scholarly journals Aggregation of Weak Fuzzy Norms

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1908
Author(s):  
Tatiana Pedraza ◽  
Jorge Ramos-Canós ◽  
Jesús Rodríguez-López
Keyword(s):  
Vector Space ◽  
Mathematical Structures ◽  
Aggregation Functions ◽  
Mathematical Process

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions.

scholarly journals Duals of Feynman integrals. Part I. Differential equations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Simon Caron-Huot ◽  
Andrzej Pokraka
Keyword(s):  
Differential Equations ◽  
Vector Space ◽  
Systematic Approach ◽  
Intersection Number ◽  
Spacetime Dimension ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Mathematical Structures ◽  
Algebraic Invariant ◽  
Dual Forms

Abstract We elucidate the vector space (twisted relative cohomology) that is Poincaré dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces — an algebraic invariant called the intersection number — extracts integral coefficients for a minimal basis, bypassing the generation of integration-by-parts identities. Dual forms turn out to be much simpler than their Feynman counterparts: they are supported on maximal cuts of various sub-topologies (boundaries). Thus, they provide a systematic approach to generalized unitarity, the reconstruction of amplitudes from on-shell data. In this paper, we introduce the idea of dual forms and study their mathematical structures. As an application, we derive compact differential equations satisfied by arbitrary one-loop integrals in non-integer spacetime dimension. A second paper of this series will detail intersection pairings and their use to extract integral coefficients.

scholarly journals Fuzzy autocatalytic set (FACS) as fuzzy vector space

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Rossiana Edhelyn ◽  
Tahir Ahmad
Keyword(s):  
Vector Space ◽  
Euclidean Distance ◽  
Waste Incineration ◽  
Fuzzy Graph ◽  
Mathematical Structures ◽  
Laplacian Matrices ◽  
Graph Type ◽  
Euclidean Distance Matrices ◽  
Type 3 ◽  
Fuzzy Vector

Dynamic model of clinical waste incineration process in Malacca has been successfully developed using Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type 3. FACS combines the concept of fuzzy graph and autocatalytic set and has been proven to yield more precise results than using crisp graph. Next, the graph of its process has been transformed from non-coordinated FACS to coordinated FACS in Euclidean space. Some mathematical structures related to the transformation are adjacency, transition and Laplacian matrices of FACS. Furthermore, it is found that FACS to be primitive, irreducible and aperiodic. The set of adjacency matrices of FACS of Fuzzy Graph Type 3 is predicted to be seen as fuzzy vector space, and the set of Euclidean distance matrices represent coordinated FACS is also expected to be fuzzy vector space as well. As a recently developed theory, FACS has great capabilities in generating new mathematical theories and structures that would enrich the theory itself. this study is made to attempt the formulation of new algebraic structure in FACS which is fuzzy vector space.

Aggregation Functions

2009 ◽  
Author(s):  
Michel Grabisch ◽  
Jean-Luc Marichal ◽  
Radko Mesiar ◽  
Endre Pap
Keyword(s):  
Aggregation Functions

On Semi - Pre irresolute Topological Vector Space

2018 ◽  
Vol 14 (3) ◽  
pp. 184-192
Author(s):  
Radhi Ali ◽  
◽  
Jalal Hussein Bayati ◽  
Suhad Hameed
Keyword(s):  
Vector Space ◽  
Topological Vector Space

AGGREGATION FUNCTIONS WITH NON-MONOTONIC MEASURES

2008 ◽  
Vol 13 (02) ◽  
Author(s):  
Marta Cardin ◽  
Silvio Giove
Keyword(s):  
Aggregation Functions

Aplikasi Deteksi Kemiripan Tugas Paper

2017 ◽  
Vol 15 (2) ◽  
pp. 5
Author(s):  
Anthony Anggrawan ◽  
Azhari
Keyword(s):  
Information Retrieval ◽  
Vector Space ◽  
Vector Space Model ◽  
Mean Average Precision ◽  
Average Precision ◽  
Information Searching ◽  
Space Model ◽  
Model Method

Information searching based on users’ query, which is hopefully able to find the documents based on users’ need, is known as Information Retrieval. This research uses Vector Space Model method in determining the similarity percentage of each student’s assignment. This research uses PHP programming and MySQL database. The finding is represented by ranking the similarity of document with query, with mean average precision value of 0,874. It shows how accurate the application with the examination done by the experts, which is gained from the evaluation with 5 queries that is compared to 25 samples of documents. If the number of counted assignments has higher similarity, thus the process of similarity counting needs more time, it depends on the assignment’s number which is submitted.

Unifying Bayesian Inference and Vector Space Models for Improved Decipherment

2015 ◽  
Author(s):  
Qing Dou ◽  
Ashish Vaswani ◽  
Kevin Knight ◽  
Chris Dyer
Keyword(s):  
Bayesian Inference ◽  
Vector Space ◽  
Vector Space Models

Aplikasi Rekomendasi Buku Pada Katalog Perpustakaan Universitas Multimedia Nusantara Menggunakan Vector Space Model

2018 ◽  
Vol 9 (2) ◽  
pp. 97-105
Author(s):  
Richard Firdaus Oeyliawan ◽  
Dennis Gunawan
Keyword(s):  
Vector Space ◽  
Vector Space Model ◽  
Vector Model ◽  
Library Management ◽  
Space Model ◽  
Library Management System ◽  
Index Terms ◽  
Library Catalogue ◽  
Language Sample ◽  
F Measure

Library is one of the facilities which provides information, knowledge resource, and acts as an academic helper for readers to get the information. The huge number of books which library has, usually make readers find the books with difficulty. Universitas Multimedia Nusantara uses the Senayan Library Management System (SLiMS) as the library catalogue. SLiMS has many features which help readers, but there is still no recommendation feature to help the readers finding the books which are relevant to the specific book that readers choose. The application has been developed using Vector Space Model to represent the document in vector model. The recommendation in this application is based on the similarity of the books description. Based on the testing phase using one-language sample of the relevant books, the F-Measure value gained is 55% using 0.1 as cosine similarity threshold. The books description and variety of languages affect the F-Measure value gained. Index Terms—Book Recommendation, Porter Stemmer, SLiMS Universitas Multimedia Nusantara, TF-IDF, Vector Space Model

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