Related papers: Probabilistic Foundations of Fuzzy Simplicial Sets…
The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear…
We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
Recently Shah et al., 2020 pointed out the pitfalls of the simplicity bias - the tendency of gradient-based algorithms to learn simple models - which include the model's high sensitivity to small input perturbations, as well as sub-optimal…
A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions.
In 2006 we proposed Quantum Fuzzy Sets, observing that states of a quantum register could serve as characteristic functions of fuzzy subsets, embedding Zadeh's unit interval into the Bloch sphere. That paper was deliberately preliminary. In…
Reasoning about the pose, i.e. position and orientation of objects is one of the cornerstones of robotic manipulation under uncertainty. In a number of joint research projects our group is developing a robotic perception system that…
Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary invariant norm and the indicator function of an upper bounding rank…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a…
Recent work in machine learning for information extraction has focused on two distinct sub-problems: the conventional problem of filling template slots from natural language text, and the problem of wrapper induction, learning simple…
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
The nature of an atom in a bonded structure -- such as in molecules, in nanoparticles or solids, at surfaces or interfaces -- depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with…
In this paper, We have introduced a new class of sequences of fuzzy numbers defined by using modulus function and generalized weighted mean over the class defined in \cite{OS}. We have proved that this class form a quasilinear complete…
In the rapidly evolving educational landscape, the unbiased assessment of soft skills is a significant challenge, particularly in higher education. This paper presents a fuzzy logic approach that employs a Granular Linguistic Model of…
Impulsive noise is a problem encountered during the acquisition and transmission of digital images. Fuzzy metrics dealing nicely with the nonlinear nature of digital images are used in vector median-based filters for noise reduction in…