Related papers: Set Linear Algebra and Set Fuzzy Linear Algebra
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For example, in the field of 3D modeling, subsets of Euclidean space can be embedded as vectors using implicit neural…
Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior…
Graph theory has successfully used to solve a wide range of problems encountered in diverse fields such as medical sciences, neural networks, control theory, transportation, clustering analysis, expert systems, image capturing, and network…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…
Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is…
Most existing fuzzy set methods use points as their input, which is the finest granularity from the perspective of granular computing. Consequently, these methods are neither efficient nor robust to label noise. Therefore, we propose a…
Vector-space representations provide geometric tools for reasoning about the similarity of a set of objects and their relationships. Recent machine learning methods for deriving vector-space embeddings of words (e.g., word2vec) have…
Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised quantifiers for natural language. That technique requires one to construct the vector space…
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
Researchers are actively trying to gain better insights into the representational properties of convolutional neural networks for guiding better network designs and for interpreting a network's computational nature. Gaining such insights…
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric…
This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the…
For the first time we represent every finite group in the form of a graph in this book. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group.…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
Taxonomy Expansion, which models complex concepts and their relations, can be formulated as a set representation learning task. The generalization of set, fuzzy set, incorporates uncertainty and measures the information within a semantic…
In this talk I will introduces two spaces: the first space is the usual n-dimensional vector space with the unusual feature that n is non-integer, the second space is composed by the linear matrices acting on the previous space (physicists…
The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial…
In this book, the authors introduce the new notion of superbimatrices and generalize it to supertrimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerize…