Related papers: An Embedding Lemma in Soft Topological Spaces
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We present a construction of the soft $T_{0}$ reflection of a soft topological space and characterize some separation axioms developed through the soft $T_{0}$ reflection.
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…
We have revised the softness property introduced by J\"org Brendle and Haim Judah (perfect sets of random reals. Israel J. Math., 83(1-2):153-176, 1993), to present a new definition of a class of posets called $\sigma$-soft-linked. Our work…
In this paper we propose and study the novel problem of explaining node embeddings by finding embedded human interpretable subspaces in already trained unsupervised node representation embeddings. We use an external knowledge base that is…
Rough set theory is one of the most widely used and significant approaches for handling incomplete information. It divides the universe in the beginning and uses equivalency relations to produce blocks. Numerous generalized rough set models…
The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V. V. Chistyakov, Metric modulars and their application, Dokl.…
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…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
It was shown by F. Low in the 1950s that the subleading terms of soft photon S-matrix elements obey a universal linear relation. In this paper we give a new interpretation to this old relation, for the case of massless QED, as an…
This article focuses on the study of Word Embedding, a feature-learning technique in Natural Language Processing that maps words or phrases to low-dimensional vectors. Beginning with the linguistic theories concerning contextual…
Semantic Embeddings are a popular way to represent knowledge in the field of zero-shot learning. We observe their interpretability and discuss their potential utility in a safety-critical context. Concretely, we propose to use them to add…
Within Bishop Set Theory, a reconstruction of Bishop's theory of sets, we study the so-called completely separated sets, that is sets equipped with a positive notion of an inequality, induced by a given set of real-valued functions. We…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.