Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Construction of commutative and associative operations by paving

Authors
Martin Kalina, Pavol Král
Corresponding Author
Martin Kalina
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.170How to use a DOI?
Keywords
T-norm, uninorm, associative operation, paving, generated t-norm.
Abstract

Paving is a method for constructing new operations from a given one. We will show that this method can be used to construct associative, commutative and monotone operations from particular given operations (from basic ‘paving stones’). We will discuss properties of the resulting operations by considering different cases of the ‘paving stones’ and the starting position of paving. Finally, we will discuss the case when the basic ‘paving stone’ is a generated operation. We show that in this case we get by paving also a generated operation, just the generator is a two-place function. We show also an example of a non-representable uninorm which is strictly increasing in both variables on the open unit square.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.170How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Martin Kalina
AU  - Pavol Král
PY  - 2015/06
DA  - 2015/06
TI  - Construction of commutative and associative operations by paving
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 1201
EP  - 1207
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.170
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.170
ID  - Kalina2015/06
ER  -