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

Karacal F.

INFORMATION SCIENCES, vol.176, no.20, pp.3011-3025, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 176 Issue: 20
  • Publication Date: 2006
  • Doi Number: 10.1016/j.ins.2005.12.010
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3011-3025
  • Karadeniz Technical University Affiliated: No

Abstract

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.