Geodesic
A T-partial order obtained from T-norms
Kybernetika, Tome 47 (2011) no. 2, pp. 300-314
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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 $a\preceq_{T}b$ iff $a=T(x,b)$ for some $x\in L$ 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.
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 $a\preceq_{T}b$ iff $a=T(x,b)$ for some $x\in L$ 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.
Classification : 03B52, 03E72
Keywords: triangular norm; bounded lattice; triangular action; $\bigvee $-distributive; idempotent element 
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Karaçal, Funda; Kesicioğlu, M. Nesibe. A T-partial order obtained from T-norms. Kybernetika, Tome 47 (2011) no. 2, pp. 300-314. http://geodesic.mathdoc.fr/item/KYB_2011_47_2_a8/

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