Characterization of Uninorms on Bounded Lattices and Pre-order They Induce
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, introdu...
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doaj-9441a3537fe64cebac41f2df7afd4b072021-02-01T15:03:34ZengAtlantis PressInternational Journal of Computational Intelligence Systems 1875-68832020-11-0114110.2991/ijcis.d.201118.001Characterization of Uninorms on Bounded Lattices and Pre-order They InduceDana HliněnáMartin KalinaIn 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.https://www.atlantis-press.com/article/125946351/viewBounded latticeDivisible uninorml-groupLocally internal uninormPreorder induced by uninormUninorm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Dana Hliněná Martin Kalina |
spellingShingle |
Dana Hliněná Martin Kalina Characterization of Uninorms on Bounded Lattices and Pre-order They Induce International Journal of Computational Intelligence Systems Bounded lattice Divisible uninorm l-group Locally internal uninorm Preorder induced by uninorm Uninorm |
author_facet |
Dana Hliněná Martin Kalina |
author_sort |
Dana Hliněná |
title |
Characterization of Uninorms on Bounded Lattices and Pre-order They Induce |
title_short |
Characterization of Uninorms on Bounded Lattices and Pre-order They Induce |
title_full |
Characterization of Uninorms on Bounded Lattices and Pre-order They Induce |
title_fullStr |
Characterization of Uninorms on Bounded Lattices and Pre-order They Induce |
title_full_unstemmed |
Characterization of Uninorms on Bounded Lattices and Pre-order They Induce |
title_sort |
characterization of uninorms on bounded lattices and pre-order they induce |
publisher |
Atlantis Press |
series |
International Journal of Computational Intelligence Systems |
issn |
1875-6883 |
publishDate |
2020-11-01 |
description |
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. |
topic |
Bounded lattice Divisible uninorm l-group Locally internal uninorm Preorder induced by uninorm Uninorm |
url |
https://www.atlantis-press.com/article/125946351/view |
work_keys_str_mv |
AT danahlinena characterizationofuninormsonboundedlatticesandpreordertheyinduce AT martinkalina characterizationofuninormsonboundedlatticesandpreordertheyinduce |
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1724315347116359680 |