Related papers: Roughness and entropy measures of a soft set

Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…

Deep neural networks (DNNs) are increasingly used in real-world applications (e.g. facial recognition). This has resulted in concerns about the fairness of decisions made by these models. Various notions and measures of fairness have been…

This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust…

Various soft materials share some common features, such as significant entropic effect, large fluctuations, sensitivity to thermodynamic conditions, and mesoscopic characteristic spatial and temporal scales. However, no quantitative…

In recent years, there has been significant attention given to the robustness assessment of neural networks. Robustness plays a critical role in ensuring reliable operation of artificial intelligence (AI) systems in complex and uncertain…

This paper proposes Expected Confidence Dependency (ECD), a novel, soft computing-oriented, accuracy driven dependency measure for feature selection within the rough set theory framework. Unlike traditional rough set dependency measures…

We turn the definition of individual fairness on its head---rather than ascertaining the fairness of a model given a predetermined metric, we find a metric for a given model that satisfies individual fairness. This can facilitate the…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…

Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…

In this paper, we study the robustness of safety properties of a linear dynamical system with respect to model uncertainties. Our paper involves three parts. In the first part, we provide symbolic (analytical) and numerical (representation…

Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet…

Metric learning has attracted a lot of interest over the last decade, but the generalization ability of such methods has not been thoroughly studied. In this paper, we introduce an adaptation of the notion of algorithmic robustness…

Molodtsov \cite{molodtsov-1999} proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Sabir and Naz \cite{shabir-2013} defined notion of bipolar soft…

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…

In deep learning applications, robustness measures the ability of neural models that handle slight changes in input data, which could lead to potential safety hazards, especially in safety-critical applications. Pre-deployment assessment of…

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…

For a fixed topological Markov shift, we consider measure-preserving dynamical systems of Gibbs measures for 2-locally constant functions on the shift. We also consider isomorphisms between two such systems. We study the set of all…

For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features.…