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Migrativity properties of 2-uninorms over semi-t-operators

Ying Li-Jun; Qin Feng

Kybernetika (2022)

  • Volume: 58, Issue: 3, page 354-375
  • ISSN: 0023-5954

Abstract

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In this paper, we analyze and characterize all solutions about α -migrativity properties of the five subclasses of 2-uninorms, i. e. C k , C k 0 , C k 1 , C 1 0 , C 0 1 , over semi-t-operators. We give the sufficient and necessary conditions that make these α -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for G ∈ C k , the α -migrativity of G over a semi-t-operator F μ , ν is closely related to the α -section of F μ , ν or the ordinal sum representation of t-norm and t-conorm corresponding to F μ , ν . But for the other four categories, the α -migrativity over a semi-t-operator F μ , ν is fully determined by the α -section of F μ , ν .

How to cite

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Li-Jun, Ying, and Feng, Qin. "Migrativity properties of 2-uninorms over semi-t-operators." Kybernetika 58.3 (2022): 354-375. <http://eudml.org/doc/298903>.

@article{Li2022,
abstract = {In this paper, we analyze and characterize all solutions about $\alpha $-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^\{k\}$, $C^\{0\}_\{k\}$, $C^\{1\}_\{k\}$, $C^\{0\}_\{1\}$, $C^\{1\}_\{0\}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha $-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^\{k\}$, the $\alpha $-migrativity of $G$ over a semi-t-operator $F_\{\mu ,\nu \}$ is closely related to the $\alpha $-section of $F_\{\mu ,\nu \}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_\{\mu ,\nu \}$. But for the other four categories, the $\alpha $-migrativity over a semi-t-operator $F_\{\mu ,\nu \}$ is fully determined by the $\alpha $-section of $F_\{\mu ,\nu \}$.},
author = {Li-Jun, Ying, Feng, Qin},
journal = {Kybernetika},
keywords = {2-uninorms; uninorms; semi-t-operators; triangular norms; triangular conorms},
language = {eng},
number = {3},
pages = {354-375},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Migrativity properties of 2-uninorms over semi-t-operators},
url = {http://eudml.org/doc/298903},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Li-Jun, Ying
AU - Feng, Qin
TI - Migrativity properties of 2-uninorms over semi-t-operators
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 3
SP - 354
EP - 375
AB - In this paper, we analyze and characterize all solutions about $\alpha $-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha $-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha $-migrativity of $G$ over a semi-t-operator $F_{\mu ,\nu }$ is closely related to the $\alpha $-section of $F_{\mu ,\nu }$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu ,\nu }$. But for the other four categories, the $\alpha $-migrativity over a semi-t-operator $F_{\mu ,\nu }$ is fully determined by the $\alpha $-section of $F_{\mu ,\nu }$.
LA - eng
KW - 2-uninorms; uninorms; semi-t-operators; triangular norms; triangular conorms
UR - http://eudml.org/doc/298903
ER -

References

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