On the direct decomposability of strong negations and S-implication operators on product lattices


Karacal F.

INFORMATION SCIENCES, cilt.176, sa.20, ss.3011-3025, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 176 Konu: 20
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.ins.2005.12.010
  • Dergi Adı: INFORMATION SCIENCES
  • Sayfa Sayıları: ss.3011-3025

Özet

In this paper, we discuss the direct product of strong negations. We characterize strong negations on product lattices that are direct products of strong negations. Furthermore, we present a method for constructing t-norms on product lattices which are not direct products. This method is quite general and useful to generate a wide class of such t-norms and solves an open problem posed in 2003 by Jenei and De Baets. Finally, we study direct decompositions of S-implication operators on product lattices. (C) 2005 Elsevier Inc. All rights reserved.