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

Authors:
Funda Karaçal
Affiliations:
Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey
Venue:
Information Sciences: an International Journal
Year:
2006

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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.