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

summary: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

Notes on locally internal uninorm on bounded lattices

summary:In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm

Construction of uninorms on bounded lattices

summary:In this paper, we propose the general methods, yielding uninorms on the bounded lattice $(L,\leq ,0,1)$, with some additional constraints on $e\in L\backslash \{0,1\}$ for a fixed neutral element $e\in L\backslash \{0,1\}$ based on underlying an arbitrary triangular norm $T_{e}$ on $[0,e]$ and an arbitrary triangular conorm $S_{e}$ on $[e,1]$. And, some illustrative examples are added for clarity