A representation of t-norms in interval-valued L-fuzzy set theory
- 作者：Glad Deschrijver
- 关键词：Lattice of closed intervals ; Interval-valued fuzzy set ; Triangular norm ; Representation ; Join-morphism ; Residuation principle
- 刊名：Fuzzy Sets and Systems
- 出版年：2008
- 期刊代码：55_01650114
- 类别：cp
- 出版时间：1 July 2008
- 卷：159
- 期：13
- 页码：1597-1618
- 文件大小：326 K
摘要
In this paper we consider the lattice 11e22352f3b9e88da09038ad">
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 
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 
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.