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Element-Oriented Construction Methods for Nullnorms on Bounded Lattices
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DOI：10.3390/axioms14120856.png)
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Abstract
En 中文
Nullnorms are aggregation functions with an annihilator and are generalizations of t-norms and t-conorms. After the introduction of the concept of nullnorms on bounded lattices by Kara & ccedil;al et al., the studies on their construction methods in such structures have been initiated. Following the paper of Kara & ccedil;al and & Scedil;anl & imath;, in which proposed element-based construction methods for t-norms and t-conorms on bounded lattices, a natural research question emerged: Are there any element-based construction methods for nullnorms on a bounded lattice L? In this paper, we address this question and propose construction methods for nullnorms with an annihilator element k is an element of L\{0,1}, depending on an element eta is an element of L\{0,k,1}, by examining the relationship between eta and k. The proposed methods are compared with some existing approaches in the literature and are shown to be distinct. These theoretical findings are further supported with illustrative examples.
Keywords:
nullnorm
bounded lattice
sublattice
t-norm
t-conorm
Journal
A
IF:
1.6
Papers:
593
Citations:
4.4K