A367442 Number of discrete uninorms defined on the finite chain L_n={0,1,...,n-1,n}.

2, 6, 22, 92, 426, 2146, 11634, 67472

Offset

1,1

Comments

The number of discrete uninorms on the finite chain L_n={0,1,...,n-1,n}, i.e., the number of monotonic increasing binary functions U: L_n^2->L_n such that U is commutative (U(x,y)=U(y,x) for all x,y in L_n), associative (U(U(x,y),z)=U(x,U(y,z)) for all x,y,z in L_n) and has neutral element e in L_n (U(x,e)=x for all x in L_n).

Links

Table of n, a(n) for n=1..8.

M. Couceiro, J. Devillet and J.L. Marichal. Characterizations of idempotent discrete uninorms, Fuzzy Sets and Systems, Volume 334, 2018, 60-72.

M. Mas, S. Massanet, D. Ruiz-Aguilera, and J. Torrens A survey on the existing classes of uninorms, Journal of Intelligent and Fuzzy Systems, Volume 29, 2015, 1021-1037.

M. Munar, S. Massanet and D. Ruiz-Aguilera, On the cardinality of some families of discrete connectives, Information Sciences, Volume 621, 2023, 708-728.

Crossrefs

Sequence in context: A124294 A124295 A074664 * A091768 A229741 A261518

Adjacent sequences: A367439 A367440 A367441 * A367443 A367444 A367445

Keyword

nonn,hard,more

Author

Marc Munar, Nov 18 2023

Status

approved