Geodesic
Some methods to obtain t-norms and t-conorms on bounded lattices
Kybernetika, Tome 55 (2019) no. 2, pp. 273-294
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In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded 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.
In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded 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.
DOI : 10.14736/kyb-2019-2-0273
Classification : 03B52, 03E72, 06B20, 94D05, 97E30
Keywords: bounded lattice; t-norm; t-conorm; ordinal sum 
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Çaylı, Gül Deniz. Some methods to obtain t-norms and t-conorms on bounded lattices. Kybernetika, Tome 55 (2019) no. 2, pp. 273-294. doi: 10.14736/kyb-2019-2-0273

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