Kybernetika 55 no. 2, 273-294, 2019

Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz ÇaylıDOI: 10.14736/kyb-2019-2-0273

Abstract:

In this study, we introduce new methods for constructing t-norms and t-conorms on a bound\-ed lattice $L$ based on a priori given t-norm acting on $ [a,1]$ and t-conorm acting on $[0,a]$ for an arbitrary element $a\in L\backslash \{0,1\}$. We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.

Keywords:

t-norm, ordinal sum, t-conorm, bounded lattice

Classification:

03B52, 06B20, 03E72, 94D05, 97E30

paper.pdf

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