# A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case

Fateme Kouchakinejad; Alexandra Šipošová

Kybernetika (2017)

- Issue: 1, page 129-136
- ISSN: 0023-5954

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topKouchakinejad, Fateme, and Šipošová, Alexandra. "A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case." Kybernetika (2017): 129-136. <http://eudml.org/doc/287943>.

@article{Kouchakinejad2017,

abstract = {For an aggregation function $A$ we know that it is bounded by $A^*$ and $A_*$ which are its super-additive and sub-additive transformations, respectively. Also, it is known that if $A^*$ is directionally convex, then $A=A^*$ and $A_*$ is linear; similarly, if $A_*$ is directionally concave, then $A=A_*$ and $A^*$ is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively.},

author = {Kouchakinejad, Fateme, Šipošová, Alexandra},

journal = {Kybernetika},

keywords = {aggregation function; overrunning and underrunning property; sub-additive and super-additive transformation},

language = {eng},

number = {1},

pages = {129-136},

publisher = {Institute of Information Theory and Automation AS CR},

title = {A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case},

url = {http://eudml.org/doc/287943},

year = {2017},

}

TY - JOUR

AU - Kouchakinejad, Fateme

AU - Šipošová, Alexandra

TI - A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case

JO - Kybernetika

PY - 2017

PB - Institute of Information Theory and Automation AS CR

IS - 1

SP - 129

EP - 136

AB - For an aggregation function $A$ we know that it is bounded by $A^*$ and $A_*$ which are its super-additive and sub-additive transformations, respectively. Also, it is known that if $A^*$ is directionally convex, then $A=A^*$ and $A_*$ is linear; similarly, if $A_*$ is directionally concave, then $A=A_*$ and $A^*$ is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively.

LA - eng

KW - aggregation function; overrunning and underrunning property; sub-additive and super-additive transformation

UR - http://eudml.org/doc/287943

ER -

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