Nullnorms on bounded lattices

Karaçal F., Ince M. A., Mesiar R.

INFORMATION SCIENCES, cilt.325, ss.227-236, 2015 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 325
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1016/j.ins.2015.06.052
  • Dergi Adı: INFORMATION SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.227-236
  • Anahtar Kelimeler: Nullnorm, Triangular norm, Triangular conorm, Bounded lattice, DISTRIBUTIVE T-NORMS, UNINORMS, OPERATORS
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

Nullnorms are generalization of triangular norms and triangular conorms with a zero element in the interior of the unit interval. In this paper, we generalize nullnorms to an arbitrary bounded lattices. We show the existence of nullnorms with zero element a for arbitrary element a is an element of L\{0, 1} using the fact that some t-norms and t-conorms on an arbitrary fixed bounded lattice L always exist. As a by-product we give a method of constructing nullnorms. Using this method, we obtain also the smallest nullnorm and the greatest nullnorm with given zero element a. Some other construction methods for nullnorms are also added. (C) 2015 Elsevier Inc. All rights reserved.