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Keywords:
triangular norm; bounded lattice; triangular action; $\bigvee $-distributive; idempotent element
triangular norm; bounded lattice; triangular action; $\bigvee $-distributive; idempotent element
Summary:
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.
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