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Fuzzy vault is a scheme providing secure authentication based on fuzzy matching of sets. A major application is the use of biometric features for authentication, whereby unencrypted storage of these features is not an option because of…
Combinatorics studies how discrete objects can be counted, arranged, and combined under specified rules. Motivated by uncertainty in real-world data and decisions, modern set-theoretic formalisms such as fuzzy sets, neutrosophic sets, rough…
We study regular inclusions of finite-dimensional von Neumann algebras from a matrix-theoretic perspective. To this end, we introduce a new combinatorial invariant of an inclusion, called the normalizer matrix, which encodes the structure…
A fuzzy theoretic analytical approach was recently introduced that leads to efficient and robust models while addressing automatically the typical issues associated to parametric deep models. However, a formal conceptualization of the fuzzy…
Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic…
Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…
Embedding methods have achieved success in face recognition by comparing facial features in a latent semantic space. However, in a fully unconstrained face setting, the facial features learned by the embedding model could be ambiguous or…
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…
The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control…
Maji et al. introduced in 2002 a method of parametric decision making using soft sets as tools and representing their tabular form as a binary matrix. In cases, however, where some or all of the parameters used for the characterization of…
Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…
We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of…
Interval Pairwise Comparison Matrices have been widely used to account for uncertain statements concerning the preferences of decision makers. Several approaches have been proposed in the literature, such as multiplicative and fuzzy…
In this paper, we introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated basic properties of it.…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
Universal machine learning interatomic potentials (uMLIPs) are reshaping atomistic simulation as foundation models, delivering near \textit{ab initio} accuracy at a fraction of the cost. Yet the lack of reliable, general uncertainty…
Diffusion models learn to reverse the progressive noising of a data distribution to create a generative model. However, the desired continuous nature of the noising process can be at odds with discrete data. To deal with this tension…
This paper initiates the study of picture fuzzy topological spaces. In order to develop a mechanism to construct picture fuzzy topological spaces, we prove some basic results related to picture fuzzy sets together with the introduction of…
Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied…
We show how hadronic bag models can be generalized to implement effects of a smooth and extended boundary. Our approach is based on fuzzy set theory and can be straightforwardly applied to any type of bag model. We illustrate the underlying…