Document Type : Research Paper

Authors

• Y. Su ^{1, 2, 3}
• Z. Wang ⁴
• A. Mesiarova-Zemankova ^{5, 6}
• R. Mesiar ^{6, 7}

¹ School of Mathematics Sciences, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China

² Jiangsu Industrial Intelligent and Low-carbon Technology Engineering Center, Suzhou, Jiangsu 215009, China

³ Suzhou Key Laboratory of Intelligent Low-carton Technology Application, Suzhou, Jiangsu 215009, China

⁴ School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, China

⁵ Mathematical Institute, Slovak Academy of Sciences, \v Stef\' anikova 49, SK- 814 73 Bratislava, Slovakia

⁶ Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, CE IT4Innovations, 30. dubna 22, 701 03 Ostrava, Czech Republic

⁷ Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology Bratislava, Radlinsk\' eho 11, 810 05 Bratislava, Slovakia

Abstract

This study presents characterizations of three classes of idempotent uninorms on a bounded lattice by the orders of their associated meet-semilattices. The first one is the class of internal uninorms, the second one is the class of idempotent uninorms defined on a lattice in which all elements are comparable with the corresponding neutral element and the third one is the class of idempotent uninorms defined on a lattice in which a single point is incomparable
with the corresponding neutral element.

Keywords

• Bounded lattice
• internal uninorm
• idempotent uninorm
• partial order