Related papers: Projection depth and $L^r$-type depths for fuzzy r…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
A graphical tool for investigating unimodality of hyperspherical data is proposed. It is based on the notion of statistical data depth function for directional data which extends the univariate concept of rank. Firstly a local version of…
We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer…
This study leverages the data representation capability of fuzzy based membership-mappings for practical secure distributed deep learning using fully homomorphic encryption. The impracticality issue of secure machine (deep) learning with…
Starting with Tukey's pioneering work in the 1970's, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensional data, functional data, and manifold-valued data. In…
Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…
We propose learning a depth covariance function with applications to geometric vision tasks. Given RGB images as input, the covariance function can be flexibly used to define priors over depth functions, predictive distributions given…
Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments,…
The simplicial depth, like other relevant multivariate statistical data depth functions, vanishes right outside the convex hull of the support of the distribution with respect to which the depth is computed. This is problematic when it is…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
In this paper, we introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions and we study the existence of the fuzzy equilibrium. As applications, two types of results are obtained. The first ones…
The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modeling. While…
This paper presents a fuzzy system approach to the prediction of nonlinear time-series and dynamical systems. To do this, the underlying mechanism governing a time-series is perceived by a modified structure of a fuzzy system in order to…
We present a holistic, topology-based visualization technique for spatial time series data based on an adaptation of Fuzzy Contour Trees. Common analysis approaches for time dependent scalar fields identify and track specific features. To…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
The purpose of this paper is to study a non-convex fuzzy multi-objective quadratic programming problem, in which both the technological coefficients and resources are fuzzy with nonlinear membership function. A computational procedure to…
Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle…
The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a…