New results on additive generator pairs of overlap and grouping functions

Liang Li-zhi; Wang Xue-ping

Kybernetika (2025)

  • Issue: 2, page 238-263
  • ISSN: 0023-5954

Abstract

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In this article, we deeply reveal the relationship between functions θ and ϑ in an overlap function additively generated by an additive generator pair ( θ , ϑ ), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions θ and ϑ . We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions.

How to cite

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Li-zhi, Liang, and Xue-ping, Wang. "New results on additive generator pairs of overlap and grouping functions." Kybernetika (2025): 238-263. <http://eudml.org/doc/299977>.

@article{Li2025,
abstract = {In this article, we deeply reveal the relationship between functions $\theta $ and $\vartheta $ in an overlap function additively generated by an additive generator pair ($\theta $,$\vartheta $), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $\theta $ and $\vartheta $. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions.},
author = {Li-zhi, Liang, Xue-ping, Wang},
journal = {Kybernetika},
keywords = {overlap function; grouping function; triangular norm; additive generator pair; distortion},
language = {eng},
number = {2},
pages = {238-263},
publisher = {Institute of Information Theory and Automation AS CR},
title = {New results on additive generator pairs of overlap and grouping functions},
url = {http://eudml.org/doc/299977},
year = {2025},
}

TY - JOUR
AU - Li-zhi, Liang
AU - Xue-ping, Wang
TI - New results on additive generator pairs of overlap and grouping functions
JO - Kybernetika
PY - 2025
PB - Institute of Information Theory and Automation AS CR
IS - 2
SP - 238
EP - 263
AB - In this article, we deeply reveal the relationship between functions $\theta $ and $\vartheta $ in an overlap function additively generated by an additive generator pair ($\theta $,$\vartheta $), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $\theta $ and $\vartheta $. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions.
LA - eng
KW - overlap function; grouping function; triangular norm; additive generator pair; distortion
UR - http://eudml.org/doc/299977
ER -

References

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