On the normalization of interval data
Fecha
2020Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
Impacto
|
10.3390/math8112092
Resumen
The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact value will be enclosed in the resulting 'normalized ...
[++]
The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact value will be enclosed in the resulting 'normalized' interval. This paper shows that this approach is not enough since the resulting 'normalized' interval can be even wider than the input intervals. So, we propose a pair of axioms that must be satisfied by an interval arithmetic in order to be applied in the normalization of intervals. We show how some known interval arithmetics behave with respect to these axioms. The paper ends with a discussion about the current paradigm of interval computations. [--]
Materias
Interval arithmetics,
Intervals,
Normalization,
Normalization of interval data,
Partition principle and interval division structures
Editor
MDPI
Publicado en
Mathematics, 2020, 8, 2092
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Versión del editor
Entidades Financiadoras
This study was funded by National Council for Scientific and Technological Development (CNPq) within the project 312053/2018-5, by Coordination for the Improvement of Higher Education Personnel (CAPES) within the project Capes-Print 88887.363001/2019-00. Ministerio de Ciencia y innovación within the project PID2019-108392GB-I00 (AEI/10.13039/501100011033).
Aparece en las colecciones
Los documentos de Academica-e están protegidos por derechos de autor con todos los derechos reservados, a no ser que se indique lo contrario.
La licencia del ítem se describe como © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
Ítems relacionados
Mostrando ítems relacionados por Título, autor o materia.
-
Interval-valued Atanassov intuitionistic OWA aggregations using admissible linear orders and their application to decision making
Miguel Turullols, Laura de ; Bustince Sola, Humberto ; Pekala, Barbara; Bentkowska, Urszula; Silva, Ivanoska da; Bedregal, Benjamin ; Mesiar, Radko; Ochoa Lezaun, Gustavo (IEEE, 2016) Artículo / ArtikuluaBased on the definition of admissible order for interval-valued Atanassov intuitionistic fuzzy sets, we study OWA operators in these sets distinguishing between the weights associated to the membership and those associated ... -
Enhancing the efficiency of the interval-valued fuzzy rule-based classifier with tuning and rule selection
Sanz Delgado, José Antonio ; Asmus, Tiago ; Osa Hernández, Borja de la ; Bustince Sola, Humberto (Springer, 2020) Contribución a congreso / Biltzarrerako ekarpenaInterval-Valued fuzzy rule-based classifier with TUning and Rule Selection, IVTURS, is a state-of-the-art fuzzy classifier. One of the key point of this method is the usage of interval-valued restricted equivalence functions ... -
Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders
Bustince Sola, Humberto ; Marco Detchart, Cedric ; Fernández Fernández, Francisco Javier ; Wagner, Christian; Garibaldi, Jonathan M. (Elsevier, 2020) Artículo / ArtikuluaIn this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; ...