Distributivity of ordinal sum implications over overlap and grouping functions

Deng Pan; Hongjun Zhou

Kybernetika (2021)

  • Volume: 57, Issue: 4, page 647-670
  • ISSN: 0023-5954

Abstract

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In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.

How to cite

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Pan, Deng, and Zhou, Hongjun. "Distributivity of ordinal sum implications over overlap and grouping functions." Kybernetika 57.4 (2021): 647-670. <http://eudml.org/doc/298059>.

@article{Pan2021,
abstract = {In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.},
author = {Pan, Deng, Zhou, Hongjun},
journal = {Kybernetika},
keywords = {distributivity; fuzzy implication functions; ordinal sum; overlap functions; grouping functions},
language = {eng},
number = {4},
pages = {647-670},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Distributivity of ordinal sum implications over overlap and grouping functions},
url = {http://eudml.org/doc/298059},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Pan, Deng
AU - Zhou, Hongjun
TI - Distributivity of ordinal sum implications over overlap and grouping functions
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 4
SP - 647
EP - 670
AB - In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.
LA - eng
KW - distributivity; fuzzy implication functions; ordinal sum; overlap functions; grouping functions
UR - http://eudml.org/doc/298059
ER -

References

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