Characterization of Uninorms on Bounded Lattices and Pre-order They Induce

Authors

Dana Hliněná^1, , Martin Kalina^{2, *,}

¹Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, Cz-616 00 Brno, Czech Republic

²Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Sk-810 05 Bratislava, Slovakia

^*Corresponding author. Email: martin.kalina@stuba.sk; kalina@math.sk

DOI

10.2991/ijcis.d.201118.001How to use a DOI?

Keywords

Bounded lattice; Divisible uninorm; l-group; Locally internal uninorm; Preorder induced by uninorm; Uninorm; t-norm with a single discontinuity point

Abstract

In Hliněná et al., Pre-orders and orders generated by uninorms, in 15th International Conference IPMU 2014, Proceedings, Part III, Montpellier, France, 2014, pp. 307–316 the authors, inspired by Karaçal and Kesicioğlu, A t-partial order obtained from t-norms, Kybernetika. 47 (2011), 300–314, introduced a pre-order induced by uninorms. This contribution is devoted to a classification of families of uninorms by means of pre-orders (and orders) they induce. Philosophically, the paper follows the original idea of Clifford, Naturally totally ordered commutative semigroups, Am. J. Math. 76 (1954), 631–646. The present paper is an extension of the paper Hliněná and Kalina, A characterization of uninorms by means of a pre-order they induce, in Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019), Atlantis Press, 2019, pp. 595–601 that was presented at EUSFLAT 2019. As a by-product, we present a t-norm that possesses a single discontinuity point.

Copyright

© 2021 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)
View full text (HTML)

TY  - JOUR
AU  - Dana Hliněná
AU  - Martin Kalina
PY  - 2020
DA  - 2020/11/23
TI  - Characterization of Uninorms on Bounded Lattices and Pre-order They Induce
JO  - International Journal of Computational Intelligence Systems
SP  - 148
EP  - 158
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.201118.001
DO  - 10.2991/ijcis.d.201118.001
ID  - Hliněná2020
ER  -