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A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli (2023)

Kybernetika

Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.

Compositions of ternary relations

Norelhouda Bakri, Lemnaouar Zedam, Bernard De Baets (2021)

Kybernetika

In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.

Ekvivalence (č. j.) nebo ekvivalence (č. mn.)?

(2012)

Učitel matematiky

edná se o shrnutí diskuze Františka Kuřiny, Vladislava Dlaba a Jindřicha Bečvára o významu slova ekvivalence. Autor článku poskytuje definice ze Slovníku spisovné češtiny a také ze Slovníku školské matematiky. Mluví ze svého pohledu jako učitel středoškolské matematiky a porovnává ho s pohledy kolegů matematiků – vědců.

Jak to vlastně je? Nekonečno

František Kuřina, Naďa Vondrová (2021)

Učitel matematiky

Autoři se zamýšlejí nad pojmem nekonečno, a to z hlediska pochopení tohoto pojmu u žáků základní a střední školy. Přinášejí příklady potenciálního a aktuálního nekonečna a upozorňují na problematiku nekonečně malých veličin. Pozornost věnují i nekonečným množinám v aritmetice a geometrii.

Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz Çaylı (2019)

Kybernetika

In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a ∈ L ∖ { 0 , 1 } . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.

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