From arithmetics of extensional fuzzy numbers to their distances

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA21023N1" target="_blank" >RIV/61988987:17610/20:A21023N1 - isvavai.cz</a>

Result on the web

<a href="https://ieeexplore.ieee.org/document/9177594" target="_blank" >https://ieeexplore.ieee.org/document/9177594</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/FUZZ48607.2020.9177594" target="_blank" >10.1109/FUZZ48607.2020.9177594</a>

Result language

angličtina

Original language name

From arithmetics of extensional fuzzy numbers to their distances

Original language description

The notion of the metric space that allows to measure a distance between objects of the given space, has a crucial importance for distinct parts of mathematics, for instance, for the approximation theory, interpolation methods, data analysis, optimization etc. In fuzzy mathematics, the same areas of applications have an analogous importance and thus, not surprisingly measuring the distance between objects possesses a desirable importance. In many cases, e.g., in fuzzy clustering, the use of the standard metric spaces is absolutely sufficient. However, if we deal with vague quantities represented by fuzzy numbers, though the application of a standard metric to fuzzy numbers is mathematically correct, it may lead to counterintuitive and undesirable results. Our investigation constructs the 'metric-like' spaces enabling to measure the distance between two fuzzy numbers in a way that is not disconnected from the used arithmetic of fuzzy numbers. Following the analogy from the classical math where the most natural distance between two numbers is the absolute value of their difference, in the case of fuzzy numbers and under the assumption that the distance is connected to the arithmetic, the most natural distance of two fuzzy numbers is the absolute values of their difference too. But then, naturally, the distance should map fuzzy numbers again to fuzzy numbers, not to crisp numbers. This article is a contribution to this area that guides readers from the fundamental notions to the final construction supported by some theoretical results.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

IEEE Conference on Fuzzy Systems

ISBN

978-172816932-3

ISSN

1098-7584

e-ISSN

1558-4739

Number of pages

8

Pages from-to

1-8

Publisher name

IEEE

Place of publication

Glasgow

Event location

Glasgow

Event date

Jan 1, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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