PROCEEDINGS IPMU '08

On idempotent discrete uninorms

D. Ruiz-Aguilera, J. Torrens, B. De Baets, J. Fodor.

This paper is devoted to classify all
idempotent uninorms defined on the
finite scale L_{n} = {0, 1, . . . , n}, called
discrete idempotent uninorms. It
is proved that any discrete idempotent
uninorm with neutral element
e ∈ L_{n} is uniquely determined by a
decreasing function g : [0, e] → [e, n]
and vice versa. Based on this correspondence,
the number of all possible
discrete idempotent uninorms
on a finite scale of n + 1 elements is
given depending on n.

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