V-Distributive and infinitely v-distributive t-norms on complete lattices


Karacal F., Khadjiev D.

FUZZY SETS AND SYSTEMS, vol.151, no.2, pp.341-352, 2005 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 151 Issue: 2
  • Publication Date: 2005
  • Doi Number: 10.1016/j.fss.2004.06.013
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.341-352

Abstract

A relation between the direct decomposability of an infinitely v-distributive t-norm on a complete lattice L and direct decompositions of the neutral element 1 of L is obtained. Some useful applications of this relation are given. In particularly, the description of all T-1-lattices without infinitely V-distributive t-norms on complete lattices and the description of all V-distributive t-norms on lattices of length 2 are given. The paper also contains the solutions of two open problems. (C) 2004 Elsevier B.V. All rights reserved.