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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 2(n).
Keywords
decreasing function, discrete idempotent uninorm, Finite ordinal scale, SET, OPERATORS, CHAIN, TRIANGULAR NORMS, symmetry, MONOTONIC OPERATIONS

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Citation

Please use this url to cite or link to this publication:

Chicago
De Baets, Bernard, Janos Fodor, Daniel Ruiz-Aguilera, and Joan Torrens. 2009. “Idempotent Uninorms on Finite Ordinal Scales.” International Journal of Uncertainty Fuzziness and Knowledge-based Systems 17 (1): 1–14.
APA
De Baets, B., Fodor, J., Ruiz-Aguilera, D., & Torrens, J. (2009). Idempotent uninorms on finite ordinal scales. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 17(1), 1–14.
Vancouver
1.
De Baets B, Fodor J, Ruiz-Aguilera D, Torrens J. Idempotent uninorms on finite ordinal scales. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. 2009;17(1):1–14.
MLA
De Baets, Bernard et al. “Idempotent Uninorms on Finite Ordinal Scales.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 17.1 (2009): 1–14. Print.
@article{693765,
  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 2(n).},
  author       = {De Baets, Bernard and Fodor, Janos and Ruiz-Aguilera, Daniel and Torrens, Joan},
  issn         = {0218-4885},
  journal      = {INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS},
  language     = {eng},
  number       = {1},
  pages        = {1--14},
  title        = {Idempotent uninorms on finite ordinal scales},
  url          = {http://dx.doi.org/10.1142/S021848850900570X},
  volume       = {17},
  year         = {2009},
}

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