| Title:
|
On $\star $- associated comonotone functions (English) |
| Author:
|
Hutník, Ondrej |
| Author:
|
Pócs, Jozef |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
268-278 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
comonotone functions |
| Keyword:
|
binary operation |
| Keyword:
|
$\star $-associatedness |
| Keyword:
|
Sugeno integral |
| MSC:
|
26A48 |
| MSC:
|
28E10 |
| idZBL:
|
Zbl 06890419 |
| idMR:
|
MR3807714 |
| DOI:
|
10.14736/kyb-2018-2-0268 |
| . |
| Date available:
|
2018-05-30T16:01:01Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147193 |
| . |
| Reference:
|
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| Reference:
|
[2] Boczek, M., Kaluszka, M.: On conditions under which some generalized Sugeno integrals coincide: A solution to Dubois problem.Fuzzy Sets and Systems 326 (2017), 81-88. MR 3694474, 10.1016/j.fss.2017.06.004 |
| 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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| . |
