University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 23 5 2026 10 01 On smooth nullnorms on bounded lattices and their extensions to smooth uninorms 1 7 10079 10.22111/ijfs.2026.10079 EN Martin Kalina Dept. Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Bratislava, Slovakia Juraj Kalafut Dept. Mathematics, Slovak University of Technology, Radlisnkeho 11, 810 05 Bratislava, Slovakia Journal Article 2026 08 15 The paper deals with smooth uninorms and smooth nullnorms on finite lattices. These operations were first introduced on the unit interval and later generalized to bounded lattices. One of the most important and most studied properties is continuity. However, when working on finite lattices (finite structures, in general), the topological continuity is not very meaningful. For this reason, Mayor and Torrens (2005) introduced several notions that replace continuity. Smoothness and divisibility are among them. We study smooth nullnorms on finite lattices looking for conditions under which, when the nullnorm is defined on a lattice L, it is possible to extend the smooth nullnorm to a smooth uninorm defined on the horizontal sum of L and a finite chain. We provide necessary and sufficient conditions for such an extension to yield a smooth uninorm. Finally, we give a necessary and sufficient condition under which a smooth uninorm is also a divisible uninorm. https://ijfs.usb.ac.ir/article_10079_d57a2e4ed478ddc6c17129ce13f82c34.pdf