Publication details

On ordinal sums of t-norms and t-conorms on bounded posets

Authors

DVOŘÁK Antonín HOLČAPEK Michal PASEKA Jan

Year of publication 2020
Type Article in Proceedings
Conference 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
MU Faculty or unit

Faculty of Science

Citation
Web https://ieeexplore.ieee.org/document/9177618
Doi http://dx.doi.org/10.1109/FUZZ48607.2020.9177618
Keywords t-norms; t-conorms; bounded posets; ordinal sum
Description This paper continues and generalizes the line of research on ordinal sum of t-norms and t-conorms on bounded lattices. We introduce a new ordinal sum construction on bounded posets based on interior and closure operators. Our proposed method provides a simple tool to introduce new classes of t-norms and t-conorms. Several necessary and sufficient conditions are presented for ensuring whether our generalized ordinal sum on a bounded posets of arbitrary t-norms is, in fact, a t-norm. We show that in this general setting the existence of our ordinal sum for t-norms requires that the respective interior operators are t-norm preserving.
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