<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define <italic>k</italic>-bounded transformations that represent only finite decompositions with at most <italic>k</italic> elements. Secondly, we introduce two other transformations that preserve the super-additivity property in some sense. Also, a remark on continuity of the classical super-additive transformation of an aggregation function is presented for one-dimensional case.</p></abstract>

In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define k-bounded transformations that represent only finite decompositions with at most k elements. Secondly, we introduce two other transformations that preserve the super-additivity property in some sense. Also, a remark on continuity of the classical super-additive transformation of an aggregation function is presented for one-dimensional case.

Remarks on Super-Additive and Sub-Additive Transformations of Aggregation Functions

Slovak University of Technology in Bratislava

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define k-bounded...

Remarks on Super-Additive and Sub-Additive Transformations of Aggregation Functions

Published Online: Mar 12, 2019

Page range: 55 - 66

Received: Oct 02, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0021

Keywords
super-additive transformation, aggregation function, continuity

© 2018 Katarína Hriňáková et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Remarks on Super-Additive and Sub-Additive Transformations of Aggregation Functions

Published Online: Mar 12, 2019

Page range: 55 - 66

Received: Oct 02, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0021

Keywordssuper-additive transformation, aggregation function, continuity

© 2018 Katarína Hriňáková et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
super-additive transformation, aggregation function, continuity