based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. further...

In this paper we will analyze discrete probability distributions in which probabilities of particular outcomes of some experiment (microstates) can be represented by the ratio of natural numbers (in other words, probabilities are represented by digital numbers of finite representation length). We will introduce several results that are based on recently proposed JoyStick Probability Selector, w...

0. Summary. This paper is concerned with the properties of convex cones and their dual cones generated by points randomly distributed on the surface of a d-sphere. For radially symmetric distributions on the points, the expected nGmber of k-faces and natural measure of the set of k-faces will be found. The expected number of vertices, or extreme points, of convex hulls of random points in E~ an...

Sensors typically have limited power of transmission. Thus desired connectivity probability (CP) between the sensors is critical in the given deployment area. The paper presents a novel approach for analysing the lower bound of CP for sensor networks under uniformly distribution of the sensors in a given area. Initially, the area is divided into a grid (mesh) of blocks. The CP for each small bl...

The probabilistic prediction of quantum theory is mystery. I solved the mystery by a geometrical interpretation of a wave function. This suggests the unification between quantum theory and the theory of relativity. This suggests Many-Worlds Interpretation is true,too.

One way of recovering watermarks in geometrically distorted images is by performing a geometrical search. In addition to the computational cost required for this method, this paper considers the more important problem of false positives. The maximal number of detections that can be performed in a geometrical search is bounded by the maximum false positive detection probability required by the w...

The quantum analogue of the classical characteristic function for a spin 1/2 assembly is considered and the probability mass function of the random vector associated with the assembly is derived. It is seen that the positive regions of Wigner and Margenau-Hill quasi distributions for the three components of spin, correspond to a trivariate probability mass function. We identify the domain of th...

Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further...

A divergence function measures how different two points are in a base space. Well-known examples are the Kullback-Leibler divergence and f-divergence, which are defined in a manifold of probability distributions. The Bregman divergence is used in a more general situation. The present paper characterizes the geometrical structure which a divergence function gives, and proves that the fdivergence...