On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73607791" target="_blank" >RIV/61989592:15310/21:73607791 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/26867184:_____/21:N0000009

Výsledek na webu

<a href="https://ijfs.usb.ac.ir/article_6173_97e5e9d3db17c8b02c64af90288bbd34.pdf" target="_blank" >https://ijfs.usb.ac.ir/article_6173_97e5e9d3db17c8b02c64af90288bbd34.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.22111/ijfs.2021.6173" target="_blank" >10.22111/ijfs.2021.6173</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights

Popis výsledku v původním jazyce

Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for aggregation operators - identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples.

Název v anglickém jazyce

On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights

Popis výsledku anglicky

Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for aggregation operators - identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Iranian Journal of Fuzzy Systems

ISSN

1735-0654

e-ISSN

—

Svazek periodika

18

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

IR - Íránská islámská republika

Počet stran výsledku

17

Strana od-do

1-17

Kód UT WoS článku

000654276900001

EID výsledku v databázi Scopus

2-s2.0-85107621684