Möbius product-based constructions of aggregation functions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Möbius product-based constructions of aggregation functions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Möbius product-based constructions of aggregation functions

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

FUZZY SETS AND SYSTEMS

ISSN

0165-0114

e-ISSN

1872-6801

Svazek periodika

448

Číslo periodika v rámci svazku

SI

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

17-34

Kód UT WoS článku

000862759400002

EID výsledku v databázi Scopus

2-s2.0-85123719214