The study on semicopula based implications

Zuming Peng

Kybernetika (2020)

  • Volume: 56, Issue: 4, page 662-694
  • ISSN: 0023-5954

Abstract

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Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula is a special family semicopula and the priori fuzzy implication is a ( U , N )-implication. Moreover, the case that the semicopula based implication is 2-increasing (directionally decreasing, respectively) is also considered.

How to cite

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Peng, Zuming. "The study on semicopula based implications." Kybernetika 56.4 (2020): 662-694. <http://eudml.org/doc/297090>.

@article{Peng2020,
abstract = {Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula is a special family semicopula and the priori fuzzy implication is a ($U,N$)-implication. Moreover, the case that the semicopula based implication is 2-increasing (directionally decreasing, respectively) is also considered.},
author = {Peng, Zuming},
journal = {Kybernetika},
keywords = {fuzzy implications; semicopula based implications; ($U,N$)-implications; semicopula; 2-increasing},
language = {eng},
number = {4},
pages = {662-694},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The study on semicopula based implications},
url = {http://eudml.org/doc/297090},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Peng, Zuming
TI - The study on semicopula based implications
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 4
SP - 662
EP - 694
AB - Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula is a special family semicopula and the priori fuzzy implication is a ($U,N$)-implication. Moreover, the case that the semicopula based implication is 2-increasing (directionally decreasing, respectively) is also considered.
LA - eng
KW - fuzzy implications; semicopula based implications; ($U,N$)-implications; semicopula; 2-increasing
UR - http://eudml.org/doc/297090
ER -

References

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