Construction of commutative and associative operations by paving
- https://doi.org/10.2991/ifsa-eusflat-15.2015.170How to use a DOI?
- T-norm, uninorm, associative operation, paving, generated t-norm.
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.
- © 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 -