Kybernetika 55 no. 6, 976-993, 2019

An extension method for t-norms on subintervals to t-norms on bounded lattices

Funda Karaçal, Ümit Ertuğrul and M. Nesibe KesicioğluDOI: 10.14736/kyb-2019-6-0976


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.


bounded lattice, T-norm, construction method, subinterval


03E72, 03B52, 03G10, 18B35


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