Related papers: Roughness and entropy measures of a soft set

Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…

This work considers the problem of estimating the unscaled relative positions of a multi-robot team in a common reference frame from bearing-only measurements. Each robot has access to a relative bearing measurement taken from the local…

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 the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably…

In this paper, we study Borel probability measures of maximal entropy for analytic subsets in a dynamical system. It is well known that higher smoothness of the map over smooth space plays important role in the study of invariant measures…

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…

The rapid development of machine learning (ML) and artificial intelligence (AI) applications requires the training of large numbers of models. This growing demand highlights the importance of training models without human supervision, while…

Rough Set based Spanning Sets were recently proposed to deal with uncertainties arising in the problem in domain of natural language processing problems. This paper presents a novel span measure using upper approximations. The key…

We present a new approach to learn compressible representations in deep architectures with an end-to-end training strategy. Our method is based on a soft (continuous) relaxation of quantization and entropy, which we anneal to their discrete…

Robustness is often regarded as a critical future challenge for real-world applications, where stability is essential. However, as models often learn tasks in a similar order, we hypothesize that easier tasks will be easier regardless of…

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…

This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…

Fault tolerance is a critical aspect of modern computing systems, ensuring correct functionality in the presence of faults. This paper presents a comprehensive survey of fault tolerance methods and software-based mitigation techniques in…

We introduce the notion of strong embeddability for a metric space. This property lies between coarse embeddability and property A. A relative version of strong embeddability is developed in terms of a family of set maps on the metric…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…

Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…

The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct…