New methods to construct uninorms on bounded lattices via uninorms defined on their sublattices

Abstract In this paper, we present two methods for constructing uninorms on a bounded lattice L based on a uninorm defined on the sublattice $$\left[ 0,a\right] $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>a</mml:mi> </mml:mfenced> </mml:math> (or $$\left[ b,1\right] $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mfenced> </mml:math> ) of L . We also examine the relationships between these methods and existing construction approaches in the literature. Furthermore, we provide several illustrative examples that demonstrate the effectiveness of the proposed constructions.