Geodesic
An extension method for t-norms on subintervals to t-norms on bounded lattices
Kybernetika, Tome 55 (2019) no. 6, pp. 976-993
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In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.
In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.
DOI : 10.14736/kyb-2019-6-0976
Classification : 03B52, 03E72, 03G10, 18B35
Keywords: T-norm; bounded lattice; construction method; subinterval 
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     title = {An extension method for t-norms on subintervals to t-norms on bounded lattices},
     journal = {Kybernetika},
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Karaçal, Funda; Ertuğrul, Ümit; Kesicioğlu, M. Nesibe. An extension method for t-norms on subintervals to t-norms on bounded lattices. Kybernetika, Tome 55 (2019) no. 6, pp. 976-993. doi: 10.14736/kyb-2019-6-0976

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