Geodesic
Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice
Kybernetika, Tome 55 (2019) no. 2, pp. 295-306
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For a t-norm T on a bounded lattice $(L, \leq)$, a partial order $\leq_{T}$ was recently defined and studied. In [11], 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 [11]. Furthermore, some examples of t-norms on $L$ such that $(L, \leq_{T}) $ is a lattice are presented.
For a t-norm T on a bounded lattice $(L, \leq)$, a partial order $\leq_{T}$ was recently defined and studied. In [11], 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 [11]. Furthermore, some examples of t-norms on $L$ such that $(L, \leq_{T}) $ is a lattice are presented.
DOI : 10.14736/kyb-2019-2-0295
Classification : 03B52, 03E72
Keywords: bounded lattice; triangular norm; T-partial order 
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Li, Lifeng; Zhang, Jianke; Zhou, Chang. Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice. Kybernetika, Tome 55 (2019) no. 2, pp. 295-306. doi: 10.14736/kyb-2019-2-0295

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