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 Ln = {0, 1, . . . , n}, called discrete idempotent uninorms. It is proved that any discrete idempotent uninorm with neutral element e ∈ Ln 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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