising an image. A new cost function is designed to find the optimal threshold in every image. The cost function is based on the intuitionistic fuzzy divergence measure of the denoised image and original image. In addition, the intuitionistic fuzzy entropy of denoised image is added to the cost function. This is ...