Related papers: Measuring the Directional Distance Between Fuzzy S…
Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In…
Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…
A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the…
We show that distances of objects at cosmological distances can be measured directly using interferometry. Our approach to interferometric parallax comes from analysis of 4-point amplitude and intensity correlations that can be generated…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu-Hausdorff distance, a well-established metric for…
Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…
This paper introduces the notion of fuzzy process as a formalism for the idea of fuzzy contact between a device and its environment. The notions of absolute correctness and relative correctness are defined. In order to work with concurrency…
Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant…
This paper presents a method to measure the similarity between different fuzzy concepts in order to optimize Semantic networks. The problem approached is the minimization of the time of research and identification of user's Objects and…
Impulsive noise is a problem encountered during the acquisition and transmission of digital images. Fuzzy metrics dealing nicely with the nonlinear nature of digital images are used in vector median-based filters for noise reduction in…
Cooperative localization is a promising solution to improve the accuracy and overcome the shortcomings of GNSS. Cooperation is often achieved by measuring the distance between users. To optimally integrate a distance measurement between two…
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
By using directional distance sensors that have unknown locations, this paper proposes a method of estimating the shape of a location-unknown target object $T$ moving with unknown speed on an unknown straight line trajectory. Regardless of…
Graphs serve as efficient tools for visualizing mathematical concepts and their interrelationships. In this paper, focusing on the discrete case with universal set with finite elements, we first introduce the rules and characteristics of…
The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
This paper discusses the properties of the spaces of fuzzy sets in a metric space with $L_p$-type $d_p$ metrics, $p\geq 1$. The $d_p$ metrics are well-defined if and only if the corresponding Haudorff distance functions are measurable. In…