Detalle Publicación

The number of t-norms on some special lattices

Título de la revista: FUZZY SETS AND SYSTEMS
ISSN: 0165-0114
Volumen: 408
Páginas: 26 - 43
Fecha de publicación: 2021
We estimate the number of triangular norms on some classes of finite lattices. One of them is obtained from two chains by identifying their zero elements, unit elements and an atom. Another one is the set of the dual lattices of the previous one. The obtained formulas involve the number of triangular norms on the corresponding chains. We derive several properties of a triangular norm for this kind of lattices, that enable us to obtain better estimates. Moreover, we obtain the number of t-norms in another class of lattices, which includes the so-called Chinese lantern. Finally, we estimate the number of Archimedean t-norms and divisible t-norms on these lattices.