Kybernetika 55 no. 2, 295-306, 2019

Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

Lifeng Li, Jianke Zhang and Chang ZhouDOI: 10.14736/kyb-2019-2-0295

Abstract:

For a t-norm T on a bounded lattice $(L, \leq)$, a partial order $\leq_{T}$ was recently defined and studied. In \cite{Karacal11}, it was pointed out that the binary relation $\leq_{T} $ is a partial order on $L$, but $(L, \leq_{T} )$ may not be a lattice in general. In this paper, several sufficient conditions under which $(L, \leq_{T} )$ is a lattice are given, as an answer to an open problem posed by the authors of \cite{Karacal11}. Furthermore, some examples of t-norms on $L$ such that $(L, \leq_{T}) $ is a lattice are presented.

Keywords:

triangular norm, bounded lattice, T-partial order

Classification:

03E72, 03B52

paper.pdf

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