Related papers: Probabilistic Foundations of Fuzzy Simplicial Sets…
We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…
In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
Clustering is a central tool in biomedical research for discovering heterogeneous patient subpopulations, where group boundaries are often diffuse rather than sharply separated. Traditional methods produce hard partitions, whereas soft…
Few-shot 3D semantic segmentation aims to generate accurate semantic masks for query point clouds with only a few annotated support examples. Existing prototype-based methods typically construct compact and deterministic prototypes from the…
Real-world data contains a vast amount of multimodal information, among which vision and language are the two most representative modalities. Moreover, increasingly heavier models, \textit{e}.\textit{g}., Transformers, have attracted the…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of…
Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scenarios. This paper studies simplicial distributions on…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
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…
In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in…
Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership…
The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
In this paper, we extend the research presented in [Wang and Zheng, Fuzzy Sets and Systems, p108581, 2023] by establishing the algebraic structure of the Gaussian Probability Density Membership Function (Gaussian-PDMF) space. We consider…
New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and…
This paper presents a novel mathematical framework for phase unwrapping in three-dimensional interferometric ISAR (3D InISAR) imaging. The approach works on a scatterer-by-scatterer basis and does not rely on any spatial continuity…