Construction of commutative and associative operations by paving

DOI

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/).

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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  - 10.2991/ifsa-eusflat-15.2015.170
ID  - Kalina2015/06
ER  -