کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
391028 | 661333 | 2008 | 22 صفحه PDF | دانلود رایگان |
In this paper we consider the lattice LI which has the closed subintervals of a complete lattice as elements. We give a representation theorem of t-norms on this lattice for which the partial mappings are join-morphisms in terms of t-norms on the underlying lattice. In fuzzy logic, t-norms which satisfy the residuation principle play an important role. Using our representation theorem, we represent t-norms on LI which satisfy the residuation principle and two border conditions in terms of t-norms on the underlying lattice. In the case that the underlying lattice of LI is the unit interval, we obtain characterizations of continuous t-norms which are natural extensions of t-norms on the unit interval and which have join-morphisms as partial mappings or alternatively satisfy the residuation principle.
Journal: Fuzzy Sets and Systems - Volume 159, Issue 13, 1 July 2008, Pages 1597-1618