Related papers: Fuzzy vectors via convex bodies

Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…

In this paper we provide a general setting to deal with level continuous fuzzy-valued functions. Namely, we embed such functions into a product of spaces of real-valued functions of two variables satisfying certain types of left-continuity,…

$n$-Dimensional fuzzy sets are a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] increasingly ordered, called n-dimensional intervals. The set of n-dimensional intervals is denoted by…

Guided by ordinary quantum mechanics we introduce new fuzzy spheres of dimensions d=1,2: we consider an ordinary quantum particle in D=d+1 dimensions subject to a rotation invariant potential well V(r) with a very sharp minimum on a sphere…

We present a novel heuristic approach that defines fuzzy geographical descriptors using data gathered from a survey with human subjects. The participants were asked to provide graphical interpretations of the descriptors `north' and `south'…

A statistical, data-driven method is presented that quantifies influences between variables of a dynamical system. The method is based on finding a suitable representation of points by fuzzy affiliations with respect to landmark points…

A systematic approach has been developed to encompass the Minkowski-type extension of Euclidean geometry such that a one-vector anisotropy is permitted, retaining simultaneously the concept of angle. For the respective geometry, the…

Let $X$ be a linear space over a field $\mathbb{K}$ and $(X, \rho, *)$ a fuzzy seminorm space where $(\rho, *)$ a fuzzy seminorm with $*$ a continuous $t$-norm. We give a fixed point theorem for Fuzzy Locally Convex Space.

We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.

In this paper, the notion of convexity of picture fuzzy multisets was introduced and some of their properties were presented after studying the concept of picture fuzzy multisets.

We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify…

In a work by Artstein-Avidan and Milman the concept of polarity is generalized from the class of convex bodies to the larger class of convex functions. While the only self-polar convex body is the Euclidean ball, it turns out that there are…

We prove Gaussian approximation theorems for specific $k$-dimensional marginals of convex bodies which possess certain symmetries. In particular, we treat bodies which possess a 1-unconditional basis, as well as simplices. Our results…

The equichordal point problem is a classical question in geometry, asking whether there exist multiple equichordal points within a single convex body. An equichordal point is defined as a point through which all chords of the convex body…

We obtain a sharp characterization of the Euclidean ball among all convex bodies K whose boundary has a pointwise k-th mean curvature not smaller than a geometric constant at almost all normal points. This geometric constant depends only on…

In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on…

Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…

In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is…

We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…

Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…