On the relationship between possibilistic and standard moments of fuzzy numbers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15210%2F22%3A73617951" target="_blank" >RIV/61989592:15210/22:73617951 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0377042722001145?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042722001145?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2022.114276" target="_blank" >10.1016/j.cam.2022.114276</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the relationship between possibilistic and standard moments of fuzzy numbers

Popis výsledku v původním jazyce

In this paper we introduce a transformation of the center of gravity, variance and higher moments of fuzzy numbers into their possibilistic counterparts. We show that this transformation applied to the standard formulae for the computation of the center of gravity, variance, and higher moments of fuzzy numbers gives the same formulae for the computation of possibilistic moments of fuzzy numbers that were introduced by Carlsson and Fullér (2001) for the possibilistic mean and variance, and also the formulae for the calculation of higher possibilistic moments as presented by Saeidifar and Pasha (2009). We also present an inverse transformation to derive the formulae for standard measures of central tendency, dispersion, and higher moments of fuzzy numbers, from their possibilistic counterparts. This way a two-way transition between the standard and the possibilistic moments of fuzzy numbers is enabled. The transformation theorems are proven for a wide family of fuzzy numbers with continuous, piecewise monotonic membership functions. Fast computation formulae for the first four possibilistic moments of fuzzy numbers are also presented for linear fuzzy numbers, their concentrations and dilations.

Název v anglickém jazyce

On the relationship between possibilistic and standard moments of fuzzy numbers

Popis výsledku anglicky

In this paper we introduce a transformation of the center of gravity, variance and higher moments of fuzzy numbers into their possibilistic counterparts. We show that this transformation applied to the standard formulae for the computation of the center of gravity, variance, and higher moments of fuzzy numbers gives the same formulae for the computation of possibilistic moments of fuzzy numbers that were introduced by Carlsson and Fullér (2001) for the possibilistic mean and variance, and also the formulae for the calculation of higher possibilistic moments as presented by Saeidifar and Pasha (2009). We also present an inverse transformation to derive the formulae for standard measures of central tendency, dispersion, and higher moments of fuzzy numbers, from their possibilistic counterparts. This way a two-way transition between the standard and the possibilistic moments of fuzzy numbers is enabled. The transformation theorems are proven for a wide family of fuzzy numbers with continuous, piecewise monotonic membership functions. Fast computation formulae for the first four possibilistic moments of fuzzy numbers are also presented for linear fuzzy numbers, their concentrations and dilations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50202 - Applied Economics, Econometrics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

1879-1778

Svazek periodika

411

Číslo periodika v rámci svazku

September 2022

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

1-14

Kód UT WoS článku

000806181600002

EID výsledku v databázi Scopus

2-s2.0-85127779802