Idempotent uninorms on finite ordinal scales

Bernard De Baets, János Fodor, Daniel Ruiz-Aguilera, Joan Torrens

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalInternational Journal of Uncertainty, Fuzziness and Knowlege-Based Systems
Volume17
Issue number1
DOIs
Publication statusPublished - Feb 2009

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Keywords

  • Decreasing function
  • Discrete idempotent uninorm
  • Finite ordinal scale
  • Symmetry

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Artificial Intelligence

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