Related papers: Fuzzy vectors via convex bodies
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and…
This article explores several fundamental aspects of fuzzy $\mathscr{F}$-metric spaces and their applications in mathematical analysis. We investigate some essential properties concerning compactness and total boundedness in fuzzy…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
Let $V$ be a finite nonempty set. A transit function is a map $R:V\times V\rightarrow 2^V$ such that $R(u,u)=\{u\}$, $R(u,v)=R(v,u)$ and $u\in R(u,v)$ hold for every $u,v\in V$. A set $K\subseteq V$ is $R$-convex if $R(u,v)\subset K$ for…
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…
Fuzzy inference systems always suffer from the lack of efficient structures or platforms for their hardware implementation. In this paper, we tried to overcome this problem by proposing new method for the implementation of those fuzzy…
Fuzzy metric spaces, grounded in t-norms and membership functions, have been widely proposed to model uncertainty in machine learning, decision systems, and artificial intelligence. Yet these frameworks treat uncertainty as an external…
Fuzzy rule-based model is a powerful tool for imitating the human way of thinking and solving uncertainty-related problems as it allows for understandable and interpretable rule bases. The objective of this paper is to study the…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…
This book introduces special classes of Fuzzy and Neutrosophic matrices. These special classes of matrices are used in the construction of multi-expert special fuzzy models using FCM, FRM and FRE and their Neutorosophic analogues…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
We introduce a finite dimensional matrix model approximation to the algebra of functions on a disc based on noncommutative geometry. The algebra is a subalgebra of the one characterizing the noncommutative plane with a * product and depends…
A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly…
This paper develops a complete foundational treatment of simplicial complexes from Euclidean spaces through geometric realizations, emphasizing concrete computations, examples, and practical verification methods. Beginning with finite point…
Intuitionistic fuzzy relations on finite universes can be represent by intuitionistic fuzzy matrices and the limiting behavior of the power matrices depends on the algebraic operation employed on the matrices. In this paper, the power of…
We define floating bodies in the class of $n$-dimensional ball-convex bodies. A right derivative of volume of these floating bodies leads to a surface area measure for ball-convex bodies which we call relative affine surface area. We show…
A convex polygon is defined as a sequence (V_0,...,V_{n-1}) of points on a plane such that the union of the edges [V_0,V_1],..., [V_{n-2},V_{n-1}], [V_{n-1},V_0] coincides with the boundary of the convex hull of the set of vertices…
Motion planning is one of the key modules in autonomous driving systems to generate trajectories for self-driving vehicles to follow. A common motion planning approach is to generate trajectories within semantic safe corridors. The…