On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights
The result's identifiers
Result code in 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>
Alternative codes found
RIV/26867184:_____/21:N0000009
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Iranian Journal of Fuzzy Systems
ISSN
1735-0654
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
4
Country of publishing house
IR - IRAN, ISLAMIC REPUBLIC OF
Number of pages
17
Pages from-to
1-17
UT code for WoS article
000654276900001
EID of the result in the Scopus database
2-s2.0-85107621684