A T-PARTIAL ORDER OBTAINED FROM T-NORMS


KARAÇAL F., KESİCİOĞLU M. N.

KYBERNETIKA, vol.47, no.2, pp.300-314, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 2
  • Publication Date: 2011
  • Title of Journal : KYBERNETIKA
  • Page Numbers: pp.300-314

Abstract

A partial order on a bounded lattice L is called t-order if it is defined by means of the t-norm on L. It is obtained that for a t-norm on a bounded lattice L the relation a <=(T) b if a = T(x,b) for some x is an element of L is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of L and a complete lattice on the subset A of all elements of L which are the supremum of a subset of atoms.