Characterization of uninorms on bounded lattices

KARAÇAL F., ERTUĞRUL Ü., Mesiar R.

FUZZY SETS AND SYSTEMS, cilt.308, ss.54-71, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 308
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1016/j.fss.2016.05.014
  • Dergi Adı: FUZZY SETS AND SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.54-71
  • Anahtar Kelimeler: Uninorm, Triangular norm, Triangular conorm, Aggregation function, Neutral element, Bounded lattice, T-NORMS, FUZZY, SET
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we propose a characterization of uninorms on a general bounded lattice L by means of a sextuple of a triangular norm, a triangular conorm, and four aggregation functions on L. Observe that in the case when L is a chain, it is enough to consider a triple consisting of a t-norm, a t-conorm and an averaging aggregation function. An example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown (note that this cannot happen if we consider uninorms acting on a chain). Two general constructions of uninorms on L are added, letting a t-norm (a t-conorm) linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions. (C) 2016 Elsevier B.V. All rights reserved.