| Title:
|
A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case (English) |
| Author:
|
Kouchakinejad, Fateme |
| Author:
|
Šipošová, Alexandra |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
129-136 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
aggregation function |
| Keyword:
|
overrunning and underrunning property |
| Keyword:
|
sub-additive and super-additive transformation |
| MSC:
|
47H04 |
| MSC:
|
47S40 |
| idZBL:
|
Zbl 06738598 |
| idMR:
|
MR3638560 |
| DOI:
|
10.14736/kyb-2017-1-0129 |
| . |
| Date available:
|
2017-04-03T10:51:10Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146712 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
