Left and right semi-uninorms on a complete lattice

Yong Su; Zhudeng Wang; Keming Tang

Kybernetika (2013)

  • Volume: 49, Issue: 6, page 948-961
  • ISSN: 0023-5954

Abstract

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Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary operation. Finally, we discuss the relations between the upper approximation left (right) semi-uninorms of a given binary operation and the lower approximation left (right) semi-uninorms of its dual operation.

How to cite

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Su, Yong, Wang, Zhudeng, and Tang, Keming. "Left and right semi-uninorms on a complete lattice." Kybernetika 49.6 (2013): 948-961. <http://eudml.org/doc/260821>.

@article{Su2013,
abstract = {Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary operation. Finally, we discuss the relations between the upper approximation left (right) semi-uninorms of a given binary operation and the lower approximation left (right) semi-uninorms of its dual operation.},
author = {Su, Yong, Wang, Zhudeng, Tang, Keming},
journal = {Kybernetika},
keywords = {fuzzy connective; uninorm; left (right) semi-uninorm; upper (lower) approximation; fuzzy connective; uninorm; left (right) semi-uninorm; upper (lower) approximation},
language = {eng},
number = {6},
pages = {948-961},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Left and right semi-uninorms on a complete lattice},
url = {http://eudml.org/doc/260821},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Su, Yong
AU - Wang, Zhudeng
AU - Tang, Keming
TI - Left and right semi-uninorms on a complete lattice
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 6
SP - 948
EP - 961
AB - Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary operation. Finally, we discuss the relations between the upper approximation left (right) semi-uninorms of a given binary operation and the lower approximation left (right) semi-uninorms of its dual operation.
LA - eng
KW - fuzzy connective; uninorm; left (right) semi-uninorm; upper (lower) approximation; fuzzy connective; uninorm; left (right) semi-uninorm; upper (lower) approximation
UR - http://eudml.org/doc/260821
ER -

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