Infinitely boolean OR-distributive t-norms on complete lattices and pseudo-complements

KARAÇAL F., SAĞIROĞLU Y.

FUZZY SETS AND SYSTEMS, vol.160, no.1, pp.32-43, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 160 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.fss.2008.03.022
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.32-43
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we have introduced the concepts of T-prime element. T-prime radical element and T-semi-prime element and have studied their properties. We have investigated the construction methods of new infinitely boolean OR-distributive t-norms from given infinitely v-distributive t-norms by means of T-prime elements and pseudo-conlplements. If every element of L is T-prime radical element. then we show that L is a complete Brouwerian lattice and T = boolean AND. If L is all algebraic lattice, T is a t-norm oil L and every compact element of L is idempotent, then we obtain that T = boolean AND. We show that L(R) is a complete lattice and that the restriction of T to L(R) is an infinitely boolean OR-distributive t-norm on L(R). When T is an infinitely boolean OR-distributive t-norm on L and 0 is a T-prime, we present infinitely boolean OR-distributive t-norms on a complete sublattice L* and study their properties. (C) 2008 Elsevier B.V. All rights reserved.