有界格上t-子模和t-子余模的构造

Constructions of t-subnorms and t-subconorms on bounded lattices

二元聚合函数的构造方法研究是一个有趣且有意义的研究课题。基于有界格子区间上一个给定的t-子模E,提出了一种在有界格L上构造t-子模Tλ,E的方法。这种构造方法可以通过归纳推广到适用于任何有界格的t-子模的另一种构造;基于有界格子区间上一个给定的t-子余模F,提出了一种在有界格L上构造t-子余模Sλ,F的方法,这种构造方法也可以通过归纳推广到适用于任何有界格的t-子余模的另一种构造。该研究不仅补充了二元聚合函数的构造方法研究中的空白领域,还对进一步研究其他二元函数聚合的构造提供了理论基础。

The construction method of binary aggregation function is an interesting and meaningful research topic.Based on a given t-subnorm E on the subinterval of a bounded lattice,we propose a method to obtain t-subnorm Tλ,E on a bounded lattice L.This construction method can be generalized to another construction of t-subnorms applicable to any bounded lattice.Based on a given t-subconorm F on the subinterval of a bounded lattice,we propose a method to obtain t-subconorm Sλ,F on bounded lattices L.This construction method also can be generalized to another construction of t-subconorms applicable to any bounded lattice.It not only supplements the blank fields in the research on the construction methods of binary aggregation functions,but also provides a theoretical basis for further research on the construction methods of other binary aggregation functions.