Möbius product-based constructions of aggregation functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616921" target="_blank" >RIV/61989592:15310/22:73616921 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011422000033" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011422000033</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2022.01.002" target="_blank" >10.1016/j.fss.2022.01.002</a>
Alternative languages
Result language
angličtina
Original language name
Möbius product-based constructions of aggregation functions
Original language description
Möbius transforms of capacities or games were considered as a tool for extensions of capacities to particular aggregation functions in several papers. This is, for example, the case of the Lovasz extension coinciding with the Choquet integral, or the Owen extension that is also known as multilinear extension. In this paper, a much deeper study of the links between the M delta bius transforms of real-valued functions defined on finite bounded posets and aggregation functions is performed. We introduce a M delta bius product of any two real-valued functions defined on an arbitrary finite bounded poset, and then, fixing the poset (2N, subset of), N = {1, ... , n}, we propose and discuss a construction method for n-ary aggregation functions based on the M delta bius product of any capacity on N and a real-valued function gx, x is an element of [0, 1]n, defined on 2N and determined by some appropriate n-ary aggregation function. We provide some necessary and some sufficient conditions for the introduced construction to yield an aggregation function for any capacity. For the binary case, a complete characterization of conditions under which our approach results in an aggregation function for each capacity m is given.
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
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SETS AND SYSTEMS
ISSN
0165-0114
e-ISSN
1872-6801
Volume of the periodical
448
Issue of the periodical within the volume
SI
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
18
Pages from-to
17-34
UT code for WoS article
000862759400002
EID of the result in the Scopus database
2-s2.0-85123719214