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

Fateme Kouchakinejad; Alexandra Šipošová

Kybernetika (2017)

  • Volume: 53, Issue: 1, page 129-136
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Kouchakinejad, Fateme, and Šipošová, Alexandra. "A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case." Kybernetika 53.1 (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},
volume = {53},
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
VL - 53
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 -

References

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  10. Šipošová, A., 10.1016/j.fss.2015.10.008, Fuzzy Sets and Systems 299 (2016), 98-104. MR3510879DOI10.1016/j.fss.2015.10.008
  11. Šipošová, A., Šipeky, L., On aggregation functions with given superadditive and subadditive transformations., In: Congress on Information Technology, Computational and Experimental Physics, Krakow (Poland) 2015, pp. 199-202. 
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