On - associated comonotone functions
Kybernetika (2018)
- Volume: 54, Issue: 2, page 268-278
- ISSN: 0023-5954
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topHutník, Ondrej, and Pócs, Jozef. "On $\star $- associated comonotone functions." Kybernetika 54.2 (2018): 268-278. <http://eudml.org/doc/294259>.
@article{Hutník2018,
abstract = {We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to $+$-associatedness of functions (as proved by Boczek and Kaluszka), but also to their $\star $-associatedness with $\star $ being an arbitrary strictly monotone and right-continuous binary operation. The second open problem deals with an existence of a pair of binary operations for which the generalized upper and lower Sugeno integrals coincide. Using a fairly elementary observation we show that there are many such operations, for instance binary operations generated by infima and suprema preserving functions.},
author = {Hutník, Ondrej, Pócs, Jozef},
journal = {Kybernetika},
keywords = {comonotone functions; binary operation; $\star $-associatedness; Sugeno integral},
language = {eng},
number = {2},
pages = {268-278},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On $\star $- associated comonotone functions},
url = {http://eudml.org/doc/294259},
volume = {54},
year = {2018},
}
TY - JOUR
AU - Hutník, Ondrej
AU - Pócs, Jozef
TI - On $\star $- associated comonotone functions
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 2
SP - 268
EP - 278
AB - We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to $+$-associatedness of functions (as proved by Boczek and Kaluszka), but also to their $\star $-associatedness with $\star $ being an arbitrary strictly monotone and right-continuous binary operation. The second open problem deals with an existence of a pair of binary operations for which the generalized upper and lower Sugeno integrals coincide. Using a fairly elementary observation we show that there are many such operations, for instance binary operations generated by infima and suprema preserving functions.
LA - eng
KW - comonotone functions; binary operation; $\star $-associatedness; Sugeno integral
UR - http://eudml.org/doc/294259
ER -
References
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