Extensions of fuzzy connectives on ACDL

Hui Liu; Bin Zhao

Kybernetika (2019)

  • Volume: 55, Issue: 3, page 472-494
  • ISSN: 0023-5954

Abstract

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The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications and also make a study on the behaviors of R -implication and reciprocal implication. Finally, we construct two classes of infinitely ⋁ -distributive uninorms and infinitely ⋀ -distributive uninorms.

How to cite

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Liu, Hui, and Zhao, Bin. "Extensions of fuzzy connectives on ACDL." Kybernetika 55.3 (2019): 472-494. <http://eudml.org/doc/294232>.

@article{Liu2019,
abstract = {The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications and also make a study on the behaviors of $R$-implication and reciprocal implication. Finally, we construct two classes of infinitely $\bigvee $-distributive uninorms and infinitely $\bigwedge $-distributive uninorms.},
author = {Liu, Hui, Zhao, Bin},
journal = {Kybernetika},
keywords = {extensions; algebraic completely distributive lattices; fuzzy connectives},
language = {eng},
number = {3},
pages = {472-494},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Extensions of fuzzy connectives on ACDL},
url = {http://eudml.org/doc/294232},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Liu, Hui
AU - Zhao, Bin
TI - Extensions of fuzzy connectives on ACDL
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 3
SP - 472
EP - 494
AB - The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications and also make a study on the behaviors of $R$-implication and reciprocal implication. Finally, we construct two classes of infinitely $\bigvee $-distributive uninorms and infinitely $\bigwedge $-distributive uninorms.
LA - eng
KW - extensions; algebraic completely distributive lattices; fuzzy connectives
UR - http://eudml.org/doc/294232
ER -

References

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