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Number of discrete uninorms defined on the finite chain L_n={0,1,...,n-1,n}.
(history; published version)
#10 by Michael De Vlieger at Sat Nov 18 10:55:29 EST 2023
STATUS

reviewed

approved

#9 by Joerg Arndt at Sat Nov 18 10:45:46 EST 2023
STATUS

proposed

reviewed

#8 by Marc Munar at Sat Nov 18 10:43:09 EST 2023
STATUS

editing

proposed

#7 by Marc Munar at Sat Nov 18 10:42:19 EST 2023
COMMENTS

The number of discrete uninorms on the finite chain L_n={0,1,...,n-1,n}, i.e., the number of monotoneic 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).

STATUS

proposed

editing

Discussion
Sat Nov 18
10:42
Marc Munar: No, it was a typo. Thanks for the warning.
#6 by Michel Marcus at Sat Nov 18 10:30:12 EST 2023
STATUS

editing

proposed

Discussion
Sat Nov 18
10:39
Joerg Arndt: "monotoneic" correct?
#5 by Michel Marcus at Sat Nov 18 10:30:06 EST 2023
LINKS

M. Mas, S. Massanet, D. Ruiz-Aguilera, J. Torrens <a href="https://doi.org/10.3233/IFS-151728">A survey on the existing classes of uninorms</a>, Journal of Intelligent and Fuzzy Systems, Volume 29, 2015, 1021-1037.

M. Mas, S. Massanet, D. Ruiz-Aguilera, and J. Torrens <a href="https://doi.org/10.3233/IFS-151728">A survey on the existing classes of uninorms</a>, Journal of Intelligent and Fuzzy Systems, Volume 29, 2015, 1021-1037.

STATUS

proposed

editing

#4 by Marc Munar at Sat Nov 18 10:27:31 EST 2023
STATUS

editing

proposed

#3 by Marc Munar at Sat Nov 18 10:27:28 EST 2023
LINKS

M. Mas, S. Massanet, D. Ruiz-Aguilera, J. Torrens <a href="https://doi.org/10.3233/IFS-151728">A survey on the existing classes of uninorms</a>, Journal of Intelligent and Fuzzy Systems, Volume 29, 2015, 1021-1037.

#2 by Marc Munar at Sat Nov 18 10:27:09 EST 2023
NAME

allocated for Marc MunarNumber of discrete uninorms defined on the finite chain L_n={0,1,...,n-1,n}.

DATA

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 monotoneic 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

M. Mas, S. Massanet, D. Ruiz-Aguilera, J. Torrens <a href="https://doi.org/10.3233/IFS-151728">A survey on the existing classes of uninorms</a>, Journal of Intelligent and Fuzzy Systems, Volume 29, 2015, 1021-1037.

M. Couceiro, J. Devillet and J.L. Marichal. <a href="https://doi.org/10.1016/j.fss.2017.06.013">Characterizations of idempotent discrete uninorms</a>, Fuzzy Sets and Systems, Volume 334, 2018, 60-72.

M. Munar, S. Massanet and D. Ruiz-Aguilera, <a href="https://doi.org/10.1016/j.ins.2022.10.121">On the cardinality of some families of discrete connectives</a>, Information Sciences, Volume 621, 2023, 708-728.

KEYWORD

allocated

nonn,hard,more

AUTHOR

Marc Munar, Nov 18 2023

STATUS

approved

editing

#1 by Marc Munar at Sat Nov 18 10:27:09 EST 2023
NAME

allocated for Marc Munar

KEYWORD

allocated

STATUS

approved